Importance of the 'Higgs' Amplitude Mode in Understanding the "Ideal Glass Transition" and the Kauzmann Entropy Paradox at the Four-Dimensional Crystal/Glass Quantum Critical Point
Caroline S. Gorham David E. Laughlin










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@articlexu_golden_2011,
	title = Golden ratio in quantum mechanics,
	volume = 1,
	journal = Nonlinear Sci. Lett. B,
	author = Xu, Lan and Zhong, Ting,
	year = 2011,
	pages = 10–11


@articlechristopher_quasicrystal_1986,
	title = Quasicrystal structure of (Al, Zn) 49Mg32,
	volume = 53,
	number = 3,
	journal = Philosophical Magazine B,
	author = Christopher and Henley, L. and Elser, Veit,
	year = 1986,
	pages = L59–L66,
	file = Full Text:/Users/carolinegorham/Zotero/storage/PJDESSIH/Christopher et al. - 1986 - Quasicrystal structure of (Al, Zn) 49Mg32.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/YPVRJQGQ/13642818608240638.html:text/html


@articleknapp_dephasing_2018,
	title = Dephasing of Majorana-based qubits,
	volume = 97,
	url = https://link.aps.org/doi/10.1103/PhysRevB.97.125404,
	doi = 10.1103/PhysRevB.97.125404,
	abstract = We analyze charging-energy-protected Majorana-based qubits, focusing on the residual dephasing that is present when the distance between Majorana zero modes (MZMs) is insufficient for full topological protection. We argue that the leading source of dephasing is 1/f charge noise. This noise affects the qubit as a result of the hybridization energy and charge distribution associated with weakly overlapping MZMs, which we calculate using a charge-conserving formalism. We estimate the coherence time to be hundreds of nanoseconds for Majorana-based qubits whose MZM separation is L∼5ξ (with ξ being the coherence length). The coherence time grows exponentially with MZM separation and eventually becomes temperature limited for L/ξ∼30.,
	number = 12,
	urldate = 2019-03-09,
	journal = Physical Review B,
	author = Knapp, Christina and Karzig, Torsten and Lutchyn, Roman M. and Nayak, Chetan,
	month = mar,
	year = 2018,
	pages = 125404,
	file = APS Snapshot:/Users/carolinegorham/Zotero/storage/RZ6A2VAS/PhysRevB.97.html:text/html;Submitted Version:/Users/carolinegorham/Zotero/storage/Q4U9JZGL/Knapp et al. - 2018 - Dephasing of Majorana-based qubits.pdf:application/pdf


@articlenieto_duality_2018,
	title = Duality, matroids, qubits, twistors and surreal numbers,
	journal = arXiv preprint arXiv:1810.04521,
	author = Nieto, Juan Antonio,
	year = 2018,
	file = Full Text:/Users/carolinegorham/Zotero/storage/TYSK75JN/Nieto - 2018 - Duality, matroids, qubits, twistors and surreal nu.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/TNTQSVMC/1810.html:text/html


@articlehohenberg_existence_1967,
	title = Existence of long-range order in one and two dimensions,
	volume = 158,
	number = 2,
	journal = Physical Review,
	author = Hohenberg, Pierre C.,
	year = 1967,
	pages = 383,
	file = Full Text:/Users/carolinegorham/Zotero/storage/3AF9S93D/Hohenberg - 1967 - Existence of long-range order in one and two dimen.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/JQIKZ8ZG/PhysRev.158.html:text/html


@articlebernevig_geometry_2003,
	title = Geometry of the three-qubit state, entanglement and division algebras,
	volume = 36,
	number = 30,
	journal = Journal of Physics A: Mathematical and General,
	author = Bernevig, Bogdan A. and Chen, Han-Dong,
	year = 2003,
	pages = 8325,
	file = Full Text:/Users/carolinegorham/Zotero/storage/XV5UJVDM/Bernevig and Chen - 2003 - Geometry of the three-qubit state, entanglement an.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/SQXTEJRY/309.html:text/html


@articlegladchenko_superconducting_2009,
	title = Superconducting nanocircuits for topologically protected qubits,
	volume = 5,
	copyright = 2008 Nature Publishing Group,
	issn = 1745-2481,
	url = https://www.nature.com/articles/nphys1151,
	doi = 10.1038/nphys1151,
	abstract = For successful realization of a quantum computer, its building blocks—the individual qubits—should be simultaneously scalable and sufficiently protected from environmental noise. Recently, a novel approach to the protection of superconducting qubits has been proposed. The idea is to prevent errors at the hardware level, by building a fault-free logical qubit from ‘faulty’ physical qubits with properly engineered interactions between them. The decoupling of such a topologically protected logical qubit from local noises is expected to grow exponentially with the number of physical qubits. Here, we report on proof-of-concept experiments with a prototype device that consists of twelve physical qubits made of nanoscale Josephson junctions. We observed that owing to properly tuned quantum fluctuations, this qubit is protected against magnetic flux variations well beyond linear order, in agreement with theoretical predictions. These results suggest that topologically protected superconducting qubits are feasible.,
	language = en,
	number = 1,
	urldate = 2019-03-05,
	journal = Nature Physics,
	author = Gladchenko, Sergey and Olaya, David and Dupont-Ferrier, Eva and Douçot, Benoit and Ioffe, Lev B. and Gershenson, Michael E.,
	month = jan,
	year = 2009,
	pages = 48–53,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/ALIS6P3P/nphys1151.html:text/html;Submitted Version:/Users/carolinegorham/Zotero/storage/YKESZMGN/Gladchenko et al. - 2009 - Superconducting nanocircuits for topologically pro.pdf:application/pdf


@articlerastelli_quantum_2013,
	title = Quantum phase slips in Josephson junction rings,
	volume = 87,
	number = 17,
	journal = Physical Review B,
	author = Rastelli, Gianluca and Pop, Ioan M. and Hekking, Frank WJ,
	year = 2013,
	pages = 174513,
	file = Full Text:/Users/carolinegorham/Zotero/storage/VDNDN45W/Rastelli et al. - 2013 - Quantum phase slips in Josephson junction rings.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/VPS8M865/PhysRevB.87.html:text/html


@bookvan_leunen_hilbert_2012,
	title = The Hilbert book model,
	publisher = Lulu. com,
	author = Van Leunen, Hans,
	year = 2012,
	file = Full Text:/Users/carolinegorham/Zotero/storage/8C886SWV/Van Leunen - 2012 - The Hilbert book model.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/8YP77P3P/books.html:text/html


@articlebradley_quantum_1984,
	title = Quantum fluctuations in chains of Josephson junctions,
	volume = 30,
	url = https://link.aps.org/doi/10.1103/PhysRevB.30.1138,
	doi = 10.1103/PhysRevB.30.1138,
	abstract = We study the effect of quantum fluctuations of the phase on the low-temperature behavior of two models of Josephson junction chains with Coulomb interactions taken into account. The first model, which represents a chain of junctions close to a ground plane, is the Hamiltonian version of the two-dimensional XY model in one space and one time dimension. We demonstrate explicitly how the Nelson-Kosterlitz jump manifests itself in the conduction properties of this system at a critical value of the superconducting grain capacitance. In the second model, the charging energy for a single junction in the chain is just the parallel-plate capacitor energy Q28C, where Q is the charge difference across the junction and C is its capacitance. We show that for any nonzero charging energy (i.e., C∞) quantum fluctuations produce exponential decay of the order-parameter correlation function. Therefore, in contrast to the first model, the Coulomb interaction always succeeds in disrupting the phase coherence of the array.,
	number = 3,
	urldate = 2019-03-04,
	journal = Physical Review B,
	author = Bradley, R. M. and Doniach, S.,
	month = aug,
	year = 1984,
	pages = 1138–1147,
	file = APS Snapshot:/Users/carolinegorham/Zotero/storage/LUU2VZUV/PhysRevB.30.html:text/html;Full Text PDF:/Users/carolinegorham/Zotero/storage/WPIJJ6AV/Bradley and Doniach - 1984 - Quantum fluctuations in chains of Josephson juncti.pdf:application/pdf


@articleendres_higgs_2012,
	title = The ‘Higgs’ amplitude mode at the two-dimensional superfluid/Mott insulator transition,
	volume = 487,
	copyright = 2012 Nature Publishing Group,
	issn = 1476-4687,
	url = https://www.nature.com/articles/nature11255,
	doi = 10.1038/nature11255,
	language = en,
	number = 7408,
	urldate = 2019-02-23,
	journal = Nature,
	author = Endres, Manuel and Fukuhara, Takeshi and Pekker, David and Cheneau, Marc and Schauβ, Peter and Gross, Christian and Demler, Eugene and Kuhr, Stefan and Bloch, Immanuel,
	month = jul,
	year = 2012,
	pages = 454–458,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/CGUBDT5V/nature11255.html:text/html;Submitted Version:/Users/carolinegorham/Zotero/storage/KIKQYWYM/Endres et al. - 2012 - The ‘Higgs’ amplitude mode at the two-dimensional .pdf:application/pdf


@articleblanter_duality_1997,
	title = Duality in Josephson junction arrays,
	volume = 58,
	journal = Nuclear Physics B-Proceedings Supplements,
	author = Blanter, Ya M. and Fazio, Rosario and Schön, Gerd,
	year = 1997,
	pages = 79–90,
	file = Full Text:/Users/carolinegorham/Zotero/storage/R479T5GF/Blanter et al. - 1997 - Duality in Josephson junction arrays.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/6L5BQFZ3/S0920563297004143.html:text/html


@articlebray_theory_2002,
	title = Theory of phase-ordering kinetics,
	volume = 51,
	issn = 0001-8732,
	url = https://doi.org/10.1080/00018730110117433,
	doi = 10.1080/00018730110117433,
	abstract = The theory of phase-ordering dynamics that is the growth of order through domain coarsening when a system is quenched from the homogeneous phase into a broken-symmetry phase, is reviewed, with the emphasis on recent developments. Interest will focus on the scaling regime that develops at long times after the quench. How can one determine the growth laws that describe the time dependence of characteristic length scales, and what can be said about the form of the associated scaling functions? Particular attention will be paid to systems described by more complicated order parameters than the simple scalars usually considered, for example vector and tensor fields. The latter are needed, for example, to describe phase ordering in nematic liquid crystals, on which there have been a number of recent experiments. The study of topological defects (domain walls, vortices, strings and monopoles) provides a unifying framework for discussing coarsening in these different systems.,
	number = 2,
	urldate = 2019-02-19,
	journal = Advances in Physics,
	author = Bray, A. J.,
	month = mar,
	year = 2002,
	pages = 481–587,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/IFIVUUZ7/00018730110117433.html:text/html;Submitted Version:/Users/carolinegorham/Zotero/storage/A89I7UC3/Bray - 2002 - Theory of phase-ordering kinetics.pdf:application/pdf


@articlecooper_experimental_2012,
	title = Experimental review of graphene,
	volume = 2012,
	journal = ISRN Condensed Matter Physics,
	author = Cooper, Daniel R. and D’Anjou, Benjamin and Ghattamaneni, Nageswara and Harack, Benjamin and Hilke, Michael and Horth, Alexandre and Majlis, Norberto and Massicotte, Mathieu and Vandsburger, Leron and Whiteway, Eric,
	year = 2012,
	file = Full Text:/Users/carolinegorham/Zotero/storage/63I642DC/Cooper et al. - 2012 - Experimental review of graphene.pdf:application/pdf


@articlekitaev_topological_2006,
	title = Topological Entanglement Entropy,
	volume = 96,
	url = https://link.aps.org/doi/10.1103/PhysRevLett.96.110404,
	doi = 10.1103/PhysRevLett.96.110404,
	abstract = We formulate a universal characterization of the many-particle quantum entanglement in the ground state of a topologically ordered two-dimensional medium with a mass gap. We consider a disk in the plane, with a smooth boundary of length L, large compared to the correlation length. In the ground state, by tracing out all degrees of freedom in the exterior of the disk, we obtain a marginal density operator ρ for the degrees of freedom in the interior. The von Neumann entropy of ρ, a measure of the entanglement of the interior and exterior variables, has the form S(ρ)=αL−γ+⋯, where the ellipsis represents terms that vanish in the limit L→∞. We show that −γ is a universal constant characterizing a global feature of the entanglement in the ground state. Using topological quantum field theory methods, we derive a formula for γ in terms of properties of the superselection sectors of the medium.,
	number = 11,
	urldate = 2019-02-11,
	journal = Physical Review Letters,
	author = Kitaev, Alexei and Preskill, John,
	month = mar,
	year = 2006,
	pages = 110404,
	file = APS Snapshot:/Users/carolinegorham/Zotero/storage/KQUMFFSD/PhysRevLett.96.html:text/html;Full Text PDF:/Users/carolinegorham/Zotero/storage/3ZDEBIE4/Kitaev and Preskill - 2006 - Topological Entanglement Entropy.pdf:application/pdf


@articlezhang_geometric_2003,
	title = Geometric theory of nonlocal two-qubit operations,
	volume = 67,
	url = https://link.aps.org/doi/10.1103/PhysRevA.67.042313,
	doi = 10.1103/PhysRevA.67.042313,
	abstract = We study nonlocal two-qubit operations from a geometric perspective. By applying a Cartan decomposition to su(4), we find that the geometric structure of nonlocal gates is a 3-torus. We derive the invariants for local transformations, and connect these local invariants to the coordinates of the 3-torus. Since different points on the 3-torus may correspond to the same local equivalence class, we use the Weyl group theory to reduce the symmetry. We show that the local equivalence classes of two-qubit gates are in one-to-one correspondence with the points in a tetrahedron except on the base. We then study the properties of perfect entanglers, that is, the two-qubit operations that can generate maximally entangled states from some initially separable states. We provide criteria to determine whether a given two-qubit gate is a perfect entangler and establish a geometric description of perfect entanglers by making use of the tetrahedral representation of nonlocal gates. We find that exactly half the nonlocal gates are perfect entanglers. We also investigate the nonlocal operations generated by a given Hamiltonian. We first study the gates that can be directly generated by a Hamiltonian. Then we explicitly construct a quantum circuit that contains at most three nonlocal gates generated by a two-body interaction Hamiltonian, together with at most four local gates generated by single-qubit terms. We prove that such a quantum circuit can simulate any arbitrary two-qubit gate exactly, and hence it provides an efficient implementation of universal quantum computation and simulation.,
	number = 4,
	urldate = 2019-02-07,
	journal = Physical Review A,
	author = Zhang, Jun and Vala, Jiri and Sastry, Shankar and Whaley, K. Birgitta,
	month = apr,
	year = 2003,
	pages = 042313,
	file = APS Snapshot:/Users/carolinegorham/Zotero/storage/UPGVUEV9/PhysRevA.67.html:text/html;Submitted Version:/Users/carolinegorham/Zotero/storage/5578VVVZ/Zhang et al. - 2003 - Geometric theory of nonlocal two-qubit operations.pdf:application/pdf


@articlehanneke_realization_2010,
	title = Realization of a programmable two-qubit quantum processor,
	volume = 6,
	copyright = 2009 Nature Publishing Group,
	issn = 1745-2481,
	url = https://www.nature.com/articles/nphys1453,
	doi = 10.1038/nphys1453,
	abstract = The universal quantum computer1 is a device capable of simulating any physical system2 and represents a major goal for the field of quantum information science. In the context of quantum information, ‘universal’ refers to the ability to carry out arbitrary unitary transformations in the system’s computational space3. Combining arbitrary single-quantum-bit (qubit) gates with an entangling two-qubit gate provides a set of gates capable of achieving universal control of any number of qubits4,5,6, provided that these gates can be carried out repeatedly and between arbitrary pairs of qubits. Although gate sets have been demonstrated in several technologies7, they have so far been tailored towards specific tasks, forming a small subset of all unitary operators. Here we demonstrate a quantum processor that can be programmed with 15 classical inputs to realize arbitrary unitary transformations on two qubits, which are stored in trapped atomic ions. Using quantum state and process tomography8, we characterize the fidelity of our implementation for 160 randomly chosen operations. This universal control is equivalent to simulating any pairwise interaction between spin-1/2 systems. A programmable multiqubit register could form a core component of a large-scale quantum processor, and the methods used here are suitable for such a device9.,
	language = en,
	number = 1,
	urldate = 2019-02-07,
	journal = Nature Physics,
	author = Hanneke, D. and Home, J. P. and Jost, J. D. and Amini, J. M. and Leibfried, D. and Wineland, D. J.,
	month = jan,
	year = 2010,
	pages = 13–16,
	file = Full Text PDF:/Users/carolinegorham/Zotero/storage/3K9CC3ZB/Hanneke et al. - 2010 - Realization of a programmable two-qubit quantum pr.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/4I9WIQJ5/nphys1453.html:text/html


@articlebell_einstein_1964,
	title = On the einstein podolsky rosen paradox,
	volume = 1,
	number = 3,
	journal = Physics Physique Fizika,
	author = Bell, John S.,
	year = 1964,
	pages = 195,
	file = Full Text:/Users/carolinegorham/Zotero/storage/AG7THMGX/Bell - 1964 - On the einstein podolsky rosen paradox.pdf:application/pdf


@articlecosta_new_2019,
	title = A New Algorithm to Study the Critical Behavior of Topological Phase Transitions,
	issn = 1678-4448,
	url = https://doi.org/10.1007/s13538-019-00636-x,
	doi = 10.1007/s13538-019-00636-x,
	abstract = Topological phase transitions such as the Berezinskii-Kosterlitz-Thouless (BKT) transition are difficult to characterize due to the difficulty in defining an appropriate order parameter or to unravel its critical properties. In this paper, we discuss the application of a newly introduced numerical algorithm that was inspired by the Fisher zeros of the partition function and is based on the partial knowledge of the zeros of the energy probability distribution (EPD zeros). This iterative method has proven to be quite general, furnishing the transition temperature with great precision and a relatively low computational effort. Since it does not need the a priori knowledge of any order parameter it provides an unbiased estimative of the transition temperature being convenient to the study of this kind of phase transition. Therefore, we applied the EPD zeros approach to the 2D XY model, which is well known for showing a BKT transition, in order to demonstrate its effectivity in the study of the BKT transition. Our results are consistent with the real and imaginary parts of the pseudo-transition temperature, T(L), having a different asymptotic behavior, which suggests a way to characterize a BKT like transition.,
	language = en,
	urldate = 2019-02-07,
	journal = Brazilian Journal of Physics,
	author = Costa, B. V. and Mól, L. A. S. and Rocha, J. C. S.,
	month = jan,
	year = 2019,
	keywords = Monte Carlo simulations, Partition function zeros, Replica-exchange Wang-Landau, Topological phase transition, XY model


@articleclauser_proposed_1969,
	title = Proposed experiment to test local hidden-variable theories,
	volume = 23,
	number = 15,
	journal = Physical review letters,
	author = Clauser, John F. and Horne, Michael A. and Shimony, Abner and Holt, Richard A.,
	year = 1969,
	pages = 880,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/3QQGUZRI/PhysRevLett.23.html:text/html


@articlebernevig_geometry_2003-1,
	title = Geometry of the three-qubit state, entanglement and division algebras,
	volume = 36,
	number = 30,
	journal = Journal of Physics A: Mathematical and General,
	author = Bernevig, Bogdan A. and Chen, Han-Dong,
	year = 2003,
	pages = 8325,
	file = Full Text:/Users/carolinegorham/Zotero/storage/665BC2IT/Bernevig and Chen - 2003 - Geometry of the three-qubit state, entanglement an.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/YPESSPPK/meta.html:text/html


@articlesingh_quantum_2008,
	title = Quantum Computing Through Quaternions.,
	volume = 5,
	number = 19,
	journal = Electronic Journal of Theoretical Physics,
	author = Singh, J. P. and Prabakaran, S.,
	year = 2008,
	file = Full Text:/Users/carolinegorham/Zotero/storage/9BC2C9HS/Singh and Prabakaran - 2008 - Quantum Computing Through Quaternions..pdf:application/pdf


@articlemosseri_two_2003,
	title = Two and three qubits geometry and Hopf fibrations,
	journal = arXiv preprint quant-ph/0310053,
	author = Mosseri, Remy,
	year = 2003,
	file = Full Text:/Users/carolinegorham/Zotero/storage/LG48IYKN/Mosseri - 2003 - Two and three qubits geometry and Hopf fibrations.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/3KSVIMQ5/0310053.html:text/html


@articlemilman_topological_2003,
	title = Topological phase for entangled two-qubit states,
	volume = 90,
	number = 23,
	journal = Physical review letters,
	author = Milman, Pérola and Mosseri, Rémy,
	year = 2003,
	pages = 230403,
	file = Full Text:/Users/carolinegorham/Zotero/storage/3W8I9TQP/Milman and Mosseri - 2003 - Topological phase for entangled two-qubit states.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/XE39U9EU/PhysRevLett.90.html:text/html


@articlesadoc_e8_1993,
	title = The E8 lattice and quasicrystals: geometry, number theory and quasicrystals,
	volume = 26,
	issn = 0305-4470,
	shorttitle = The E8 lattice and quasicrystals,
	url = https://doi.org/10.1088
	doi = 10.1088/0305-4470/26/8/009,
	language = en,
	number = 8,
	urldate = 2019-01-31,
	journal = Journal of Physics A: Mathematical and General,
	author = Sadoc, J. F. and Mosseri, R.,
	month = apr,
	year = 1993,
	pages = 1789–1809,
	annote = The authors study the quasiperiodic structures which can be derived from E8. This lattice, suitably oriented, leads to a 4D quasicrystal which has (3,3,5) symmetry. They develop a modified version of the out and projection method. The high-dimensional lattice is first foliated into successive shells surrounding a vertex. The shells are embedded into 7D S7 spheres. They then use the so-called Hopf fibration of S7 to gather families of E8 shell sites into S3 fibres which contain 24 sites (or a multiple of 24) which are symmetrically disposed in S3. This has two advantages: first, in the selection process, a whole fibre is either selected or rejected, which reduces the computation; more importantly, the selection process for a fiber amounts to simple arithmetical criteria. The whole process leads to a shell-by-shell analysis of the 4D quasicrystal, which can be brought onto a 2D-1D algorithm similar to the Fibonacci chain construction. They propose an arithmetic formula which gives the number of points on the shells. This 4D quasicrystal has the interesting feature that it can be sliced into lower-dimensional quasicrystals, for example with icosahedral and tetrahedral symmetry in three dimensions.


@articleconway_quasiperiodic_1986,
	title = Quasiperiodic tiling in two and three dimensions,
	volume = 19,
	issn = 0305-4470,
	url = https://doi.org/10.1088
	doi = 10.1088/0305-4470/19/17/027,
	language = en,
	number = 17,
	urldate = 2019-01-31,
	journal = Journal of Physics A: Mathematical and General,
	author = Conway, J. H. and Knowles, K. M.,
	month = dec,
	year = 1986,
	pages = 3645–3653,
	annote = Algebraic criteria which allow the vertices of two- and three-dimensional Penrose tiling patterns to be specified are presented. The application of these criteria to the interpretation of electron microscope observations from quasicrystalline structures is discussed.


@articlefeuerbacher_dislocations_2012,
	title = Dislocations in icosahedral quasicrystals,
	volume = 41,
	url = https://pubs.rsc.org/en/content/articlelanding/2012/cs/c2cs35150a,
	doi = 10.1039/C2CS35150A,
	language = en,
	number = 20,
	urldate = 2019-01-31,
	journal = Chemical Society Reviews,
	author = Feuerbacher, Michael,
	year = 2012,
	pages = 6745–6759,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/FAQAAWRP/unauth.html:text/html;Submitted Version:/Users/carolinegorham/Zotero/storage/9KAX59XF/Feuerbacher - 2012 - Dislocations in icosahedral quasicrystals.pdf:application/pdf


@articlecharap_gravitational_1977,
	title = Gravitational effects on Yang-Mills topology,
	volume = 69,
	issn = 0370-2693,
	url = http://www.sciencedirect.com/science/article/pii/0370269377908413,
	doi = 10.1016/0370-2693(77)90841-3,
	abstract = Exact pseudoparticle solutions to the SU (2) Yang-Mills-Einstein equations are presented. The Yang-Mills solution has vanishing stress tensor and so does not disturb the geometry, which we take to be that of a Schwarzschild black-hole. By contrast, the topology of the Yang-Mills solution is determined by that of the gravitational field. Remarkably, this implies that gravity, independent of its coupling strength, may influence elementary particle phenomena via its non-trivial topology.,
	number = 4,
	urldate = 2019-01-29,
	journal = Physics Letters B,
	author = Charap, J. M. and Duff, M. J.,
	month = jan,
	year = 1977,
	pages = 445–447,
	file = ScienceDirect Snapshot:/Users/carolinegorham/Zotero/storage/LAQFEJAF/0370269377908413.html:text/html


@articlecharap_gravitational_1977-1,
	title = Gravitational effects on Yang-Mills topology,
	volume = 69,
	issn = 0370-2693,
	url = http://www.sciencedirect.com/science/article/pii/0370269377908413,
	doi = 10.1016/0370-2693(77)90841-3,
	abstract = Exact pseudoparticle solutions to the SU (2) Yang-Mills-Einstein equations are presented. The Yang-Mills solution has vanishing stress tensor and so does not disturb the geometry, which we take to be that of a Schwarzschild black-hole. By contrast, the topology of the Yang-Mills solution is determined by that of the gravitational field. Remarkably, this implies that gravity, independent of its coupling strength, may influence elementary particle phenomena via its non-trivial topology.,
	number = 4,
	urldate = 2019-01-29,
	journal = Physics Letters B,
	author = Charap, J. M. and Duff, M. J.,
	month = jan,
	year = 1977,
	pages = 445–447,
	file = ScienceDirect Snapshot:/Users/carolinegorham/Zotero/storage/YJVQFJNP/0370269377908413.html:text/html


@articleatiyah_topological_1978,
	title = Topological aspects of Yang-Mills theory,
	volume = 61,
	issn = 1432-0916,
	url = https://doi.org/10.1007/BF01609489,
	doi = 10.1007/BF01609489,
	abstract = The space of mapsS3 →G has components which give the topological quantum number of Yang-Mills theory for the groupG. Each component of the space has further topological invariants. WhenG=SU(2) we show that these invariants (the homology groups) are “captured” by the space of instantons. Using these invariants we show that potentials must exist for which the massless Dirac equation (in Euclidean 4-space) has arbitrarily many independent solutions (for fixed instanton number).,
	language = en,
	number = 2,
	urldate = 2019-01-29,
	journal = Communications in Mathematical Physics,
	author = Atiyah, M. F. and Jones, J. D. S.,
	month = jun,
	year = 1978,
	keywords = Complex System, Neural Network, Nonlinear Dynamics, Quantum Number, Statistical Physic,
	pages = 97–118


@incollectionlaughlin_elementary_1987,
	address = New York, NY,
	series = Graduate Texts in Contemporary Physics,
	title = Elementary Theory: the Incompressible Quantum Fluid,
	isbn = 978-1-4684-0499-9,
	shorttitle = Elementary Theory,
	url = https://doi.org/10.1007/978-1-4684-0499-9_7,
	abstract = In this lecture, I shall outline what I believe to be the correct fundamental picture of the fractional quantum Hall effect. The principal features of this picture are that the 1/3 state and its daughters are a new type of many-body condensate, that there are analogs of electrons and holes in the integral quantum Hall effect which in this case carry fractional charge, that the Hall plateau observed in experiments is due to localization of these fractionally charged quasiparticles, and that the rules for combining quasiparticles to make daughter states and excitons are simple. The key facts the theory has to explain are these: 1. The effect occurs when electrons are at a particular density, determined by the magnetic field strength. The separation between neighboring electrons locks in at particular values. 2. The fractional quantum Hall effect looks to the eye like the integral quantum Hall effect, except that the Hall conductance, in the case of the 1/3 step, is 1/3 e 2 h. There is a plateau. Changing the electron density a small amount does not alter the Hall conductance, but changing it a large amount does. 3. The 1/3 effect turns on in GaAs at about 1 K when the magnetic field is 15 Tesla. 4. The effect occurs only in the cleanest samples. Excessive dirt destroys it. 5. Other fractions (2/5, 2/7, …) also occur but they are more easily destroyed by dirt and require lower temperatures to be observed. The most ‘stable’ states have small denominators.,
	language = en,
	urldate = 2019-01-29,
	booktitle = The Quantum Hall Effect,
	publisher = Springer US,
	author = Laughlin, Robert B.,
	editor = Prange, Richard E. and Girvin, Steven M.,
	year = 1987,
	doi = 10.1007/978-1-4684-0499-9_7,
	keywords = Elementary Theory, Landau Level, Quantum Hall Effect, Radial Distribution Function, Wave Function,
	pages = 233–301


@articlegorham_topological_2019,
	title = Topological description of the solidification of undercooled fluids and the temperature dependence of the thermal conductivity of crystalline and glassy solids above approximately 50 K,
	volume = 31,
	issn = 0953-8984,
	url = https://doi.org/10.1088
	doi = 10.1088/1361-648X/aaf8d2,
	language = en,
	number = 10,
	urldate = 2019-01-29,
	journal = Journal of Physics: Condensed Matter,
	author = Gorham, Caroline S. and Laughlin, David E.,
	month = jan,
	year = 2019,
	pages = 105701,
	annote = Topological origins of the thermal transport properties of crystalline and non-crystalline solid states are considered herein, by the adoption of a quaternion orientational order parameter to describe solidification. Global orientational order, achieved by spontaneous symmetry breaking, is prevented at finite temperatures for systems that exist in restricted dimensions (Mermin–Wagner theorem). Just as complex ordered systems exist in restricted dimensions in 2D and 1D, owing to the dimensionality of the order parameter, quaternion ordered systems in 4D and 3D exist in restricted dimensions. Just below the melting temperature, misorientational fluctuations in the form of spontaneously generated topological defects prevent the development of the solid state. Such solidifying systems are well-described using O(4) quantum rotor models, and a defect-driven Berezinskii–Kosterlitz–Thouless transition is anticipated to separate an undercooled fluid from a crystalline solid state. In restricted dimensions, in addition to orientationally-ordered ground states, orientationally-disordered ground states may be realized by tuning a non-thermal parameter in the relevant O(n) quantum rotor model Hamiltonian. Thus, glassy solid states are anticipated to exist as distinct ground states of O(4) quantum rotor models. Within this topological framework for solidification, the finite Kauzmann temperature marks a first-order transition between crystalline and glassy solid states at a ‘self-dual’ critical point that belongs to O(4) quantum rotor models. This transition is a higher-dimensional analogue to the quantum phase transition that belongs to O(2) Josephson junction arrays (JJAs). The thermal transport properties of crystalline and glassy solid states, above approximately 50 K, are considered alongside the electrical transport properties of JJAs across the superconductor-to-superinsulator transition.,
	file = IOP Full Text PDF:/Users/carolinegorham/Zotero/storage/RN8S2XNR/Gorham and Laughlin - 2019 - Topological description of the solidification of u.pdf:application/pdf


@articlediamantini_topological_2008,
	title = Topological order in frustrated Josephson junction arrays,
	volume = 83,
	issn = 0295-5075,
	url = https://doi.org/10.1209
	doi = 10.1209/0295-5075/83/21003,
	language = en,
	number = 2,
	urldate = 2019-01-27,
	journal = EPL (Europhysics Letters),
	author = Diamantini, M. C. and Sodano, P. and Trugenberger, C. A.,
	month = jul,
	year = 2008,
	pages = 21003,
	annote = We show that electrically and magnetically frustrated Josephson junction arrays (JJAs) realize topological order with a non-trivial ground-state degeneracy on manifolds with non-trivial topology. The low-energy theory has the same gauge dynamics of the unfrustrated JJAs but for different, “fractional" degrees of freedom, a principle reminescent of Jain's composite electrons in the fractional quantum Hall effect.,
	file = Submitted Version:/Users/carolinegorham/Zotero/storage/BQ2Y49TA/Diamantini et al. - 2008 - Topological order in frustrated Josephson junction.pdf:application/pdf


@articlekremen_imaging_2018,
	title = Imaging quantum fluctuations near criticality,
	volume = 14,
	copyright = 2018 The Author(s),
	issn = 1745-2481,
	url = https://www.nature.com/articles/s41567-018-0264-z,
	doi = 10.1038/s41567-018-0264-z,
	abstract = Quantum fluctuations in space and time can now be directly imaged using a scanning superconducting quantum interference device. The technique allows access to the local dynamics of a system close to a quantum phase transition.,
	language = en,
	number = 12,
	urldate = 2019-01-23,
	journal = Nature Physics,
	author = Kremen, A. and Khan, H. and Loh, Y. L. and Baturina, T. I. and Trivedi, N. and Frydman, A. and Kalisky, B.,
	month = dec,
	year = 2018,
	pages = 1205–1210,
	file = Full Text PDF:/Users/carolinegorham/Zotero/storage/JGHY8S4E/Kremen et al. - 2018 - Imaging quantum fluctuations near criticality.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/35QWJ9RE/s41567-018-0264-z.html:text/html


@miscnoauthor_imaging_nodate,
	title = Imaging quantum fluctuations near criticality  Nature Physics,
	url = https://www.nature.com/articles/s41567-018-0264-z,
	urldate = 2019-01-23,
	file = Imaging quantum fluctuations near criticality | Nature Physics:/Users/carolinegorham/Zotero/storage/P62L6A4V/s41567-018-0264-z.html:text/html


@articlekimata_magnetic_2019,
	title = Magnetic and magnetic inverse spin Hall effects in a non-collinear antiferromagnet,
	copyright = 2019 Springer Nature Limited,
	issn = 1476-4687,
	url = https://www.nature.com/articles/s41586-018-0853-0,
	doi = 10.1038/s41586-018-0853-0,
	abstract = A magnetic contribution to the spin Hall effect is observed in the non-collinear antiferromagnet Mn3Sn, which is attributed to momentum-dependent spin splitting produced by non-collinear magnetic order.,
	language = en,
	urldate = 2019-01-18,
	journal = Nature,
	author = Kimata, Motoi and Chen, Hua and Kondou, Kouta and Sugimoto, Satoshi and Muduli, Prasanta K. and Ikhlas, Muhammad and Omori, Yasutomo and Tomita, Takahiro and MacDonald, Allan H. and Nakatsuji, Satoru and Otani, Yoshichika,
	month = jan,
	year = 2019,
	pages = 1,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/Y6YFSZ9V/s41586-018-0853-0.html:text/html


@articlecaio_topological_2019,
	title = Topological marker currents in Chern insulators,
	copyright = 2019 The Author(s), under exclusive licence to Springer Nature Limited,
	issn = 1745-2481,
	url = https://www.nature.com/articles/s41567-018-0390-7,
	doi = 10.1038/s41567-018-0390-7,
	abstract = While topological states are often characterized by their global properties related to the topological invariants, the introduced real-space topological markers provide new insights to these states.,
	language = en,
	urldate = 2019-01-18,
	journal = Nature Physics,
	author = Caio, M. D. and Möller, G. and Cooper, N. R. and Bhaseen, M. J.,
	month = jan,
	year = 2019,
	pages = 1,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/6ZXCSHCS/s41567-018-0390-7.html:text/html;Submitted Version:/Users/carolinegorham/Zotero/storage/YV59XIF7/Caio et al. - 2019 - Topological marker currents in Chern insulators.pdf:application/pdf


@miscnoauthor_magnetic_nodate,
	title = Magnetic and magnetic inverse spin Hall effects in a non-collinear antiferromagnet  Nature,
	url = https://www.nature.com/articles/s41586-018-0853-0,
	urldate = 2019-01-16


@articlediamantini_superconductor-superinsulator_2018,
	title = The Superconductor-Superinsulator Transition: S-duality and the QCD on the Desktop,
	issn = 1557-1947,
	shorttitle = The Superconductor-Superinsulator Transition,
	url = https://doi.org/10.1007/s10948-018-4943-x,
	doi = 10.1007/s10948-018-4943-x,
	abstract = We show that the nature of quantum phases around the superconductor-insulator transition (SIT) is controlled by charge-vortex topological interactions, and does not depend on the details of material parameters and disorder. We find three distinct phases, superconductor, superinsulator, and bosonic topological insulator. The superinsulator is a state of matter with infinite resistance in a finite temperature range, which is the S-dual of the superconductor and in which charge transport is prevented by electric strings binding charges of opposite sign. The electric strings ensuring linear confinement of charges are generated by instantons and are dual to superconducting Abrikosov vortices. Material parameters and disorder enter the London penetration depth of the superconductor, the string tension of the superinsulator and the quantum fluctuation parameter driving the transition between them. They are entirely encoded in four phenomenological parameters of a topological gauge theory of the SIT. Finally, we point out that, in the context of strong coupling gauge theories, the many-body localization phenomenon that is often referred to as an underlying mechanism for superinsulation is a mere transcription of the well-known phenomenon of confinement into solid-state physics language and is entirely driven by endogenous disorder embodied by instantons with no need of exogenous disorder.,
	language = en,
	urldate = 2019-01-13,
	journal = Journal of Superconductivity and Novel Magnetism,
	author = Diamantini, M. Cristina and Gammaitoni, Luca and Trugenberger, Carlo A. and Vinokur, Valerii M.,
	month = dec,
	year = 2018,
	keywords = Gauge field, Quantum phase transition, Superinsulator,
	file = Springer Full Text PDF:/Users/carolinegorham/Zotero/storage/895MUZJ4/Diamantini et al. - 2018 - The Superconductor-Superinsulator Transition S-du.pdf:application/pdf


@articlebanerjee_emergent_2018,
	title = Emergent de Sitter Cosmology from Decaying Anti–de Sitter Space,
	volume = 121,
	url = https://link.aps.org/doi/10.1103/PhysRevLett.121.261301,
	doi = 10.1103/PhysRevLett.121.261301,
	abstract = Recent developments in string compactifications demonstrate obstructions to the simplest constructions of low energy cosmologies with positive vacuum energy. The existence of obstacles to creating scale-separated de Sitter solutions indicates a UV/IR puzzle for embedding cosmological vacua in a unitary theory of quantum gravity. Motivated by this puzzle, we propose an embedding of positive energy Friedmann-Lemaître-Robertson-Walker cosmology within string theory. Our proposal involves confining 4D gravity on a brane which mediates the decay from a nonsupersymmetric five-dimensional anti–de Sitter false vacuum to a true vacuum. In this way, it is natural for a 4D observer to experience an effective positive cosmological constant coupled to matter and radiation, avoiding the need for scale separation or a fundamental de Sitter vacuum.,
	number = 26,
	urldate = 2018-12-31,
	journal = Physical Review Letters,
	author = Banerjee, Souvik and Danielsson, Ulf and Dibitetto, Giuseppe and Giri, Suvendu and Schillo, Marjorie,
	month = dec,
	year = 2018,
	pages = 261301,
	file = APS Snapshot:/Users/carolinegorham/Zotero/storage/XX6ADA78/PhysRevLett.121.html:text/html;Full Text PDF:/Users/carolinegorham/Zotero/storage/GVWWVTQ5/Banerjee et al. - 2018 - Emergent de Sitter Cosmology from Decaying Anti–d.pdf:application/pdf


@articleeckern_quantum_1989,
	title = Quantum vortex dynamics in granular superconducting films,
	volume = 39,
	number = 10,
	journal = Physical Review B,
	author = Eckern, Ulrich and Schmid, Albert,
	year = 1989,
	pages = 6441,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/ENCW8VDX/PhysRevB.39.html:text/html


@articlechang_x_nodate,
	title = X 5 Berry phase in solid state physics,
	author = Chang, Ming-Che,
	file = Full Text:/Users/carolinegorham/Zotero/storage/336RGVR7/Chang - X 5 Berry phase in solid state physics.pdf:application/pdf


@bookkittel_thermal_1970,
	title = Thermal physics,
	volume = 9690,
	publisher = Wiley New York,
	author = Kittel, Charles and Kroemer, Herbert,
	year = 1970


@bookwilks_third_1961,
	title = The third law of thermodynamics,
	publisher = Clarendon Press,
	author = Wilks, John,
	year = 1961


@articlehu_second_2010,
	title = Second sound and the density response function in uniform superfluid atomic gases,
	volume = 12,
	number = 4,
	journal = New Journal of Physics,
	author = Hu, H. and Taylor, E. and Liu, X. J. and Stringari, S. and Griffin, A.,
	year = 2010,
	pages = 043040,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/NBYQB7PM/meta.html:text/html;Snapshot:/Users/carolinegorham/Zotero/storage/YMRAKBCD/meta.html:text/html


@incollectionschmitt_superfluidity_2015,
	address = Cham,
	series = Lecture Notes in Physics,
	title = Superfluidity in Quantum Field Theory,
	isbn = 978-3-319-07947-9,
	url = https://doi.org/10.1007/978-3-319-07947-9_3,
	abstract = The theoretical treatment of superfluid helium used in the previous section was phenomenological in the sense that the microscopic degrees of freedom, the helium atoms, never appeared in our description. We took it as given that there is a gapless excitation, and we modelled its form in terms of phonons and rotons, if you wish because experiments tell us so.,
	language = en,
	urldate = 2018-12-24,
	booktitle = Introduction to Superfluidity: Field-theoretical Approach and Applications,
	publisher = Springer International Publishing,
	author = Schmitt, Andreas,
	editor = Schmitt, Andreas,
	year = 2015,
	doi = 10.1007/978-3-319-07947-9_3,
	keywords = Bose Condensate, Goldstone Mode, Helium Atom, Spontaneous Symmetry Breaking, Superfluid Helium,
	pages = 33–52


@articlelandau_theory_1941,
	title = Theory of the Superfluidity of Helium II,
	volume = 60,
	number = 4,
	journal = Physical Review,
	author = Landau, L.,
	year = 1941,
	pages = 356,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/P8EZJGX9/Landau - 1941 - Theory of the Superfluidity of Helium II.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/BRI5WVF5/PhysRev.60.html:text/html


@articlekapitza_heat_1941,
	title = Heat transfer and superfluidity of helium II,
	volume = 60,
	number = 4,
	journal = Physical Review,
	author = Kapitza, P. L.,
	year = 1941,
	pages = 354,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/ZNTVD6TF/PhysRev.60.html:text/html


@articleherbut_dual_1998,
	title = Dual theory of the superfluid-Bose-glass transition in the disordered Bose-Hubbard model in one and two dimensions,
	volume = 57,
	number = 21,
	journal = Physical Review B,
	author = Herbut, Igor F.,
	year = 1998,
	pages = 13729,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/R2H95XPV/Herbut - 1998 - Dual theory of the superfluid-Bose-glass transitio.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/D24MJC2T/PhysRevB.57.html:text/html


@articlegriffin_first_1997,
	title = First and second sound in a uniform Bose gas,
	volume = 56,
	url = https://link.aps.org/doi/10.1103/PhysRevA.56.4839,
	doi = 10.1103/PhysRevA.56.4839,
	abstract = We have recently derived two-fluid hydrodynamic equations for a trapped weakly interacting Bose gas. In this paper we use these equations to discuss first and second sound in a uniform Bose gas. These results are shown to agree with the predictions of the usual two-fluid equations of Landau when the thermodynamic functions are evaluated for a weakly interacting gas. In a uniform gas, second sound mainly corresponds to an oscillation of the superfluid (the condensate) and is the low-frequency continuation of the Bogoliubov-Goldstone symmetry-breaking mode.,
	number = 6,
	urldate = 2018-12-24,
	journal = Physical Review A,
	author = Griffin, A. and Zaremba, E.,
	month = dec,
	year = 1997,
	pages = 4839–4844,
	file = APS Snapshot:/Users/carolinegorham/Zotero/storage/DP7C7KPH/PhysRevA.56.html:text/html;Submitted Version:/Users/carolinegorham/Zotero/storage/FJLAWSX7/Griffin and Zaremba - 1997 - First and second sound in a uniform Bose gas.pdf:application/pdf


@articlefreericks_phase_1994,
	title = Phase diagram of the Bose-Hubbard model,
	volume = 26,
	number = 7,
	journal = EPL (Europhysics Letters),
	author = Freericks, J. K. and Monien, H.,
	year = 1994,
	pages = 545,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/997BEWMF/Freericks and Monien - 1994 - Phase diagram of the Bose-Hubbard model.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/ZZTHWXIQ/meta.html:text/html


@articlespaldin_multiferroics:_2017,
	title = Multiferroics: from the cosmically large to the subatomically small,
	volume = 2,
	shorttitle = Multiferroics,
	number = 4,
	journal = Nature Reviews. Materials,
	author = Spaldin, Nicola A.,
	year = 2017,
	pages = 17017,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/MCJUEE45/sfx_local.html:text/html


@articlegriffin_scaling_2012,
	title = Scaling Behavior and Beyond Equilibrium in the Hexagonal Manganites,
	volume = 2,
	url = https://link.aps.org/doi/10.1103/PhysRevX.2.041022,
	doi = 10.1103/PhysRevX.2.041022,
	abstract = We show that the improper ferroelectric phase transition in the multiferroic hexagonal manganites displays appropriate symmetry-breaking characteristics for testing the Kibble-Zurek mechanism originally proposed to describe early-universe phase transitions. We present an analysis of the Kibble-Zurek theory of topological defect formation applied to the hexagonal manganites, discuss the conditions determining the range of cooling rates in which Kibble-Zurek behavior is expected, and show that recent literature data are consistent with our predictions. Finally, we explore experimentally the crossover out of the Kibble-Zurek regime and find a surprising reversal of the scaling behavior.,
	number = 4,
	urldate = 2018-12-13,
	journal = Physical Review X,
	author = Griffin, S. M. and Lilienblum, M. and Delaney, K. T. and Kumagai, Y. and Fiebig, M. and Spaldin, N. A.,
	month = dec,
	year = 2012,
	pages = 041022,
	file = APS Snapshot:/Users/carolinegorham/Zotero/storage/HFIPVHA5/PhysRevX.2.html:text/html;Full Text PDF:/Users/carolinegorham/Zotero/storage/IHNREUQ5/Griffin et al. - 2012 - Scaling Behavior and Beyond Equilibrium in the Hex.pdf:application/pdf


@articlesasaki_crystallization_2017,
	title = Crystallization and vitrification of electrons in a glass-forming charge liquid,
	volume = 357,
	copyright = Copyright © 2017 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works. http://www.sciencemag.org/about/science-licenses-journal-article-reuseThis is an article distributed under the terms of the Science Journals Default License.,
	issn = 0036-8075, 1095-9203,
	url = http://science.sciencemag.org/content/357/6358/1381,
	doi = 10.1126/science.aal3120,
	abstract = Ordering and disordering electrons
When a liquid is cooled rapidly, it can form a glass, a state stuck between liquid and solid. Two groups looked in detail into analogous dynamics in electronic systems. Sato et al. and Sasaki et al. studied layered organic materials with a triangular in-plane lattice. These materials can assume a state in which their charge distribution has a regular pattern—an electronic or charge crystal. When the materials were cooled rapidly, a charge glass was formed instead and then allowed to crystallize. The dynamics of crystallization showed similarities to the analogous processes in conventional glasses.
Science, this issue p. 1378, p. 1381
Charge ordering (CO) is a phenomenon in which electrons in solids crystallize into a periodic pattern of charge-rich and charge-poor sites owing to strong electron correlations. This usually results in long-range order. In geometrically frustrated systems, however, a glassy electronic state without long-range CO has been observed. We found that a charge-ordered organic material with an isosceles triangular lattice shows charge dynamics associated with crystallization and vitrification of electrons, which can be understood in the context of an energy landscape arising from the degeneracy of various CO patterns. The dynamics suggest that the same nucleation and growth processes that characterize conventional glass-forming liquids guide the crystallization of electrons. These similarities may provide insight into our understanding of the liquid-glass transition.
Transport measurements are used to uncover the dynamics of glass and crystal formation in frustrated electronic systems.
Transport measurements are used to uncover the dynamics of glass and crystal formation in frustrated electronic systems.,
	language = en,
	number = 6358,
	urldate = 2018-12-05,
	journal = Science,
	author = Sasaki, S. and Hashimoto, K. and Kobayashi, R. and Itoh, K. and Iguchi, S. and Nishio, Y. and Ikemoto, Y. and Moriwaki, T. and Yoneyama, N. and Watanabe, M. and Ueda, A. and Mori, H. and Kobayashi, K. and Kumai, R. and Murakami, Y. and Müller, J. and Sasaki, T.,
	month = sep,
	year = 2017,
	pmid = 28963251,
	pages = 1381–1385,
	file = Full Text PDF:/Users/carolinegorham/Zotero/storage/U3C79CW9/Sasaki et al. - 2017 - Crystallization and vitrification of electrons in .pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/8I26Y6DG/tab-pdf.html:text/html


@articledoye_effect_1996,
	title = The effect of the range of the potential on the structure and stability of simple liquids: from clusters to bulk, from sodium to C60,
	volume = 29,
	shorttitle = The effect of the range of the potential on the structure and stability of simple liquids,
	number = 21,
	journal = Journal of Physics B: Atomic, Molecular and Optical Physics,
	author = Doye, Jonathan PK and Wales, David J.,
	year = 1996,
	pages = 4859,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/33DSCKCR/Doye and Wales - 1996 - The effect of the range of the potential on the st.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/6D46ARHT/meta.html:text/html


@miscnoauthor_effect_nodate,
	title = The effect of the range of the potential on the structure... - Google Scholar,
	url = https://scholar.google.com/scholar?hl=en   as_sdt=0
	urldate = 2018-12-05,
	file = The effect of the range of the potential on the structure... - Google Scholar:/Users/carolinegorham/Zotero/storage/TQTBEFNC/scholar.html:text/html


@articledebenedetti_theory_2001,
	title = Theory of supercooled liquids and glasses: Energy landscape and statistical geometry perspectives,
	shorttitle = Theory of supercooled liquids and glasses,
	author = Debenedetti, Pablo G. and Truskett, Thomas M. and Lewis, Catherine P. and Stillinger, Frank H.,
	year = 2001,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/W7FKF6WA/S006523770128003X.html:text/html


@articlestillinger_kauzmann_2001,
	title = The Kauzmann paradox revisited,
	volume = 105,
	number = 47,
	journal = The Journal of Physical Chemistry B,
	author = Stillinger, Frank H. and Debenedetti, Pablo G. and Truskett, Thomas M.,
	year = 2001,
	pages = 11809–11816,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/4GK4SFHC/jp011840i.html:text/html;Snapshot:/Users/carolinegorham/Zotero/storage/83L7BCUJ/jp011840i.html:text/html


@articledebenedetti_theory_2001-1,
	title = Theory of supercooled liquids and glasses: Energy landscape and statistical geometry perspectives,
	shorttitle = Theory of supercooled liquids and glasses,
	author = Debenedetti, Pablo G. and Truskett, Thomas M. and Lewis, Catherine P. and Stillinger, Frank H.,
	year = 2001,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/2TGRX8PD/Debenedetti et al. - 2001 - Theory of supercooled liquids and glasses Energy .pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/8XN4DND5/S006523770128003X.html:text/html


@articlerawat_quaternion_2009,
	title = Quaternion Dirac Equation and Supersymmetry,
	volume = 48,
	issn = 0020-7748, 1572-9575,
	url = http://arxiv.org/abs/hep-th/0701131,
	doi = 10.1007/s10773-009-0003-4,
	abstract = Quaternion Dirac equation has been analyzed and its supersymetrization has been discussed consistently. It has been shown that the quaternion Dirac equation automatically describes the spin structure with its spin up and spin down components of two component quaternion Dirac spinors associated with positive and negative energies. It has also been shown that the supersymmetrization of quaternion Dirac equation works well for different cases associated with zero mass, non zero mass, scalar potential and generalized electromagnetic potentials. Accordingly we have discussed the splitting of supersymmetrized Dirac equation in terms of electric and magnetic fields.,
	number = 8,
	urldate = 2018-11-28,
	journal = International Journal of Theoretical Physics,
	author = Rawat, Seema and Negi, O. P. S.,
	month = aug,
	year = 2009,
	note = arXiv: hep-th/0701131,
	keywords = High Energy Physics - Theory,
	pages = 2222–2234,
	file = arXiv hep-th/0701131 PDF:/Users/carolinegorham/Zotero/storage/ALD9UUX8/Rawat and Negi - 2009 - Quaternion Dirac Equation and Supersymmetry.pdf:application/pdf;arXiv.org Snapshot:/Users/carolinegorham/Zotero/storage/LSG77QUC/0701131.html:text/html


@articlechristian_quantum_2018,
	title = Quantum correlations are weaved by the spinors of the Euclidean primitives,
	volume = 5,
	copyright = © 2018 The Authors.. Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited.,
	issn = 2054-5703,
	url = http://rsos.royalsocietypublishing.org/content/5/5/180526,
	doi = 10.1098/rsos.180526,
	abstract = The exceptional Lie group E8 plays a prominent role in both mathematics and theoretical physics. It is the largest symmetry group associated with the most general possible normed division algebra, namely, that of the non-associative real octonions, which—thanks to their non-associativity—form the only possible closed set of spinors (or rotors) that can parallelize the 7-sphere. By contrast, here we show how a similar 7-sphere also arises naturally from the algebraic interplay of the graded Euclidean primitives, such as points, lines, planes and volumes, which characterize the three-dimensional conformal geometry of the ambient physical space, set within its eight-dimensional Clifford-algebraic representation. Remarkably, the resulting algebra remains associative, and allows us to understand the origins and strengths of all quantum correlations locally, in terms of the geometry of the compactified physical space, namely, that of a quaternionic 3-sphere, S3, with S7 being its algebraic representation space. Every quantum correlation can thus be understood as a correlation among a set of points of this S7, computed using manifestly local spinors within S3, thereby extending the stringent bounds of ±2 set by Bell inequalities to the bounds of ±2√2±22‾√mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"mml:mrowmml:mo±/mml:momml:mn2/mml:mnmml:msqrtmml:mn2/mml:mn/mml:msqrt/mml:mrow/mml:math on the strengths of all possible strong correlations, in the same quantitatively precise manner as that predicted within quantum mechanics. The resulting geometrical framework thus overcomes Bell’s theorem by producing a strictly deterministic and realistic framework that allows a locally causal understanding of all quantum correlations, without requiring either remote contextuality or backward causation. We demonstrate this by first proving a general theorem concerning the geometrical origins of the correlations predicted by arbitrarily entangled quantum states, and then reproducing the correlations predicted by the EPR-Bohm and the GHZ states. The raison d’être of strong correlations turns out to be the Möbius-like twists in the Hopf bundles of S3 and S7.,
	language = en,
	number = 5,
	urldate = 2018-11-26,
	journal = Royal Society Open Science,
	author = Christian, Joy,
	month = may,
	year = 2018,
	pages = 180526,
	file = Full Text PDF:/Users/carolinegorham/Zotero/storage/T33JVG7A/Christian - 2018 - Quantum correlations are weaved by the spinors of .pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/WH9KXGXP/180526.html:text/html


@articleising_beitrag_1925,
	title = Beitrag zur theorie des ferromagnetismus,
	volume = 31,
	number = 1,
	journal = Zeitschrift für Physik,
	author = Ising, Ernst,
	year = 1925,
	pages = 253–258


@articleonsager_crystal_1944,
	title = Crystal statistics. I. A two-dimensional model with an order-disorder transition,
	volume = 65,
	number = 3-4,
	journal = Physical Review,
	author = Onsager, Lars,
	year = 1944,
	pages = 117,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/6KYGKG4C/PhysRev.65.html:text/html


@miscteoh_4d_nodate,
	title = 4D Euclidean space,
	url = http://eusebeia.dyndns.org/4d/,
	urldate = 2018-11-23,
	author = Teoh,
	file = 4D Euclidean space:/Users/carolinegorham/Zotero/storage/42C4FUEE/4d.html:text/html


@miscwebb_stella4d:_2003,
	title = Stella4D: Polyhedron Navigator,
	shorttitle = Stella,
	url = https://www.software3d.com/Stella.php,
	author = Webb, Robert,
	year = 2003,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/BIX3KZBK/PolyNavigator.html:text/html;Snapshot:/Users/carolinegorham/Zotero/storage/XXISK4FT/PolyNavigator.html:text/html


@incollectionwidom_short_1988,
	title = Short and long-range icosahedral order in crystals, glass, and quasicrystals,
	volume = 1,
	booktitle = Aperiodicity and Order,
	publisher = Elsevier,
	author = WIDOM, MICHAEL,
	year = 1988,
	pages = 59–110,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/RNW3D42Y/B978012040601250007X.html:text/html


@miscweeks_kaleidotile_nodate,
	title = KaleidoTile,
	url = http://www.geometrygames.org/KaleidoTile,
	journal = KaleidoTile. A computer program for creating spherical, Euclidean and hyperbolic tilings,
	author = Weeks, Jeff


@articlesethna_meissner_1992,
	title = Meissner Effect and Constraints,
	journal = arXiv preprint cond-mat/9204010,
	author = Sethna, James P. and Huang, Ming,
	year = 1992,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/2WAETJXA/Sethna and Huang - 1992 - Meissner Effect and Constraints.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/MV9GR3VQ/9204010.html:text/html


@articlejackiw_zero_1981,
	title = Zero modes of the vortex-fermion system,
	volume = 190,
	issn = 0550-3213,
	url = http://www.sciencedirect.com/science/article/pii/0550321381900444,
	doi = 10.1016/0550-3213(81)90044-4,
	abstract = Electric charge of a fermion that is coupled only to the gauge field of an abelian vortex need not be quantized, in contrast the situation for a magnetic monopole field. Correspondingly, zero-energy modes of the Dirac equation are not determined topologically. On the basis of mathematical and physical arguments we suggest that a complete description of the fermion-vortex system should include a fermion-scalar field interaction. This quantizes the charge and leads to a non-linear Dirac equation which possesses n zero-eigenvalue modes in the n-vortex background field. The result suggests that an index theorem exists for this Dirac equation on the non-compact space R2. When regularity requirements on the wave function are relaxed, additional normalizable zero-energy modes are present, even in the vacuum sector, n = 0, and fermions are converted to bosons.,
	number = 4,
	urldate = 2018-11-18,
	journal = Nuclear Physics B,
	author = Jackiw, R. and Rossi, P.,
	month = dec,
	year = 1981,
	pages = 681–691,
	file = ScienceDirect Snapshot:/Users/carolinegorham/Zotero/storage/MYL9N4HP/0550321381900444.html:text/html


@articleread_paired_2000,
	title = Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries and the fractional quantum Hall effect,
	volume = 61,
	url = https://link.aps.org/doi/10.1103/PhysRevB.61.10267,
	doi = 10.1103/PhysRevB.61.10267,
	abstract = We analyze pairing of fermions in two dimensions for fully gapped cases with broken parity (P) and time reversal (T), especially cases in which the gap function is an orbital angular momentum (l) eigenstate, in particular l=−1 (p wave, spinless, or spin triplet) and l=−2 (d wave, spin singlet). For l≠0, these fall into two phases, weak and strong pairing, which may be distinguished topologically. In the cases with conserved spin, we derive explicitly the Hall conductivity for spin as the corresponding topological invariant. For the spinless p-wave case, the weak-pairing phase has a pair wave function that is asympototically the same as that in the Moore-Read (Pfaffian) quantum Hall state, and we argue that its other properties (edge states, quasihole, and toroidal ground states) are also the same, indicating that nonabelian statistics is a generic property of such a paired phase. The strong-pairing phase is an abelian state, and the transition between the two phases involves a bulk Majorana fermion, the mass of which changes sign at the transition. For the d-wave case, we argue that the Haldane-Rezayi state is not the generic behavior of a phase but describes the asymptotics at the critical point between weak and strong pairing, and has gapless fermion excitations in the bulk. In this case the weak-pairing phase is an abelian phase, which has been considered previously. In the p-wave case with an unbroken U(1) symmetry, which can be applied to the double layer quantum Hall problem, the weak-pairing phase has the properties of the 331 state, and with nonzero tunneling there is a transition to the Moore-Read phase. The effects of disorder on noninteracting quasiparticles are considered. The gapped phases survive, but there is an intermediate thermally conducting phase in the spinless p-wave case, in which the quasiparticles are extended.,
	number = 15,
	urldate = 2018-11-18,
	journal = Physical Review B,
	author = Read, N. and Green, Dmitry,
	month = apr,
	year = 2000,
	pages = 10267–10297,
	file = APS Snapshot:/Users/carolinegorham/Zotero/storage/YWVP7YIT/PhysRevB.61.html:text/html;Submitted Version:/Users/carolinegorham/Zotero/storage/V8K2F65Q/Read and Green - 2000 - Paired states of fermions in two dimensions with b.pdf:application/pdf


@articleramos_low-temperature_1997,
	title = Low-temperature thermal conductivity of glasses within the soft-potential model,
	volume = 55,
	doi = 0.1103/PhysRevB.55.5749,
	number = 9,
	journal = Phys. Rev. B,
	author = Ramos, M. A. and Buchenau, U.,
	month = mar,
	year = 1997,
	keywords = polycrystalline, fractal, fracton, thermal conductivity, soft modes, model,
	pages = 5749–5754


@articlephillips_t^3_1985,
	title = Tˆ3 specific-heat anomaly in network solids,
	volume = 32,
	url = http://link.aps.org/doi/10.1103/PhysRevB.32.5356,
	doi = 10.1103/PhysRevB.32.5356,
	number = 8,
	journal = Phys. Rev. B,
	author = Phillips, J. C.,
	month = oct,
	year = 1985,
	keywords = fractal, fracton, tunneling, network, heat capacity, amorphous model,
	pages = 5356–5361


@articlegraebner_phonon_1986,
	title = Phonon localization in glasses,
	volume = 34,
	url = http://link.aps.org/doi/10.1103/PhysRevB.34.5696,
	doi = 10.1103/PhysRevB.34.5696,
	number = 8,
	author = Graebner, J. E. and Golding, B. and Allen, L. C.,
	month = oct,
	year = 1986,
	keywords = fracton,
	pages = 5696–5701


@articlekitaev_fault-tolerant_2003,
	title = Fault-tolerant quantum computation by anyons,
	volume = 303,
	number = 1,
	journal = Annals of Physics,
	author = Kitaev, A. Yu,
	year = 2003,
	pages = 2–30,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/S543X8B2/Kitaev - 2003 - Fault-tolerant quantum computation by anyons.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/QSMDTLYL/S0003491602000180.html:text/html


@articlemajorana_teoria_2008,
	title = Teoria simmetrica dell’elettrone e del positrone,
	volume = 14,
	issn = 1827-6121,
	url = https://doi.org/10.1007/BF02961314,
	doi = 10.1007/BF02961314,
	abstract = Si dimostra la possibilità di pervenire a una piena simmetrizzazione formale della teoria quantistica dell’elettrone e del positrone facendo uso di un nuovo processo di quantizzazione. Il significato delle equazioni diDiracne risulta alquanto modificato e non vi è più luogo a parlare di stati di energia negativa; nè a presumere per ogni altro tipo di particelle, partieolarmente neutre, l’esistenza di « antiparticelle » corrispondenti ai « vuoti » cut energia negativa.,
	language = it,
	number = 4,
	urldate = 2018-11-17,
	journal = Il Nuovo Cimento (1924-1942),
	author = Majorana, Ettore,
	month = sep,
	year = 2008,
	pages = 171


@articlewilczek_majorana_2009,
	title = Majorana returns,
	volume = 5,
	copyright = 2009 Nature Publishing Group,
	issn = 1745-2481,
	url = https://www.nature.com/articles/nphys1380,
	doi = 10.1038/nphys1380,
	abstract = In his short career, Ettore Majorana made several profound contributions. One of them, his concept of 'Majorana fermions' — particles that are their own antiparticle — is finding ever wider relevance in modern physics.,
	language = en,
	urldate = 2018-11-17,
	journal = Nature Physics,
	author = Wilczek, Frank,
	month = sep,
	year = 2009,
	pages = 614–618,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/WC6SMJ3J/nphys1380.html:text/html


@articlemoore_nonabelions_1991,
	title = Nonabelions in the fractional quantum Hall effect,
	volume = 360,
	number = 2-3,
	journal = Nuclear Physics B,
	author = Moore, Gregory and Read, Nicholas,
	year = 1991,
	pages = 362–396,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/56LBUQ7W/Moore and Read - 1991 - Nonabelions in the fractional quantum Hall effect.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/ZGVZJ6CM/055032139190407O.html:text/html


@articlefranz_viewpoint:_2010,
	title = Viewpoint: Race for Majorana fermions,
	volume = 3,
	copyright = ©2010 by the American Physical Society. All rights reserved.,
	shorttitle = Viewpoint,
	url = https://physics.aps.org/articles/v3/24,
	abstract = The race for realizing Majorana fermions—elusive particles that act as their own antiparticles—heats up, but we still await ideal materials to work with.,
	language = en,
	urldate = 2018-11-17,
	journal = Physics,
	author = Franz, Marcel,
	month = mar,
	year = 2010,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/MY3PGUHQ/24.html:text/html


@articlefranz_topological_2010,
	title = Topological insulators: Starting a new family,
	volume = 9,
	copyright = 2010 Nature Publishing Group,
	issn = 1476-4660,
	shorttitle = Topological insulators,
	url = https://www.nature.com/articles/nmat2783,
	doi = 10.1038/nmat2783,
	abstract = Ternary intermetallic Heusler compounds, originally discovered by a German mining engineer and chemist in 1903, may show exotic topological insulator behaviour unknown to science just five years ago.,
	language = en,
	number = 7,
	urldate = 2018-11-17,
	journal = Nature Materials,
	author = Franz, Marcel,
	month = jul,
	year = 2010,
	pages = 536–537,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/UX65S6R5/nmat2783.html:text/html


@articlefranz_topological_2010-1,
	title = Topological insulators: Starting a new family,
	volume = 9,
	shorttitle = Topological insulators,
	number = 7,
	journal = Nature materials,
	author = Franz, Marcel,
	year = 2010,
	pages = 536,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/MYUCUJYQ/Franz - 2010 - Topological insulators Starting a new family.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/DYKW4U8N/nmat2783.html:text/html


@articlemaciejko_quantum_2011,
	title = The quantum spin Hall effect,
	volume = 2,
	number = 1,
	journal = Annu. Rev. Condens. Matter Phys.,
	author = Maciejko, Joseph and Hughes, Taylor L. and Zhang, Shou-Cheng,
	year = 2011,
	pages = 31–53,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/YDB9SSLU/annurev-conmatphys-062910-140538.html:text/html;Snapshot:/Users/carolinegorham/Zotero/storage/USHCTKRM/annurev-conmatphys-062910-140538.html:text/html


@articlekramers_theorie_1930,
	title = Théorie générale de la rotation paramagnétique dans les cristaux,
	volume = 33,
	journal = Proc. Acad. Amst,
	author = Kramers, Hendrik Antoon,
	year = 1930,
	pages = 959–972


@articlekane_z2_2005,
	title = Z2 topological order and the quantum spin Hall effect,
	volume = 95,
	number = 14,
	journal = Physical review letters,
	author = Kane, Charles L. and Mele, Eugene J.,
	year = 2005,
	pages = 146802,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/76QASZQT/Kane and Mele - 2005 - Z 2 topological order and the quantum spin Hall ef.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/IRJ72I94/PhysRevLett.95.html:text/html


@articlexiao_berry_2010,
	title = Berry phase effects on electronic properties,
	volume = 82,
	number = 3,
	journal = Reviews of modern physics,
	author = Xiao, Di and Chang, Ming-Che and Niu, Qian,
	year = 2010,
	pages = 1959,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/UCIGMZGA/Xiao et al. - 2010 - Berry phase effects on electronic properties.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/U6SPGVR3/RevModPhys.82.html:text/html


@articlemoore_birth_2010,
	title = The birth of topological insulators,
	volume = 464,
	copyright = 2010 Nature Publishing Group,
	issn = 1476-4687,
	url = https://www.nature.com/articles/nature08916,
	doi = 10.1038/nature08916,
	abstract = Certain insulators have exotic metallic states on their surfaces. These states are formed by topological effects that also render the electrons travelling on such surfaces insensitive to scattering by impurities. Such topological insulators may provide new routes to generating novel phases and particles, possibly finding uses in technological applications in spintronics and quantum computing.,
	language = en,
	urldate = 2018-11-15,
	journal = Nature,
	author = Moore, Joel E.,
	month = mar,
	year = 2010,
	pages = 194–198,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/MA876862/nature08916.html:text/html


@miscgolden_topological_nodate,
	title = Topological Insulators - a beginners guide,
	url = https://iop.fnwi.uva.nl/cmp/TI.html,
	urldate = 2018-11-15,
	author = Golden, Mark,
	file = Topological Insulators - a beginners guide:/Users/carolinegorham/Zotero/storage/6UXWRJBZ/TI.html:text/html


@articlehasan_colloquium:_2010,
	title = Colloquium: Topological insulators,
	volume = 82,
	shorttitle = Colloquium,
	url = https://link.aps.org/doi/10.1103/RevModPhys.82.3045,
	doi = 10.1103/RevModPhys.82.3045,
	abstract = Topological insulators are electronic materials that have a bulk band gap like an ordinary insulator but have protected conducting states on their edge or surface. These states are possible due to the combination of spin-orbit interactions and time-reversal symmetry. The two-dimensional (2D) topological insulator is a quantum spin Hall insulator, which is a close cousin of the integer quantum Hall state. A three-dimensional (3D) topological insulator supports novel spin-polarized 2D Dirac fermions on its surface. In this Colloquium the theoretical foundation for topological insulators and superconductors is reviewed and recent experiments are described in which the signatures of topological insulators have been observed. Transport experiments on HgTe∕CdTe quantum wells are described that demonstrate the existence of the edge states predicted for the quantum spin Hall insulator. Experiments on Bi1−xSbx, Bi2Se3, Bi2Te3, and Sb2Te3 are then discussed that establish these materials as 3D topological insulators and directly probe the topology of their surface states. Exotic states are described that can occur at the surface of a 3D topological insulator due to an induced energy gap. A magnetic gap leads to a novel quantum Hall state that gives rise to a topological magnetoelectric effect. A superconducting energy gap leads to a state that supports Majorana fermions and may provide a new venue for realizing proposals for topological quantum computation. Prospects for observing these exotic states are also discussed, as well as other potential device applications of topological insulators.,
	number = 4,
	urldate = 2018-11-15,
	journal = Reviews of Modern Physics,
	author = Hasan, M. Z. and Kane, C. L.,
	month = nov,
	year = 2010,
	pages = 3045–3067,
	file = APS Snapshot:/Users/carolinegorham/Zotero/storage/RHMUVKG4/RevModPhys.82.html:text/html;Full Text:/Users/carolinegorham/Zotero/storage/S4LZMH22/Hasan and Kane - 2010 - Colloquium Topological insulators.pdf:application/pdf


@articlegoswami_dissipation_2006,
	title = Dissipation, topology, and quantum phase transition in a one-dimensional Josephson junction array,
	volume = 73,
	url = https://link.aps.org/doi/10.1103/PhysRevB.73.094516,
	doi = 10.1103/PhysRevB.73.094516,
	abstract = We study the phase diagram and quantum critical properties of a resistively shunted Josephson junction array in one dimension from a strong coupling analysis. After mapping the dissipative quantum phase model to an effective sine-Gordon model we study the renormalization group flow and the phase diagram. We try to bridge the phase diagrams obtained from the weak and the strong coupling renormalization group calculations to extract a more comprehensive picture of the complete phase diagram. The relevance of our theory to experiments in nanowires is discussed.,
	number = 9,
	urldate = 2018-11-15,
	journal = Physical Review B,
	author = Goswami, Pallab and Chakravarty, Sudip,
	month = mar,
	year = 2006,
	pages = 094516,
	file = APS Snapshot:/Users/carolinegorham/Zotero/storage/SEB7BGLV/PhysRevB.73.html:text/html;Submitted Version:/Users/carolinegorham/Zotero/storage/4NMV3UDI/Goswami and Chakravarty - 2006 - Dissipation, topology, and quantum phase transitio.pdf:application/pdf


@articlefert_magnetic_2017,
	title = Magnetic skyrmions: advances in physics and potential applications,
	volume = 2,
	issn = 2058-8437,
	shorttitle = Magnetic skyrmions,
	url = http://www.nature.com/articles/natrevmats201731,
	doi = 10.1038/natrevmats.2017.31,
	abstract = Magnetic skyrmions are small swirling topological defects in the magnetization texture. Their stabilization and dynamics depend strongly on their topological properties. In most cases, they are induced by chiral interactions between atomic spins in non-centrosymmetric magnetic compounds or in thin films with broken inversion symmetry. Skyrmions can be extremely small, with diameters in the nanometre range, and behave as particles that can be moved, created and annihilated, which makes them suitable for ‘abacus’-type applications in information storage and logic technologies. Until recently, skyrmions had been observed only at low temperature and, in most cases, under large applied magnetic fields. An intense research effort has led to the identification of thin-film and multilayer structures in which skyrmions are now stable at room temperature and can be manipulated by electrical currents. The development of skyrmion-based topological spintronics holds promise for applications in the mid-term furure, even though many challenges, such as the achievement of writing, processing and reading functionalities at room temperature and in all-electrical manipulation schemes, still lie ahead.,
	language = en,
	number = 7,
	urldate = 2018-11-15,
	journal = Nature Reviews Materials,
	author = Fert, Albert and Reyren, Nicolas and Cros, Vincent,
	month = jul,
	year = 2017,
	pages = 17031,
	file = Full Text PDF:/Users/carolinegorham/Zotero/storage/LMY5FYBE/Fert et al. - 2017 - Magnetic skyrmions advances in physics and potent.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/QHT3B7SL/natrevmats201731.html:text/html


@articlesampaio_nucleation_2013,
	title = Nucleation, stability and current-induced motion of isolated magnetic skyrmions in nanostructures,
	volume = 8,
	copyright = 2013 Nature Publishing Group,
	issn = 1748-3395,
	url = https://www.nature.com/articles/nnano.2013.210,
	doi = 10.1038/nnano.2013.210,
	abstract = Magnetic skyrmions are topologically stable spin configurations, which usually originate from chiral interactions known as Dzyaloshinskii–Moriya interactions. Skyrmion lattices were initially observed in bulk non-centrosymmetric crystals, but have more recently been noted in ultrathin films, where their existence is explained by interfacial Dzyaloshinskii–Moriya interactions induced by the proximity to an adjacent layer with strong spin–orbit coupling. Skyrmions are promising candidates as information carriers for future information-processing devices due to their small size (down to a few nanometres) and to the very small current densities needed to displace skyrmion lattices. However, any practical application will probably require the creation, manipulation and detection of isolated skyrmions in magnetic thin-film nanostructures. Here, we demonstrate by numerical investigations that an isolated skyrmion can be a stable configuration in a nanostructure, can be locally nucleated by injection of spin-polarized current, and can be displaced by current-induced spin torques, even in the presence of large defects.,
	language = en,
	number = 11,
	urldate = 2018-11-15,
	journal = Nature Nanotechnology,
	author = Sampaio, J. and Cros, V. and Rohart, S. and Thiaville, A. and Fert, A.,
	month = nov,
	year = 2013,
	pages = 839–844,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/TRXIYCR5/nnano.2013.html:text/html


@articleparkin_magnetic_2008,
	title = Magnetic domain-wall racetrack memory,
	volume = 320,
	number = 5873,
	journal = Science,
	author = Parkin, Stuart SP and Hayashi, Masamitsu and Thomas, Luc,
	year = 2008,
	pages = 190–194,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/KFSR623X/Parkin et al. - 2008 - Magnetic domain-wall racetrack memory.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/MTC4EBHT/190.html:text/html


@articlefelser_skyrmions_2013,
	title = Skyrmions,
	volume = 52,
	issn = 1521-3773,
	url = https://onlinelibrary.wiley.com/doi/abs/10.1002/anie.201207056,
	doi = 10.1002/anie.201207056,
	language = en,
	number = 6,
	urldate = 2018-11-14,
	journal = Angewandte Chemie International Edition,
	author = Felser, Claudia,
	month = feb,
	year = 2013,
	pages = 1631–1634,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/TEIQKW6D/anie.html:text/html


@phdthesisgorham_formation_2018,
	type = PhD Thesis,
	title = On the formation of crystalline and non-crystalline solid states and their thermal transport properties: A topological perspective via a quaternion orientational order parameter,
	shorttitle = On the formation of crystalline and non-crystalline solid states and their thermal transport properties,
	school = Carnegie Mellon University Pittsburgh, PA,
	author = Gorham, Caroline S.,
	year = 2018


@articlemandelbaum_four-dimensional_1980,
	title = Four-dimensional topology: an introduction,
	volume = 2,
	shorttitle = Four-dimensional topology,
	number = 1,
	journal = Bulletin of the American Mathematical Society,
	author = Mandelbaum, Richard,
	year = 1980,
	pages = 1–159,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/8CJ3XSZG/S0273-0979-1980-14687-X.html:text/html


@miscnoauthor_mandelbaum_nodate,
	title = Mandelbaum : Four-dimensional topology: an introduction - Google Scholar,
	url = https://scholar.google.com/scholar?hl=en   as_sdt=0
	urldate = 2018-11-09,
	file = Mandelbaum   Four-dimensional topology  an introduction - Google Scholar:/Users/carolinegorham/Zotero/storage/3MYIJ67K/scholar.html:text/html


@bookzeeman_introduction_1966,
	title = An introduction to topology: The classification theorem for surfaces,
	shorttitle = An introduction to topology,
	publisher = Mathematics Institute, University of Warwick,
	author = Zeeman, Eric-Christopher,
	year = 1966


@articlehoffman_adding_1993,
	title = Adding handles to the helicoid,
	volume = 29,
	number = 1,
	journal = Bulletin of The American Mathematical Society,
	author = Hoffman, David and Wei, Fu Sheng and Karcher, Hermann,
	year = 1993,
	pages = 77–84,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/S9SS64EX/Hoffman et al. - 1993 - Adding handles to the helicoid.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/VVYHTBDM/S0273-0979-1993-00401-4.html:text/html


@articlezeeman_unknotting_1960,
	title = Unknotting spheres in five dimensions,
	volume = 66,
	journal = Bull. Amer. Math. Soc,
	author = Zeeman, E. Christopher,
	year = 1960,
	pages = 198


@articletucker_branched_1936,
	title = Branched and folded coverings,
	volume = 42,
	issn = 0002-9904, 1936-881X,
	url = https://www.ams.org/home/page/,
	doi = 10.1090/S0002-9904-1936-06446-3,
	abstract = Our mission is to further the interests of mathematical research, scholarship and education.,
	language = en-US,
	number = 12,
	urldate = 2018-11-09,
	journal = Bulletin of the American Mathematical Society,
	author = Tucker, A. W.,
	year = 1936,
	pages = 859–862,
	file = Full Text PDF:/Users/carolinegorham/Zotero/storage/KSF59FYP/Tucker - 1936 - Branched and folded coverings.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/NTI8G739/S0002-9904-1936-06446-3.html:text/html


@articleum_thermal_1988,
	title = Thermal conductivity and viscosity via phonon-phonon, phonon-roton, and roton-roton scattering in thin $ˆ{4}\mathrm{He}$ films,
	volume = 38,
	url = https://link.aps.org/doi/10.1103/PhysRevB.38.8838,
	doi = 10.1103/PhysRevB.38.8838,
	abstract = The coefficients of the thermal conductivity (κ) and first viscosity (η) in thin helium films are evaluated explicitly as a function of temperature via phonon-phonon, phonon-roton, and roton-roton scattering. Above about 0.8 K, phonon-roton scattering and five-phonon processes are the main contributors to both coefficients. Below about 0.8 K, both coefficients increase exponentially with decreasing temperature. At temperatures below 0.3 K, κph has a T−5 dependence, while ηph shows exponential and T−1 dependencies. In the case of ηph, the former is due to phonon-roton scattering and the latter originates from three-phonon processes. The coefficient κr from roton-roton scattering varies as T−1, and the roton part ηr of the first viscosity is independent of temperature.,
	number = 13,
	urldate = 2018-11-08,
	journal = Physical Review B,
	author = Um, Chung-In and Jun, Chul-Won and Kahng, Woo-Hyung and George, Thomas F.,
	month = nov,
	year = 1988,
	pages = 8838–8849,
	file = APS Snapshot:/Users/carolinegorham/Zotero/storage/IX3R9AY2/PhysRevB.38.html:text/html


@articleum_coefficient_1988,
	title = Coefficient of first viscosity via three-phonon processes in bulk liquid helium,
	volume = 38,
	number = 13,
	journal = Physical Review B,
	author = Um, C. I. and Jun, C. W. and Kahng, W. H. and George, Thomas F.,
	year = 1988,
	pages = 8834,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/8WIN39SY/PhysRevB.38.html:text/html


@articlechomaz_observation_2018,
	title = Observation of roton mode population in a dipolar quantum gas,
	volume = 14,
	copyright = 2018 The Author(s),
	issn = 1745-2481,
	url = https://www.nature.com/articles/s41567-018-0054-7,
	doi = 10.1038/s41567-018-0054-7,
	abstract = The roton energy spectrum, originally introduced by Landau, explains the thermodynamic behaviour of strongly interacting liquid helium at low temperature. Now, a similar spectrum has been observed in weakly interacting dipolar quantum gas.,
	language = en,
	number = 5,
	urldate = 2018-11-08,
	journal = Nature Physics,
	author = Chomaz, L. and Bijnen, R. M. W. van and Petter, D. and Faraoni, G. and Baier, S. and Becher, J. H. and Mark, M. J. and Wächtler, F. and Santos, L. and Ferlaino, F.,
	month = may,
	year = 2018,
	pages = 442–446,
	file = Full Text PDF:/Users/carolinegorham/Zotero/storage/SV3377JL/Chomaz et al. - 2018 - Observation of roton mode population in a dipolar .pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/VCUPL5D9/s41567-018-0054-7.html:text/html


@articleglyde_role_1993,
	title = The role of the condensate in the existence of phonons and rotons,
	volume = 93,
	issn = 1573-7357,
	url = https://doi.org/10.1007/BF00692035,
	doi = 10.1007/BF00692035,
	abstract = Interpretations of the characteristic phonon-roton excitations in superfluid4He are discussed to assess the role of the condensate. In the celebrated Landau, Feynman, Feenberg and subsequent Correlated Basic Function methods, the phonon-roton excitations are interpreted as collective density excitations. This picture, suitably modified at higher Q to take account of the correlated motion of neighbors (backflow), provides our best description of neutron scattering data at low temperature. The condensate does not play an explicit role. In the Field Theory, second quantized formulation of Bogoliubov, Hugenholtz and Pines, Gavoret and Nozières and the subsequent Dielectric Function formulation, the condensate plays an explicit role. Because of the condensate, both regular density (particle-hole) and single particle excitations contribute to the density response. The regular density (two-particle) and single particle excitations mix as particles scatter into and out of the condensate. This Density-Quasiparticle picture provides a good description of the temperature dependence of neutron scattering data. From this description, the phonon at low Q is interpreted as a joint density/quasiparticle mode strongly coupled via the condensate. At higher Q, the sharp maxon-roton is interpreted as a quasiparticle excitation less strongly coupled into the density. The sharp maxon-roton peak is a unique feature of the condensate and could not be observed in S(Q, ω) without a condensate.,
	language = en,
	number = 5,
	urldate = 2018-11-08,
	journal = Journal of Low Temperature Physics,
	author = Glyde, Henry R.,
	month = dec,
	year = 1993,
	keywords = 61.12-q, 67.40-W, 67.40D6,
	pages = 861–878,
	file = Springer Full Text PDF:/Users/carolinegorham/Zotero/storage/FY59ZQ2Q/Glyde - 1993 - The role of the condensate in the existence of pho.pdf:application/pdf


@articlehendry_generation_1994,
	title = Generation of defects in superfluid 4He as an analogue of the formation of cosmic strings,
	volume = 368,
	number = 6469,
	journal = Nature,
	author = Hendry, P. C. and Lawson, N. Stuart and Lee, R. A. M. and McClintock, Peter VE and Williams, C. D. H.,
	year = 1994,
	pages = 315,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/UMLQ6GG2/Hendry et al. - 1994 - Generation of defects in superfluid 4He as an anal.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/JAK83HPI/368315a0.html:text/html


@articleyurke_evolving_1994,
	title = An evolving Universe in a pot of liquid helium,
	volume = 7,
	issn = 2058-7058,
	url = http://stacks.iop.org/2058-7058/7/i=7/a=28,
	doi = 10.1088/2058-7058/7/7/28,
	abstract = Condensed matter physics and cosmology might be thought to share little common ground. The behaviour of helium near absolute zero and the earliest stages of the Big Bang, when the Universe was at extremely high temperatures, would be expected to have even less in common. But this is not the case because phase transitions play a central role in both condensed matter and cosmology. Now, experiments with liquid helium, by Peter McClintock and co-workers at Lancaster and Exeter universities in the UK, have provided new evidence supporting the theory that "defects" generated as the early Universe underwent a phase transition are responsible for the large-scale structure we see today (P C Hendry et al. Nature (1994) 368 315).,
	language = en,
	number = 7,
	urldate = 2018-11-08,
	journal = Physics World,
	author = Yurke, Bernard,
	year = 1994,
	pages = 28,
	file = IOP Full Text PDF:/Users/carolinegorham/Zotero/storage/77PB2HJS/Yurke - 1994 - An evolving Universe in a pot of liquid helium.pdf:application/pdf


@articlekraus_topological_2012,
	title = Topological states and adiabatic pumping in quasicrystals,
	volume = 109,
	number = 10,
	journal = Physical review letters,
	author = Kraus, Yaacov E. and Lahini, Yoav and Ringel, Zohar and Verbin, Mor and Zilberberg, Oded,
	year = 2012,
	pages = 106402,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/FXD36K5T/PhysRevLett.109.html:text/html


@articlekraus_four-dimensional_2013,
	title = Four-dimensional quantum Hall effect in a two-dimensional quasicrystal,
	volume = 111,
	number = 22,
	journal = Physical review letters,
	author = Kraus, Yaacov E. and Ringel, Zohar and Zilberberg, Oded,
	year = 2013,
	pages = 226401,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/5XRU4IR8/PhysRevLett.111.html:text/html


@articlekraus_four-dimensional_2013-1,
	title = Four-dimensional quantum Hall effect in a two-dimensional quasicrystal,
	volume = 111,
	number = 22,
	journal = Physical review letters,
	author = Kraus, Yaacov E. and Ringel, Zohar and Zilberberg, Oded,
	year = 2013,
	pages = 226401,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/9WS7DXSF/PhysRevLett.111.html:text/html


@articleyuan_synthetic_2018,
	title = Synthetic Dimension in Photonics,
	url = https://arxiv.org/abs/1807.11468,
	doi = 10.1364/OPTICA.5.001396,
	language = en,
	urldate = 2018-11-07,
	author = Yuan, Luqi and Lin, Qian and Xiao, Meng and Fan, Shanhui,
	month = jul,
	year = 2018,
	file = Full Text PDF:/Users/carolinegorham/Zotero/storage/EKXYVXS4/Yuan et al. - 2018 - Synthetic Dimension in Photonics.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/3DTQYJ9X/1807.html:text/html


@articleceli_synthetic_2014,
	title = Synthetic gauge fields in synthetic dimensions,
	volume = 112,
	number = 4,
	journal = Physical review letters,
	author = Celi, Alessio and Massignan, Pietro and Ruseckas, Julius and Goldman, Nathan and Spielman, Ian B. and Juzeliūnas, G. and Lewenstein, M.,
	year = 2014,
	pages = 043001,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/SJ5Y97KF/PhysRevLett.112.html:text/html


@articlemancini_observation_2015,
	title = Observation of chiral edge states with neutral fermions in synthetic Hall ribbons,
	volume = 349,
	number = 6255,
	journal = Science,
	author = Mancini, Marco and Pagano, Guido and Cappellini, Giacomo and Livi, Lorenzo and Rider, Marie and Catani, Jacopo and Sias, Carlo and Zoller, Peter and Inguscio, Massimo and Dalmonte, Marcello,
	year = 2015,
	pages = 1510–1513,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/9DUZ3N7B/Mancini et al. - 2015 - Observation of chiral edge states with neutral fer.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/ZH8396KV/1510.html:text/html


@miscnoauthor_exploring_nodate,
	title = Exploring 4D quantum Hall physics with a 2D topological charge pump  Nature,
	url = http://www.nature.com/articles/nature25000,
	urldate = 2018-11-06,
	file = Exploring 4D quantum Hall physics with a 2D topological charge pump | Nature:/Users/carolinegorham/Zotero/storage/8LEDR557/nature25000.html:text/html


@articlelohse_exploring_2018,
	title = Exploring 4D Quantum Hall Physics with a 2D Topological Charge Pump,
	volume = 553,
	issn = 0028-0836, 1476-4687,
	url = http://arxiv.org/abs/1705.08371,
	doi = 10.1038/nature25000,
	abstract = The discovery of topological states of matter has profoundly augmented our understanding of phase transitions in physical systems. Instead of local order parameters, topological phases are described by global topological invariants and are therefore robust against perturbations. A prominent example thereof is the two-dimensional integer quantum Hall effect. It is characterized by the first Chern number which manifests in the quantized Hall response induced by an external electric field. Generalizing the quantum Hall effect to four-dimensional systems leads to the appearance of a novel non-linear Hall response that is quantized as well, but described by a 4D topological invariant - the second Chern number. Here, we report on the first observation of a bulk response with intrinsic 4D topology and the measurement of the associated second Chern number. By implementing a 2D topological charge pump with ultracold bosonic atoms in an angled optical superlattice, we realize a dynamical version of the 4D integer quantum Hall effect. Using a small atom cloud as a local probe, we fully characterize the non-linear response of the system by in-situ imaging and site-resolved band mapping. Our findings pave the way to experimentally probe higher-dimensional quantum Hall systems, where new topological phases with exotic excitations are predicted.,
	number = 7686,
	urldate = 2018-11-06,
	journal = Nature,
	author = Lohse, Michael and Schweizer, Christian and Price, Hannah M. and Zilberberg, Oded and Bloch, Immanuel,
	month = jan,
	year = 2018,
	note = arXiv: 1705.08371,
	keywords = Condensed Matter - Mesoscale and Nanoscale Physics, Quantum Physics, Condensed Matter - Quantum Gases, Physics - Optics,
	pages = 55–58,
	file = arXiv 1705.08371 PDF:/Users/carolinegorham/Zotero/storage/I53HAMGZ/Lohse et al. - 2018 - Exploring 4D Quantum Hall Physics with a 2D Topolo.pdf:application/pdf;arXiv.org Snapshot:/Users/carolinegorham/Zotero/storage/26EEILZ8/1705.html:text/html


@articlele_hur_many-body_2016,
	series = Polariton physics / Physique des polaritons,
	title = Many-body quantum electrodynamics networks: Non-equilibrium condensed matter physics with light,
	volume = 17,
	issn = 1631-0705,
	shorttitle = Many-body quantum electrodynamics networks,
	url = http://www.sciencedirect.com/science/article/pii/S1631070516300317,
	doi = 10.1016/j.crhy.2016.05.003,
	abstract = We review recent developments regarding the quantum dynamics and many-body physics with light, in superconducting circuits and Josephson analogues, by analogy with atomic physics. We start with quantum impurity models addressing dissipative and driven systems. Both theorists and experimentalists are making efforts towards the characterization of these non-equilibrium quantum systems. We show how Josephson junction systems can implement the equivalent of the Kondo effect with microwave photons. The Kondo effect can be characterized by a renormalized light frequency and a peak in the Rayleigh elastic transmission of a photon. We also address the physics of hybrid systems comprising mesoscopic quantum dot devices coupled with an electromagnetic resonator. Then, we discuss extensions to Quantum Electrodynamics (QED) Networks allowing one to engineer the Jaynes–Cummings lattice and Rabi lattice models through the presence of superconducting qubits in the cavities. This opens the door to novel many-body physics with light out of equilibrium, in relation with the Mott–superfluid transition observed with ultra-cold atoms in optical lattices. Then, we summarize recent theoretical predictions for realizing topological phases with light. Synthetic gauge fields and spin–orbit couplings have been successfully implemented in quantum materials and with ultra-cold atoms in optical lattices — using time-dependent Floquet perturbations periodic in time, for example — as well as in photonic lattice systems. Finally, we discuss the Josephson effect related to Bose–Hubbard models in ladder and two-dimensional geometries, producing phase coherence and Meissner currents. The Bose–Hubbard model is related to the Jaynes–Cummings lattice model in the large detuning limit between light and matter (the superconducting qubits). In the presence of synthetic gauge fields, we show that Meissner currents subsist in an insulating Mott phase.
Résumé
Nous passons en revue des développements récents concernant la dynamique quantique hors équilibre et la physique de la lumière dans des circuits supraconducteurs et analogues de Josephson, par analogie avec les systèmes de physique atomique. Nous commençons par des modèles quantiques d'impuretés reliés à des systèmes dissipatifs et contrôlés. Théoriciens et expérimentateurs accomplissent des efforts en vue de la caractérisation de ces systèmes quantiques hors équilibre. Nous montrons comment les systèmes de jonctions Josephson peuvent servir à implémenter l'équivalent de l'effet Kondo avec des photons micro-onde. L'effet Kondo peut se caractériser par une fréquence lumineuse renormalisée et par un pic dans la transmission élastique Rayleigh d'un photon. Nous nous intéressons aussi à la physique des systèmes hybrides comprenant des dispositifs à points quantiques mésoscopiques couplés à un résonateur électromagnétique. Ensuite, nous discuterons des modèles de réseaux d'électrodynamique quantiques (QED) permettant de concevoir des modèles de réseaux de Jaynes–Cummings et de Rabi, via la présence de qubits supraconducteurs dans les cavités. Ceci ouvre la porte nouvelle physique pour le problème à N-corps dans les systèmes lumineux hors équilibre, en relation avec la transition Mott-superfluide observée avec des atomes ultra-froids dans des réseaux optiques. Nous résumons aussi des prédictions théoriques récentes pour réaliser des phases topologiques avec de la lumière. Des champs de jauge synthétiques et des couplages spin–orbite ont été mis en œuvre avec succès dans les matériaux quantiques et dans les systèmes d'atomes ultra-froids piégés dans des réseaux optiques – en utilisant des perturbations de Floquet périodiques dans le temps – ainsi que dans les systèmes de réseaux photoniques artificiels. Finalement, nous discutons l'effet Josephson lié aux modèles de Bose–Hubbard dans des géométries en échelle ainsi qu'à deux dimensions, produisant de la cohérence de phase et des courants Meissner. Le modèle de Bose–Hubbard est aussi lié au modèle de Jaynes–Cummings sur réseau. En présence de champs de jauge synthétiques, nous montrons que les courants Meissner subsistent dans une phase de Mott isolante.,
	number = 8,
	urldate = 2018-11-06,
	journal = Comptes Rendus Physique,
	author = Le Hur, Karyn and Henriet, Loïc and Petrescu, Alexandru and Plekhanov, Kirill and Roux, Guillaume and Schiró, Marco,
	month = oct,
	year = 2016,
	keywords = Condensed-matter physics with light, Dissipative and driven quantum impurity models, Effet Josephson et nanoscience, Jaynes–Cummings and Rabi lattices, Josephson effect and nanoscience, Modèles d'impuretés quantiques et contrôlés, Phases topologiques et champs de jauge, Physique de la matière condensée avec la lumière, Réseaux de Jaynes-Cummings et de Rabi, Réseaux électodynamiques quantiques à circuit supraconducteur, Superconducting circuit quantum electrodynamics networks, Topological phases and synthetic gauge fields,
	pages = 808–835,
	file = ScienceDirect Full Text PDF:/Users/carolinegorham/Zotero/storage/X96ANTM9/Le Hur et al. - 2016 - Many-body quantum electrodynamics networks Non-eq.pdf:application/pdf;ScienceDirect Snapshot:/Users/carolinegorham/Zotero/storage/SPKZQHJU/S1631070516300317.html:text/html


@booksrivastava_physics_1990,
	title = The physics of phonons,
	publisher = CRC press,
	author = Srivastava, Gyaneshwar P.,
	year = 1990,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/XSWR67N7/books.html:text/html


@articleavron_optimal_2001,
	title = Optimal quantum pumps,
	volume = 87,
	number = 23,
	journal = Physical review letters,
	author = Avron, J. E. and Elgart, A. and Graf, G. M. and Sadun, L.,
	year = 2001,
	pages = 236601,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/AUUGEZML/Avron et al. - 2001 - Optimal quantum pumps.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/QVRM9MXG/PhysRevLett.87.html:text/html


@articlebrouwer_scattering_1998,
	title = Scattering approach to parametric pumping,
	volume = 58,
	number = 16,
	journal = Physical Review B,
	author = Brouwer, P. W.,
	year = 1998,
	pages = R10135,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/UEZJ25FG/Brouwer - 1998 - Scattering approach to parametric pumping.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/27EE4BMK/PhysRevB.58.html:text/html


@articleswitkes_adiabatic_1999,
	title = An adiabatic quantum electron pump,
	volume = 283,
	number = 5409,
	journal = Science,
	author = Switkes, M. and Marcus, C. M. and Campman, K. and Gossard, A. C.,
	year = 1999,
	pages = 1905–1908,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/7WI43LH6/Switkes et al. - 1999 - An adiabatic quantum electron pump.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/K73Y6WK3/1905.html:text/html


@articleniu_towards_1990,
	title = Towards a quantum pump of electric charges,
	volume = 64,
	url = https://link.aps.org/doi/10.1103/PhysRevLett.64.1812,
	doi = 10.1103/PhysRevLett.64.1812,
	abstract = Here we give a critical examination of the possibility of realizing a quantum pump of electric charges. The physics is based on the theory of quantum adiabatic particle transport initially due to Thouless. We present theoretical guidelines on the experimental conditions for observing this phenomenon. We argue that potentially very accurate quantization of charge transport or electron current can be achieved, once these conditions are approximately satisfied. An example of experimental setup is outlined to demonstrate the practical possibilities. Some comments are also made on the scientific significance of such a quantum device.,
	number = 15,
	urldate = 2018-11-02,
	journal = Physical Review Letters,
	author = Niu, Q.,
	month = apr,
	year = 1990,
	pages = 1812–1815,
	file = APS Snapshot:/Users/carolinegorham/Zotero/storage/2CTT9JF2/PhysRevLett.64.html:text/html


@articlethouless_quantization_1983,
	title = Quantization of particle transport,
	volume = 27,
	number = 10,
	journal = Physical Review B,
	author = Thouless, D. J.,
	year = 1983,
	pages = 6083,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/LHNBCSTS/Thouless - 1983 - Quantization of particle transport.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/YJM32F9G/PhysRevB.27.html:text/html


@articleosadchy_hofstadter_2001,
	title = Hofstadter butterfly as quantum phase diagram,
	volume = 42,
	number = 12,
	journal = Journal of Mathematical Physics,
	author = Osadchy, Daniel and Avron, J. E.,
	year = 2001,
	pages = 5665–5671,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/KMDLAPPV/Osadchy and Avron - 2001 - Hofstadter butterfly as quantum phase diagram.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/TLRHPMRR/1.html:text/html


@articlehofstadter_energy_1976,
	title = Energy levels and wave functions of Bloch electrons in rational and irrational magnetic fields,
	volume = 14,
	url = https://link.aps.org/doi/10.1103/PhysRevB.14.2239,
	doi = 10.1103/PhysRevB.14.2239,
	abstract = An effective single-band Hamiltonian representing a crystal electron in a uniform magnetic field is constructed from the tight-binding form of a Bloch band by replacing ℏ→k by the operator →p−e→Ac. The resultant Schrödinger equation becomes a finite-difference equation whose eigenvalues can be computed by a matrix method. The magnetic flux which passes through a lattice cell, divided by a flux quantum, yields a dimensionless parameter whose rationality or irrationality highly influences the nature of the computed spectrum. The graph of the spectrum over a wide range of "rational" fields is plotted. A recursive structure is discovered in the graph, which enables a number of theorems to be proven, bearing particularly on the question of continuity. The recursive structure is not unlike that predicted by Azbel', using a continued fraction for the dimensionless parameter. An iterative algorithm for deriving the clustering pattern of the magnetic subbands is given, which follows from the recursive structure. From this algorithm, the nature of the spectrum at an "irrational" field can be deduced; it is seen to be an uncountable but measure-zero set of points (a Cantor set). Despite these-features, it is shown that the graph is continuous as the magnetic field varies. It is also shown how a spectrum with simplified properties can be derived from the rigorously derived spectrum, by introducing a spread in the field values. This spectrum satisfies all the intuitively desirable properties of a spectrum. The spectrum here presented is shown to agree with that predicted by A. Rauh in a completely different model for crystal electrons in a magnetic field. A new type of magnetic "superlattice" is introduced, constructed so that its unit cell intercepts precisely one quantum of flux. It is shown that this cell represents the periodicity of solutions of the difference equation. It is also shown how this superlattice allows the determination of the wave function at nonlattice sites. Evidence is offered that the wave functions belonging to irrational fields are everywhere defined and are continuous in this model, whereas those belonging to rational fields are only defined on a discrete set of points. A method for investigating these predictions experimentally is sketched.,
	number = 6,
	urldate = 2018-11-02,
	journal = Physical Review B,
	author = Hofstadter, Douglas R.,
	month = sep,
	year = 1976,
	pages = 2239–2249,
	file = APS Snapshot:/Users/carolinegorham/Zotero/storage/VV95BX8I/PhysRevB.14.html:text/html


@articlevon_klitzing_quantized_1986,
	title = The quantized Hall effect,
	volume = 58,
	number = 3,
	journal = Reviews of Modern Physics,
	author = Von Klitzing, Klaus,
	year = 1986,
	pages = 519,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/EW43A3S8/Von Klitzing - 1986 - The quantized Hall effect.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/RJRPJIGH/RevModPhys.58.html:text/html


@articlepaalanen_quantized_1982,
	title = Quantized Hall effect at low temperatures,
	volume = 25,
	number = 8,
	journal = Physical Review B,
	author = Paalanen, M. A. and Tsui, D. C. and Gossard, A. C.,
	year = 1982,
	pages = 5566,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/IL2VY87Z/Paalanen et al. - 1982 - Quantized Hall effect at low temperatures.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/QCHNXDMR/PhysRevB.25.html:text/html


@articleschwarzschild_currents_1986,
	title = Currents in Normal‐Metal Rings Exhibit Aharonov–Bohm Effect,
	volume = 39,
	issn = 0031-9228, 1945-0699,
	url = http://physicstoday.scitation.org/doi/10.1063/1.2814843,
	doi = 10.1063/1.2814843,
	language = en,
	number = 1,
	urldate = 2018-11-01,
	journal = Physics Today,
	author = Schwarzschild, Bertram,
	month = jan,
	year = 1986,
	pages = 17–20


@articlelaughlin_quantized_1981,
	title = Quantized Hall conductivity in two dimensions,
	volume = 23,
	number = 10,
	journal = Physical Review B,
	author = Laughlin, Robert B.,
	year = 1981,
	pages = 5632,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/JZDA48NG/PhysRevB.23.html:text/html


@articleavron_topological_2003,
	title = A topological look at the quantum Hall effect,
	volume = 56,
	number = 8,
	journal = Physics today,
	author = Avron, Joseph E. and Osadchy, Daniel and Seiler, Ruedi,
	year = 2003,
	pages = 38–42


@articleavron_charge_1994,
	title = Charge deficiency, charge transport and comparison of dimensions,
	volume = 159,
	number = 2,
	journal = Communications in mathematical physics,
	author = Avron, Joseph E. and Seiler, Ruedi and Simon, Barry,
	year = 1994,
	pages = 399–422,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/5E33ZCDM/Avron et al. - 1994 - Charge deficiency, charge transport and comparison.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/SMI9X3WL/BF02102644.html:text/html


@articlebellissard_noncommutative_1994,
	title = The noncommutative geometry of the quantum Hall effect,
	volume = 35,
	number = 10,
	journal = Journal of Mathematical Physics,
	author = Bellissard, Jean and van Elst, Andreas and Schulz-Baldes, Hermann,
	year = 1994,
	pages = 5373–5451,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/6RXNEWY4/Bellissard et al. - 1994 - The noncommutative geometry of the quantum Hall ef.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/WKU9DJJT/1.html:text/html


@articlethouless_quantized_1982,
	title = Quantized Hall conductance in a two-dimensional periodic potential,
	volume = 49,
	number = 6,
	journal = Physical Review Letters,
	author = Thouless, David J. and Kohmoto, Mahito and Nightingale, M. Peter and den Nijs, Md,
	year = 1982,
	pages = 405,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/JPABXUX7/Thouless et al. - 1982 - Quantized Hall conductance in a two-dimensional pe.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/74HJ8K8R/PhysRevLett.49.html:text/html


@articleamet_supercurrent_2016,
	title = Supercurrent in the quantum Hall regime,
	volume = 352,
	copyright = Copyright © 2016, American Association for the Advancement of Science,
	issn = 0036-8075, 1095-9203,
	url = http://science.sciencemag.org/content/352/6288/966,
	doi = 10.1126/science.aad6203,
	abstract = Making a graphene super-edge
In superconductors, the electrical current is carried by “Cooper pairs,” formed out of an electron and a hole. This supercurrent will happily cross a thin barrier between two superconductors. But what if a strong magnetic field were applied at the barrier, forcing charge carriers to travel only along the edge of the barrier? Amet et al. explored this regime in a sample consisting of two superconducting electrodes and a graphene barrier under magnetic fields of up to 2 tesla (see the Perspective by Mason). Their transport measurements were consistent with a model in which the supercurrent was carried by the edge states in graphene.
Science, this issue p. 966; see also p. 891
A promising route for creating topological states and excitations is to combine superconductivity and the quantum Hall (QH) effect. Despite this potential, signatures of superconductivity in the QH regime remain scarce, and a superconducting current through a QH weak link has been challenging to observe. We demonstrate the existence of a distinct supercurrent mechanism in encapsulated graphene samples contacted by superconducting electrodes, in magnetic fields as high as 2 tesla. The observation of a supercurrent in the QH regime marks an important step in the quest for exotic topological excitations, such as Majorana fermions and parafermions, which may find applications in fault-tolerant quantum computing.
Transport measurements show that quantum Hall edge states carry the supercurrent in a graphene Josephson junction.
Transport measurements show that quantum Hall edge states carry the supercurrent in a graphene Josephson junction.,
	language = en,
	number = 6288,
	urldate = 2018-10-30,
	journal = Science,
	author = Amet, F. and Ke, C. T. and Borzenets, I. V. and Wang, J. and Watanabe, K. and Taniguchi, T. and Deacon, R. S. and Yamamoto, M. and Bomze, Y. and Tarucha, S. and Finkelstein, G.,
	month = may,
	year = 2016,
	pmid = 27199424,
	pages = 966–969,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/IYZ562T2/966.html:text/html;Submitted Version:/Users/carolinegorham/Zotero/storage/2LDS8GXJ/Amet et al. - 2016 - Supercurrent in the quantum Hall regime.pdf:application/pdf


@articlelord_sphere_2001,
	title = Sphere packing, helices and the polytope {3, 3, 5},
	volume = 15,
	issn = 1434-6079,
	url = https://doi.org/10.1007/s100530170149,
	doi = 10.1007/s100530170149,
	abstract = The packing of tetrahedra in face contact is well-known to be relevant to atomic clustering in many complex alloys. We briefly review some of the structures that can arise in this way, and introduce methods of dealing with the geometry of the polytope {3, 3, 5}, which is highly relevant to an understanding of these structures. Finally, we present a method of projection from S3 to E3 that enables coordinates for the key vertices of the collagen model of Sadoc and Rivier to be calculated.,
	language = en,
	number = 3,
	urldate = 2018-10-22,
	journal = The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics,
	author = Lord, E.A. and Ranganathan, S.,
	month = sep,
	year = 2001,
	keywords = PACS. 36.40.-c Atomic and molecular clusters – 87.15.-v Biomolecules: structure and physical properties,
	pages = 335–343


@booksakurai_modern_2014,
	title = Modern quantum mechanics,
	publisher = Pearson,
	author = Sakurai, Jun John and Napolitano, Jim,
	year = 2014


@articleavron_topological_2007,
	title = A Topological Look at the Quantum Hall Effect,
	volume = 56,
	issn = 0031-9228,
	url = https://physicstoday.scitation.org/doi/10.1063/1.1611351,
	doi = 10.1063/1.1611351,
	abstract = The amazingly precise quantization of Hall conductance in a two-dimensional electron gas can be understood in terms of a topological invariant known as the Chern number.,
	language = en,
	number = 8,
	urldate = 2018-10-22,
	journal = Physics Today,
	author = Avron, Joseph E. and Osadchy, Daniel and Seiler, Ruedi,
	month = jan,
	year = 2007,
	pages = 38,
	file = Full Text PDF:/Users/carolinegorham/Zotero/storage/WQ5LBF8G/Avron et al. - 2007 - A Topological Look at the Quantum Hall Effect.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/HS6QT3QM/1.html:text/html


@bookbernevig_topological_2013,
	title = Topological insulators and topological superconductors,
	publisher = Princeton university press,
	author = Bernevig, B. Andrei and Hughes, Taylor L.,
	year = 2013,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/9HVFIFGU/Bernevig and Hughes - 2013 - Topological insulators and topological superconduc.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/WU989RHF/books.html:text/html


@articlekitaev_periodic_2009,
	title = Periodic table for topological insulators and superconductors,
	volume = 1134,
	issn = 0094-243X,
	url = https://aip.scitation.org/doi/abs/10.1063/1.3149495,
	doi = 10.1063/1.3149495,
	number = 1,
	urldate = 2018-10-22,
	journal = AIP Conference Proceedings,
	author = Kitaev, Alexei,
	month = may,
	year = 2009,
	pages = 22–30,
	file = Full Text PDF:/Users/carolinegorham/Zotero/storage/HRYESB9W/Kitaev - 2009 - Periodic table for topological insulators and supe.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/FBBWGEMF/1.html:text/html


@articlehasan_colloquium:_2010-1,
	title = Colloquium: Topological insulators,
	volume = 82,
	shorttitle = Colloquium,
	url = https://link.aps.org/doi/10.1103/RevModPhys.82.3045,
	doi = 10.1103/RevModPhys.82.3045,
	abstract = Topological insulators are electronic materials that have a bulk band gap like an ordinary insulator but have protected conducting states on their edge or surface. These states are possible due to the combination of spin-orbit interactions and time-reversal symmetry. The two-dimensional (2D) topological insulator is a quantum spin Hall insulator, which is a close cousin of the integer quantum Hall state. A three-dimensional (3D) topological insulator supports novel spin-polarized 2D Dirac fermions on its surface. In this Colloquium the theoretical foundation for topological insulators and superconductors is reviewed and recent experiments are described in which the signatures of topological insulators have been observed. Transport experiments on HgTe∕CdTe quantum wells are described that demonstrate the existence of the edge states predicted for the quantum spin Hall insulator. Experiments on Bi1−xSbx, Bi2Se3, Bi2Te3, and Sb2Te3 are then discussed that establish these materials as 3D topological insulators and directly probe the topology of their surface states. Exotic states are described that can occur at the surface of a 3D topological insulator due to an induced energy gap. A magnetic gap leads to a novel quantum Hall state that gives rise to a topological magnetoelectric effect. A superconducting energy gap leads to a state that supports Majorana fermions and may provide a new venue for realizing proposals for topological quantum computation. Prospects for observing these exotic states are also discussed, as well as other potential device applications of topological insulators.,
	number = 4,
	urldate = 2018-10-22,
	journal = Reviews of Modern Physics,
	author = Hasan, M. Z. and Kane, C. L.,
	month = nov,
	year = 2010,
	pages = 3045–3067,
	file = APS Snapshot:/Users/carolinegorham/Zotero/storage/7QKAMKSA/RevModPhys.82.html:text/html;Full Text:/Users/carolinegorham/Zotero/storage/7Q8DLZS6/Hasan and Kane - 2010 - Colloquium Topological insulators.pdf:application/pdf


@articleqi_topological_2011,
	title = Topological insulators and superconductors,
	volume = 83,
	url = https://link.aps.org/doi/10.1103/RevModPhys.83.1057,
	doi = 10.1103/RevModPhys.83.1057,
	abstract = Topological insulators are new states of quantum matter which cannot be adiabatically connected to conventional insulators and semiconductors. They are characterized by a full insulating gap in the bulk and gapless edge or surface states which are protected by time-reversal symmetry. These topological materials have been theoretically predicted and experimentally observed in a variety of systems, including HgTe quantum wells, BiSb alloys, and Bi2Te3 and Bi2Se3 crystals. Theoretical models, materials properties, and experimental results on two-dimensional and three-dimensional topological insulators are reviewed, and both the topological band theory and the topological field theory are discussed. Topological superconductors have a full pairing gap in the bulk and gapless surface states consisting of Majorana fermions. The theory of topological superconductors is reviewed, in close analogy to the theory of topological insulators.,
	number = 4,
	urldate = 2018-10-22,
	journal = Reviews of Modern Physics,
	author = Qi, Xiao-Liang and Zhang, Shou-Cheng,
	month = oct,
	year = 2011,
	pages = 1057–1110,
	file = APS Snapshot:/Users/carolinegorham/Zotero/storage/UDVQ9UAQ/RevModPhys.83.html:text/html;Submitted Version:/Users/carolinegorham/Zotero/storage/YQ8YENEU/Qi and Zhang - 2011 - Topological insulators and superconductors.pdf:application/pdf


@articlezak_berrys_1989,
	title = Berry’s phase for energy bands in solids,
	volume = 62,
	number = 23,
	journal = Physical review letters,
	author = Zak, J.,
	year = 1989,
	pages = 2747,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/4RX4UVFM/Zak - 1989 - Berry’s phase for energy bands in solids.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/VGEMG7YX/PhysRevLett.62.html:text/html


@miscnoauthor_zak_nodate,
	title = zak berry's phase - Google Scholar,
	url = https://scholar.google.com/scholar?hl=en   as_sdt=0
	urldate = 2018-10-21,
	file = zak berry's phase - Google Scholar:/Users/carolinegorham/Zotero/storage/5K42JNK8/scholar.html:text/html


@articlezak_berrys_1989-1,
	title = Berry’s phase for energy bands in solids,
	volume = 62,
	number = 23,
	journal = Physical review letters,
	author = Zak, J.,
	year = 1989,
	pages = 2747,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/XYIXPP5N/Zak - 1989 - Berry’s phase for energy bands in solids.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/RSW2W8NV/PhysRevLett.62.html:text/html


@articleloerting_multiple_2009,
	title = Multiple amorphous-amorphous transitions,
	volume = 143,
	journal = Adv. Chem. Phys,
	author = Loerting, Thomas and Brazhkin, Vadim V. and Morishita, Tetsuya,
	year = 2009,
	pages = 29–82,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/384SBYAP/Loerting et al. - 2009 - Multiple amorphous-amorphous transitions.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/GZT3BQGI/books.html:text/html


@miscnoauthor_catalog_nodate,
	title = A Catalog of Polytope Images,
	url = http://www.math.cmu.edu/ fho/jenn/polytopes/index.html,
	urldate = 2018-10-21,
	file = A Catalog of Polytope Images:/Users/carolinegorham/Zotero/storage/22PA4N62/index.html:text/html


@articlechern_simple_1944,
	title = A Simple Intrinsic Proof of the Gauss-Bonnet Formula for Closed Riemannian Manifolds,
	volume = 45,
	issn = 0003-486X,
	url = https://www.jstor.org/stable/1969302,
	doi = 10.2307/1969302,
	number = 4,
	urldate = 2018-10-19,
	journal = Annals of Mathematics,
	author = Chern, Shiing-Shen,
	year = 1944,
	pages = 747–752


@articlepage_inhomogeneous_1987,
	title = Inhomogeneous Einstein metrics on complex line bundles,
	volume = 4,
	issn = 0264-9381,
	url = http://stacks.iop.org/0264-9381/4/i=2/a=005,
	doi = 10.1088/0264-9381/4/2/005,
	abstract = Recent developments in higher-dimensional unified field theories have led to a great deal of interest in compact spaces admitting Einstein metrics. Almost all the physics literature on such spaces has been concerned with the very atypical case in which the space is homogeneous. The authors present a very simple construction of a wide class of inhomogeneous compact Einstein spaces with positive Ricci curvature found earlier by Berard-Bergery, (1982) which arise as certain 2-sphere bundles over an arbitrary Einstein-Kahler base space of positive Ricci curvature. Solutions on complete non-compact manifolds also exist, with negative or zero Ricci curvature.,
	language = en,
	number = 2,
	urldate = 2018-10-19,
	journal = Classical and Quantum Gravity,
	author = Page, D. N. and Pope, C. N.,
	year = 1987,
	pages = 213


@articleknill_graph_2011,
	title = A graph theoretical Gauss-Bonnet-Chern theorem,
	journal = arXiv preprint arXiv:1111.5395,
	author = Knill, Oliver,
	year = 2011,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/VB2MPPBF/Knill - 2011 - A graph theoretical Gauss-Bonnet-Chern theorem.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/MJHW9A7I/1111.html:text/html


@articlegabbrielli_dense_2014,
	title = Dense periodic packings of tori,
	volume = 89,
	number = 2,
	journal = Physical Review E,
	author = Gabbrielli, Ruggero and Jiao, Yang and Torquato, Salvatore,
	year = 2014,
	pages = 022133,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/JLWG4NWS/PhysRevE.89.html:text/html


@articleghimire_large_2018,
	title = Large anomalous Hall effect in the chiral-lattice antiferromagnet CoNb 3 S 6,
	volume = 9,
	copyright = 2018 The Author(s),
	issn = 2041-1723,
	url = https://www.nature.com/articles/s41467-018-05756-7,
	doi = 10.1038/s41467-018-05756-7,
	abstract = Anomalous Hall effect (AHE) in antiferromagnets is intriguing and requires further understanding. Here the authors report large AHE in a chiral-lattice antiferromagnet CoNb3S6 of which the origin can be due to complex magnetic texture or broken time-reversal symmetry on the electronic band structure.,
	language = en,
	number = 1,
	urldate = 2018-10-19,
	journal = Nature Communications,
	author = Ghimire, Nirmal J. and Botana, A. S. and Jiang, J. S. and Zhang, Junjie and Chen, Y.-S. and Mitchell, J. F.,
	month = aug,
	year = 2018,
	pages = 3280,
	file = Full Text PDF:/Users/carolinegorham/Zotero/storage/RQUI8HNM/Ghimire et al. - 2018 - Large anomalous Hall effect in the chiral-lattice .pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/P3FCST5X/s41467-018-05756-7.html:text/html


@articleye_transport_2015,
	title = Transport signatures of Fermi surface topology change in BiTeI,
	volume = 91,
	number = 20,
	journal = Physical Review B,
	author = Ye, Linda and Checkelsky, Joseph G. and Kagawa, Fumitaka and Tokura, Yoshinori,
	year = 2015,
	pages = 201104,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/5B2R7KUU/PhysRevB.91.html:text/html


@miscnoauthor_advances_nodate,
	title = Advances in Chemical Physics - Google Books,
	url = https://books.google.com/books?hl=en   lr=   id=v_Z437z5B4oC   oi=fnd   pg=PA29   dq=MULTIPLE+AMORPHOUS
	urldate = 2018-10-18,
	file = Advances in Chemical Physics - Google Books:/Users/carolinegorham/Zotero/storage/EETMJ9UT/books.html:text/html


@articletuegel_hall_2017,
	title = Hall viscosity and the acoustic Faraday effect,
	volume = 96,
	number = 17,
	journal = Physical Review B,
	author = Tuegel, Thomas I. and Hughes, Taylor L.,
	year = 2017,
	pages = 174524,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/XGHZCKHX/Tuegel and Hughes - 2017 - Hall viscosity and the acoustic Faraday effect.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/BVL9MYKM/PhysRevB.96.html:text/html


@articleprice_quantum_2014,
	title = Quantum Mechanics with a Momentum-Space Artificial Magnetic Field,
	volume = 113,
	url = https://link.aps.org/doi/10.1103/PhysRevLett.113.190403,
	doi = 10.1103/PhysRevLett.113.190403,
	abstract = The Berry curvature is a geometrical property of an energy band which acts as a momentum space magnetic field in the effective Hamiltonian describing single-particle quantum dynamics. We show how this perspective may be exploited to study systems directly relevant to ultracold gases and photonics. Given the exchanged roles of momentum and position, we demonstrate that the global topology of momentum space is crucially important. We propose an experiment to study the Harper-Hofstadter Hamiltonian with a harmonic trap that will illustrate the advantages of this approach and that will also constitute the first realization of magnetism on a torus.,
	number = 19,
	urldate = 2018-10-17,
	journal = Physical Review Letters,
	author = Price, Hannah M. and Ozawa, Tomoki and Carusotto, Iacopo,
	month = nov,
	year = 2014,
	pages = 190403,
	file = APS Snapshot:/Users/carolinegorham/Zotero/storage/35HHHD2P/PhysRevLett.113.html:text/html;Submitted Version:/Users/carolinegorham/Zotero/storage/DNEGRCNA/Price et al. - 2014 - Quantum Mechanics with a Momentum-Space Artificial.pdf:application/pdf


@articleeverschor-sitte_real-space_2014,
	title = Real-space Berry phases: Skyrmion soccer,
	volume = 115,
	shorttitle = Real-space Berry phases,
	number = 17,
	journal = Journal of Applied Physics,
	author = Everschor-Sitte, Karin and Sitte, Matthias,
	year = 2014,
	pages = 172602,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/KK5VQ9HZ/Everschor-Sitte and Sitte - 2014 - Real-space Berry phases Skyrmion soccer.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/UMZCI96E/1.html:text/html


@articlesatake_gauss-bonnet_1957,
	title = The Gauss-Bonnet Theorem for V-manifolds,
	volume = 9,
	issn = 0025-5645, 1881-1167,
	url = https://www.jstage.jst.go.jp/article/jmath1948/9/4/9_4_464/_article/-char/ja/,
	doi = 10.2969/jmsj/00940464,
	abstract = 総合学術電子ジャーナルサイト「J-STAGE」－国内で発行された学術論文全文を読むことのできる、日本最大級の総合電子ジャーナルプラットフォームです。,
	language = en,
	number = 4,
	urldate = 2018-10-14,
	journal = Journal of the Mathematical Society of Japan,
	author = Satake, Ichiro,
	year = 1957,
	pages = 464–492,
	file = Full Text PDF:/Users/carolinegorham/Zotero/storage/CJR9I8VB/Satake - 1957 - The Gauss-Bonnet Theorem for V-manifolds.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/8QCKV8RU/ja.html:text/html


@incollectiongoldsmid_thermoelectric_2016,
	address = Berlin, Heidelberg,
	series = Springer Series in Materials Science,
	title = The Thermoelectric and Related Effects,
	isbn = 978-3-662-49256-7,
	url = https://doi.org/10.1007/978-3-662-49256-7_1,
	abstract = This chapter defines the Peltier and Seebeck effects and introduces the concept of the thermocouple. It gives the relationships between the Peltier, Seebeck and Thomson coefficients. It also describes the related effects that appear in a magnetic field and defines the Hall, Nernst, Ettingshausen and Righi–Leduc coefficients.,
	language = en,
	urldate = 2018-10-13,
	booktitle = Introduction to Thermoelectricity,
	publisher = Springer Berlin Heidelberg,
	author = Goldsmid, H. Julian,
	editor = Goldsmid, H. Julian,
	year = 2016,
	doi = 10.1007/978-3-662-49256-7_1,
	keywords = Peltier Effect, Seebeck Coefficient, Thermoelectric Effect, Thermoelectric Material, Transverse Magnetic Field,
	pages = 1–7


@articlelin_superconductivity_2015,
	series = Superconducting Materials: Conventional, Unconventional and Undetermined,
	title = Superconductivity of very thin films: The superconductor–insulator transition,
	volume = 514,
	issn = 0921-4534,
	shorttitle = Superconductivity of very thin films,
	url = http://www.sciencedirect.com/science/article/pii/S0921453415000143,
	doi = 10.1016/j.physc.2015.01.005,
	abstract = The study of thin superconducting films has been an important component of the science of superconductivity for more than six decades. It played a major role in the development of currently accepted views of the macroscopic and microscopic nature of the superconducting state. In recent years the focus of research in the field has shifted to the study of ultrathin films and surface and interface layers. This has permitted the exploration of one of the important topics of condensed matter physics, the superconductor–insulator transition. This review will discuss this phenomenon as realized in the study of metallic films, cuprates, and metallic interfaces. These are in effect model systems for behaviors that may be found in more complex systems of contemporary interest.,
	urldate = 2018-10-13,
	journal = Physica C: Superconductivity and its Applications,
	author = Lin, Yen-Hsiang and Nelson, J. and Goldman, A. M.,
	month = jul,
	year = 2015,
	keywords = Quantum phase transition, SIT, Superconductor–insulator,
	pages = 130–141,
	file = ScienceDirect Snapshot:/Users/carolinegorham/Zotero/storage/ZF7SKQGZ/S0921453415000143.html:text/html


@articlehou_ettingshausen_2012,
	title = Ettingshausen effect due to Majorana modes,
	volume = 14,
	issn = 1367-2630,
	url = http://stacks.iop.org/1367-2630/14/i=10/a=105005,
	doi = 10.1088/1367-2630/14/10/105005,
	abstract = The presence of Majorana zero-energy modes at vortex cores in a topological superconductor implies that each vortex carries an extra entropy s 0 , given by ( k B /2)ln 2, that is independent of temperature. By utilizing this special property of Majorana modes, the edges of a topological superconductor can be cooled (or heated) by the motion of the vortices across the edges. As vortices flow in the transverse direction with respect to an external imposed supercurrent, due to the Lorentz force, a thermoelectric effect analogous to the Ettingshausen effect is expected to occur between opposing edges. We propose an experiment to observe this thermoelectric effect, which could directly probe the intrinsic entropy of Majorana zero-energy modes.,
	language = en,
	number = 10,
	urldate = 2018-10-13,
	journal = New Journal of Physics,
	author = Hou, C.-Y. and Shtengel, K. and Refael, G. and Goldbart, P. M.,
	year = 2012,
	pages = 105005,
	file = IOP Full Text PDF:/Users/carolinegorham/Zotero/storage/JKXJUAR2/Hou et al. - 2012 - Ettingshausen effect due to Majorana modes.pdf:application/pdf


@articlesacepe_pseudogap_2010,
	title = Pseudogap in a thin film of a conventional superconductor,
	volume = 1,
	copyright = 2010 Nature Publishing Group,
	issn = 2041-1723,
	url = https://www.nature.com/articles/ncomms1140,
	doi = 10.1038/ncomms1140,
	abstract = A superconducting state is characterized by the gap in the electronic density of states, which vanishes at the superconducting transition temperature Tc. It was discovered that in high-temperature superconductors, a noticeable depression in the density of states, the pseudogap, still remains even at temperatures above Tc. Here, we show that a pseudogap exists in a conventional superconductor, ultrathin titanium nitride films, over a wide range of temperatures above Tc. Our study reveals that this pseudogap state is induced by superconducting fluctuations and favoured by two-dimensionality and by the proximity to the transition to the insulating state. A general character of the observed phenomenon provides a powerful tool to discriminate between fluctuations as the origin of the pseudogap state and other contributions in the layered high-temperature superconductor compounds.,
	language = en,
	urldate = 2018-10-10,
	journal = Nature Communications,
	author = Sacépé, Benjamin and Chapelier, Claude and Baturina, Tatyana I. and Vinokur, Valerii M. and Baklanov, Mikhail R. and Sanquer, Marc,
	month = dec,
	year = 2010,
	pages = 140,
	file = Full Text PDF:/Users/carolinegorham/Zotero/storage/IHT48K89/Sacépé et al. - 2010 - Pseudogap in a thin film of a conventional superco.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/NTG3LL6B/ncomms1140.html:text/html


@articlemartinis_superconducting_2009,
	title = Superconducting phase qubits,
	volume = 8,
	number = 2-3,
	journal = Quantum Information Processing,
	author = Martinis, John M.,
	year = 2009,
	pages = 81–103,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/LIBNWJDQ/Martinis - 2009 - Superconducting phase qubits.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/D6WM62JR/s11128-009-0105-1.html:text/html


@articlenakamura_coherent_1999,
	title = Coherent control of macroscopic quantum states in a single-Cooper-pair box,
	volume = 398,
	number = 6730,
	journal = nature,
	author = Nakamura, Yasunobu and Pashkin, Yu A. and Tsai, J. S.,
	year = 1999,
	pages = 786,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/RY2LJ6MP/Nakamura et al. - 1999 - Coherent control of macroscopic quantum states in .pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/XP3SGK8K/19718.html:text/html


@articlecooper_observation_2004,
	title = Observation of quantum oscillations between a Josephson phase qubit and a microscopic resonator using fast readout,
	volume = 93,
	number = 18,
	journal = Physical Review Letters,
	author = Cooper, K. B. and Steffen, Matthias and McDermott, Robert and Simmonds, Raymond W. and Oh, Seongshik and Hite, Dustin A. and Pappas, David P. and Martinis, John M.,
	year = 2004,
	pages = 180401,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/DLGGCV37/PhysRevLett.93.html:text/html


@articleguichard_phase-charge_2010,
	title = Phase-charge duality in Josephson junction circuits: Role of inertia and effect of microwave irradiation,
	volume = 81,
	issn = 1098-0121, 1550-235X,
	shorttitle = Phase-charge duality in Josephson junction circuits,
	url = http://arxiv.org/abs/0909.3749,
	doi = 10.1103/PhysRevB.81.064508,
	abstract = We investigate the physics of coherent quantum phase slips in two distinct circuits containing small Josephson junctions: (i) a single junction embedded in an inductive environment and (ii) a long chain of junctions. Starting from the standard Josephson Hamiltonian, the single junction circuit can be analyzed using quasi-classical methods; we formulate the conditions under which the resulting quasi-charge dynamics is exactly dual to the usual phase dynamics associated with Josephson tunneling. For the chain we use the fact that its collective behavior can be characterized by one variable: the number $m$ of quantum phase slips present on it. We conclude that the dynamics of the conjugate quasi-charge is again exactly dual to the standard phase dynamics of a single Josephson junction. In both cases we elucidate the role of the inductance, essential to obtain exact duality. These conclusions have profound consequences for the behavior of single junctions and chains under microwave irradiation. Since both systems are governed by a model exactly dual to the standard resistively and capacitively shunted junction model, we expect the appearance of current-Shapiro steps. We numerically calculate the corresponding current-voltage characteristics in a wide range of parameters. Our results are of interest in view of a metrological current standard.,
	number = 6,
	urldate = 2018-10-10,
	journal = Physical Review B,
	author = Guichard, W. and Hekking, F. W. J.,
	month = feb,
	year = 2010,
	note = arXiv: 0909.3749,
	keywords = Condensed Matter - Mesoscale and Nanoscale Physics, Condensed Matter - Superconductivity,
	file = arXiv 0909.3749 PDF:/Users/carolinegorham/Zotero/storage/EL3PR52T/Guichard and Hekking - 2010 - Phase-charge duality in Josephson junction circuit.pdf:application/pdf;arXiv.org Snapshot:/Users/carolinegorham/Zotero/storage/NLFNEHGH/0909.html:text/html


@articleergul_localizing_2013,
	title = Localizing quantum phase slips in one-dimensional Josephson junction chains,
	volume = 15,
	issn = 1367-2630,
	url = http://stacks.iop.org/1367-2630/15/i=9/a=095014,
	doi = 10.1088/1367-2630/15/9/095014,
	abstract = We studied quantum phase-slip (QPS) phenomena in long one-dimensional Josephson junction series arrays with tunable Josephson coupling. These chains were fabricated with as many as 2888 junctions, where one sample had a separately tunable link in the middle of the chain. Measurements were made of the zero-bias resistance, R 0 , as well as current–voltage characteristics (IVC). The finite R 0 is explained by QPS and shows an exponential dependence on ##IMG## [http://ej.iop.org/images/1367-2630/15/9/095014/nj476272ieqn1.gif] $\sqrt E_\mathrm J/E_\mathrm C$ with a distinct change in the exponent at R 0 = R Q = h /4 e 2 . When R 0  R Q , the IVC clearly shows a remnant of the Coulomb blockade, which evolves to a zero-current state with a sharp critical voltage as E J is tuned to a smaller value. The zero-current state below the critical voltage is due to coherent QPSs and we show that these are enhanced when the central link is weaker than all other links. Above the critical voltage, a negative, differential resistance is observed, which nearly restores the zero-current state.,
	language = en,
	number = 9,
	urldate = 2018-10-10,
	journal = New Journal of Physics,
	author = Ergül, Adem and Lidmar, Jack and Johansson, Jan and Azizoğlu, Yağız and Schaeffer, David and Haviland, David B.,
	year = 2013,
	pages = 095014,
	file = IOP Full Text PDF:/Users/carolinegorham/Zotero/storage/Z2DBCG7N/Ergül et al. - 2013 - Localizing quantum phase slips in one-dimensional .pdf:application/pdf


@articlemartinis_rabi_2002,
	title = Rabi Oscillations in a Large Josephson-Junction Qubit,
	volume = 89,
	url = https://link.aps.org/doi/10.1103/PhysRevLett.89.117901,
	doi = 10.1103/PhysRevLett.89.117901,
	abstract = We have designed and operated a circuit based on a large-area current-biased Josephson junction whose two lowest energy quantum levels are used to implement a solid-state qubit. The circuit allows measurement of the qubit states with a fidelity of 85% while providing sufficient decoupling from external sources of relaxation and decoherence to allow coherent manipulation of the qubit state, as demonstrated by the observation of Rabi oscillations. This qubit circuit is the basis of a scalable quantum computer.,
	number = 11,
	urldate = 2018-10-09,
	journal = Physical Review Letters,
	author = Martinis, John M. and Nam, S. and Aumentado, J. and Urbina, C.,
	month = aug,
	year = 2002,
	pages = 117901,
	file = APS Snapshot:/Users/carolinegorham/Zotero/storage/TFM7S5VZ/PhysRevLett.89.html:text/html


@articlemakhlin_quantum-state_2001,
	title = Quantum-state engineering with Josephson-junction devices,
	volume = 73,
	url = https://link.aps.org/doi/10.1103/RevModPhys.73.357,
	doi = 10.1103/RevModPhys.73.357,
	abstract = Quantum-state engineering, i.e., active control over the coherent dynamics of suitable quantum-mechanical systems, has become a fascinating prospect of modern physics. With concepts developed in atomic and molecular physics and in the context of NMR, the field has been stimulated further by the perspectives of quantum computation and communication. Low-capacitance Josephson tunneling junctions offer a promising way to realize quantum bits (qubits) for quantum information processing. The article reviews the properties of these devices and the practical and fundamental obstacles to their use. Two kinds of device have been proposed, based on either charge or phase (flux) degrees of freedom. Single- and two-qubit quantum manipulations can be controlled by gate voltages in one case and by magnetic fields in the other case. Both kinds of device can be fabricated with present technology. In flux qubit devices, an important milestone, the observation of superpositions of different flux states in the system eigenstates, has been achieved. The Josephson charge qubit has even demonstrated coherent superpositions of states readable in the time domain. There are two major problems that must be solved before these devices can be used for quantum information processing. One must have a long phase coherence time, which requires that external sources of dephasing be minimized. The review discusses relevant parameters and provides estimates of the decoherence time. Another problem is in the readout of the final state of the system. This issue is illustrated with a possible realization by a single-electron transistor capacitively coupled to the Josephson device, but general properties of measuring devices are also discussed. Finally, the review describes how the basic physical manipulations on an ideal device can be combined to perform useful operations.,
	number = 2,
	urldate = 2018-10-09,
	journal = Reviews of Modern Physics,
	author = Makhlin, Yuriy and Schön, Gerd and Shnirman, Alexander,
	month = may,
	year = 2001,
	pages = 357–400,
	file = APS Snapshot:/Users/carolinegorham/Zotero/storage/LZSMC2AC/RevModPhys.73.html:text/html


@articlefreeman_thermal_1986,
	title = Thermal conductivity of amorphous solids,
	volume = 34,
	doi = 10.1103/PhysRevB.34.5684,
	journal = Physical Review B,
	author = Freeman, J. J. and Anderson, A. C.,
	year = 1986,
	keywords = polycrystalline, need paper,
	pages = 5684–5690


@bookblundell_superconductivity:_2009,
	title = Superconductivity: a very short introduction,
	shorttitle = Superconductivity,
	publisher = OUP Oxford,
	author = Blundell, Stephen J.,
	year = 2009


@booklondon_superfluids_1961,
	title = Superfluids (Vol. II): Macroscopic Theory of Superfluid Helium,
	shorttitle = Superfluids,
	publisher = Dover Publications,
	author = London, Fritz,
	year = 1961


@bookbinder_monte_1988,
	title = Monte Carlo Simulations in statistical mechanics,
	publisher = Springer, Berlin,
	author = Binder, K. and Heerman, D. W.,
	year = 1988


@bookfrenkel_understanding_2001,
	title = Understanding molecular simulation: from algorithms to applications,
	volume = 1,
	shorttitle = Understanding molecular simulation,
	publisher = Academic press,
	author = Frenkel, Daan and Smit, Berend,
	year = 2001


@articlekhonik_amorphous_2017,
	title = Amorphous physics and materials: Interstitialcy theory of condensed matter states and its application to non-crystalline metallic materials,
	volume = 26,
	issn = 1674-1056,
	shorttitle = Amorphous physics and materials,
	url = http://stacks.iop.org/1674-1056/26/i=1/a=016401,
	doi = 10.1088/1674-1056/26/1/016401,
	abstract = A comprehensive review of a novel promising framework for the understanding of non-crystalline metallic materials, i.e., interstitialcy theory of condensed matter states (ITCM), is presented. The background of the ITCM and its basic results for equilibrium/supercooled liquids and glasses are given. It is emphasized that the ITCM provides a new consistent, clear, and testable approach, which uncovers the generic relationship between the properties of the maternal crystal, equilibrium/supercooled liquid and glass obtained by melt quenching.,
	language = en,
	number = 1,
	urldate = 2018-02-25,
	journal = Chinese Physics B,
	author = Khonik, V. A.,
	year = 2017,
	pages = 016401


@booklondon_superfluids_1950,
	title = Superfluids (Vol. I): Macroscopic Theory of Superconductivity,
	shorttitle = Superfluids,
	publisher = Wiley,
	author = London, Fritz,
	year = 1950


@articlelyons_elementary_2003,
	title = An elementary introduction to the Hopf fibration,
	volume = 76,
	number = 2,
	journal = Mathematics magazine,
	author = Lyons, David W.,
	year = 2003,
	pages = 87–98


@articlemosseri_geometry_2001,
	title = Geometry of entangled states, Bloch spheres and Hopf fibrations,
	volume = 34,
	number = 47,
	journal = Journal of Physics A: Mathematical and General,
	author = Mosseri, Rémy and Dandoloff, Rossen,
	year = 2001,
	pages = 10243


@articlewatanabe_redundancies_2013,
	title = Redundancies in Nambu-Goldstone Bosons,
	volume = 110,
	url = https://link.aps.org/doi/10.1103/PhysRevLett.110.181601,
	doi = 10.1103/PhysRevLett.110.181601,
	abstract = We propose a simple criterion to identify when Nambu-Goldstone bosons for different symmetries are redundant. It solves an old mystery why crystals have phonons for spontaneously broken translations but no gapless excitations for equally spontaneously broken rotations. Similarly for a superfluid, the Nambu-Goldstone boson for spontaneously broken Galilean symmetry is redundant with phonons. The most nontrivial example is Tkachenko mode for a vortex lattice in a superfluid, where phonons are redundant to the Tkachenko mode which is identified as the Boboliubov mode.,
	number = 18,
	urldate = 2018-03-04,
	journal = Physical Review Letters,
	author = Watanabe, Haruki and Murayama, Hitoshi,
	month = may,
	year = 2013,
	pages = 181601


@articlenelson_dislocation-mediated_1979,
	title = Dislocation-mediated melting in two dimensions,
	volume = 19,
	url = https://link.aps.org/doi/10.1103/PhysRevB.19.2457,
	doi = 10.1103/PhysRevB.19.2457,
	abstract = A theory of dislocation-mediated melting in two dimensions is described in detail, with an emphasis on results for triangular lattices on both smooth and periodic substrates. The transition from solid to liquid on a smooth substrate takes place in two steps with increasing temperatures. Dissociation of dislocation pairs first drives a transition out of a low-temperature solid phase, with algebraic decay of translational order and long-range orientational order. This transition is into a "liquid-crystal" phase characterized by exponential decay of translational order, but power-law decay of sixfold orientational order. Dissociation of disclination pairs at a higher temperature then produces an isotropic fluid. The behavior of the specific heat, structure factor, and various elastic constants near these transitions is worked out. We also discuss the applicability of our results to melting on a periodic substrate. Dislocation unbinding should describe melting of a "floating" (and, in general, incommensurate) adsorbate solid into a high-temperature fluid phase. The orientation bias imposed by the substrate can alter or eliminate the disclination-unbinding transition, however. Transitions from a floating solid into a low-temperature registered or partially registered phase can also be mapped onto the dislocation-unbinding transition, but only at certain special values of the coverage. Substrate reciprocallattice vectors play the role of Burger's vectors in this case.,
	number = 5,
	urldate = 2018-03-09,
	journal = Physical Review B,
	author = Nelson, David R. and Halperin, B. I.,
	month = mar,
	year = 1979,
	pages = 2457–2484


@bookbrink_nuclear_2005,
	title = Nuclear Superfluidity: pairing in finite systems,
	volume = 24,
	shorttitle = Nuclear Superfluidity,
	publisher = Cambridge University Press,
	author = Brink, David M. and Broglia, Ricardo A.,
	year = 2005


@articlewatanabe_redundancies_2013-1,
	title = Redundancies in Nambu-Goldstone Bosons,
	volume = 110,
	url = https://link.aps.org/doi/10.1103/PhysRevLett.110.181601,
	doi = 10.1103/PhysRevLett.110.181601,
	abstract = We propose a simple criterion to identify when Nambu-Goldstone bosons for different symmetries are redundant. It solves an old mystery why crystals have phonons for spontaneously broken translations but no gapless excitations for equally spontaneously broken rotations. Similarly for a superfluid, the Nambu-Goldstone boson for spontaneously broken Galilean symmetry is redundant with phonons. The most nontrivial example is Tkachenko mode for a vortex lattice in a superfluid, where phonons are redundant to the Tkachenko mode which is identified as the Boboliubov mode.,
	number = 18,
	urldate = 2018-03-04,
	journal = Physical Review Letters,
	author = Watanabe, Haruki and Murayama, Hitoshi,
	month = may,
	year = 2013,
	pages = 181601


@articlekikoin_dynamical_2004,
	title = Dynamical symmetries in nanophysics,
	journal = arXiv preprint cond-mat/0407063,
	author = Kikoin, K. and Avishai, Y. and Kiselev, M. N.,
	year = 2004


@articlewilliams_helical_1975,
	title = Helical disclination lines in smectics a,
	volume = 32,
	issn = 0031-8086,
	url = https://doi.org/10.1080/14786437508219956,
	doi = 10.1080/14786437508219956,
	abstract = It is shown that helical disclination lines exist in smectics A; they can play the role of focal conics for the smectic planes or be true disclination lines. In the latter case, they are a source of screw dislocation lines. Single helices are terminations of twist walls made up of screw dislocation lines. Double helices are equivalent to large screw dislocation lines.,
	number = 2,
	urldate = 2018-03-09,
	journal = The Philosophical Magazine: A Journal of Theoretical Experimental and Applied Physics,
	author = Williams, C. E.,
	month = aug,
	year = 1975,
	pages = 313–321


@articlenabarro_theory_1967,
	title = Theory of crystal dislocations,
	author = Nabarro, Frank RN,
	year = 1967


@articleangell_configurational_1972,
	title = Configurational Excitations in Condensed Matter, and the“Bond Lattice”Model for the Liquid-Glass Transition,
	volume = 57,
	number = 1,
	journal = The Journal of chemical physics,
	author = Angell, C. A. and Rao, K. J.,
	year = 1972,
	pages = 470–481


@articletian_coupling_2016,
	title = Coupling effect on the Berry phase,
	volume = 6,
	url = https://aip.scitation.org/doi/full/10.1063/1.4967215,
	doi = 10.1063/1.4967215,
	abstract = The Berry phase has universal applications in various fields. Here, we explore the coupling effect on the Berry phase of a two-level system adiabatically driven by a rotating classical field and interacting with a single quantized mode. Our simulations clearly reveal that the Berry phase change is quadratic proportional to the coupling constant if it is less than the level spacing between neighboring instantaneous eigenstates. Remarkably, if the nearest neighbouring level spacing is comparable with the coupling constant, this simple quadratic dependence is lost. Around this resonance, the Berry phase can be significantly tuned by slightly adjusting the parameters, such as the coupling constant, the frequency of the quantized mode, and the transition frequency. These numerical results, agreeing well with the perturbation theory calculations, provide an alternative approach to tune the Berry phase near the resonance, which is useful in quantum information science, i.e. designing quantum logic gates.,
	number = 11,
	urldate = 2018-03-22,
	journal = AIP Advances,
	author = Tian, Lijing and Yang, Zhi and Shi, Q. W. and Li, Qunxiang and Wang, X. P.,
	month = nov,
	year = 2016,
	pages = 115103


@articleturnbull_under_1969,
	title = Under what conditions can a glass be formed?,
	volume = 10,
	number = 5,
	journal = Contemporary physics,
	author = Turnbull, David,
	year = 1969,
	pages = 473–488


@articleserfaty_microscopic_2017,
	title = Microscopic description of Log and Coulomb gases,
	journal = arXiv preprint arXiv:1709.04089,
	author = Serfaty, Sylvia,
	year = 2017


@articlegirvin_circuit_2009,
	title = Circuit QED and engineering charge-based superconducting qubits,
	volume = 2009,
	number = T137,
	journal = Physica Scripta,
	author = Girvin, S. M. and Devoret, M. H. and Schoelkopf, R. J.,
	year = 2009,
	pages = 014012


@articlebruder_superconductormott-insulator_1993,
	title = Superconductor–Mott-insulator transition in Bose systems with finite-range interactions,
	volume = 47,
	number = 1,
	journal = Physical Review B,
	author = Bruder, C. and Fazio, Rosario and Schön, Gerd,
	year = 1993,
	pages = 342


@articlemooij_superconductorinsulator_2015,
	title = Superconductor–insulator transition in nanowires and nanowire arrays,
	volume = 17,
	issn = 1367-2630,
	url = http://stacks.iop.org/1367-2630/17/i=3/a=033006,
	doi = 10.1088/1367-2630/17/3/033006,
	abstract = Superconducting nanowires are the dual elements to Josephson junctions, with quantum phase-slip (QPS) processes replacing the tunneling of Cooper pairs. When the QPS amplitude E S is much smaller than the inductive energy E L , the nanowire responds as a superconducting inductor. When the inductive energy is small, the response is capacitive. The crossover at low temperatures as a function of E S / E L is discussed and compared with earlier experimental results. For one-dimensional and two-dimensional arrays of nanowires quantum phase transitions are expected as a function of E S / E L . They can be tuned by a homogeneous magnetic frustration.,
	language = en,
	number = 3,
	urldate = 2018-03-25,
	journal = New Journal of Physics,
	author = Mooij, J. E. and Schön, G. and Shnirman, A. and Fuse, T. and Harmans, C. J. P. M. and Rotzinger, H. and Verbruggen, A. H.,
	year = 2015,
	pages = 033006


@articleergul_localizing_2013-1,
	title = Localizing quantum phase slips in one-dimensional Josephson junction chains,
	volume = 15,
	number = 9,
	journal = New Journal of Physics,
	author = Ergül, Adem and Lidmar, Jack and Johansson, Jan and Azizoğlu, Yağız and Schaeffer, David and Haviland, David B.,
	year = 2013,
	pages = 095014


@articlechung_superconductor_1997,
	title = The superconductor - insulator transition in a Josephson junction chain with quantum fluctuation,
	volume = 9,
	issn = 0953-8984,
	url = http://stacks.iop.org/0953-8984/9/i=46/a=002,
	doi = 10.1088/0953-8984/9/46/002,
	abstract = The superconductor - insulator transition in a Josephson junction chain with quantum fluctuation is studied by a density matrix renormalization group. The critical Josephson coupling is found to be ##IMG## [http://ej.iop.org/images/0953-8984/9/46/002/img1.gif] , while the Villain approximation gives ##IMG## [http://ej.iop.org/images/0953-8984/9/46/002/img2.gif] . When extending the phase space from ##IMG## [http://ej.iop.org/images/0953-8984/9/46/002/img3.gif] to ##IMG## [http://ej.iop.org/images/0953-8984/9/46/002/img4.gif] , corresponding to a very small quasi-particle tunnelling effect, the superconductor - insulator transition still exists but at a larger critical coupling ##IMG## [http://ej.iop.org/images/0953-8984/9/46/002/img5.gif] .,
	language = en,
	number = 46,
	urldate = 2018-03-25,
	journal = Journal of Physics: Condensed Matter,
	author = Chung, S. G.,
	year = 1997,
	pages = L619


@articleandersson_modeling_2015,
	title = Modeling and simulations of quantum phase slips in ultrathin superconducting wires,
	volume = 91,
	url = https://link.aps.org/doi/10.1103/PhysRevB.91.134504,
	doi = 10.1103/PhysRevB.91.134504,
	abstract = We study quantum phase slips (QPS) in ultrathin superconducting wires. Starting from an effective one-dimensional microscopic model, which includes electromagnetic fluctuations, we map the problem to a (1+1)-dimensional gas of interacting instantons. We introduce a method to calculate the tunneling amplitude of quantum phase slips directly from Monte Carlo simulations. This allows us to go beyond the dilute instanton gas approximation and study the problem without any limitations of the density of QPS. We find that the tunneling amplitude shows a characteristic scaling behavior near the superconductor-insulator transition. We also calculate the voltage-charge relation of the insulating state, which is the dual of the Josephson current-phase relation in ordinary superconducting weak links. This evolves from a sinusoidal form in the regime of dilute QPS to more exotic shapes for higher QPS densities, where interactions are important.,
	number = 13,
	urldate = 2018-03-26,
	journal = Physical Review B,
	author = Andersson, Andreas and Lidmar, Jack,
	month = apr,
	year = 2015,
	pages = 134504


@articlepop_measurement_2010,
	title = Measurement of the effect of quantum phase slips in a Josephson junction chain,
	volume = 6,
	number = 8,
	journal = Nature Physics,
	author = Pop, Ioan-Mihai and Protopopov, I. and Lecocq, Florent and Peng, Zhihui and Pannetier, Bernard and Buisson, Olivier and Guichard, Wiebke,
	year = 2010,
	pages = 589


@articlefeng_curvature_2012,
	title = Curvature effect on the capacitance of electric double layers at ionic liquid/onion-like carbon interfaces,
	volume = 8,
	number = 3,
	journal = Journal of chemical theory and computation,
	author = Feng, Guang and Jiang, De-en and Cummings, Peter T.,
	year = 2012,
	pages = 1058–1063


@articleastafiev_coherent_2012,
	title = Coherent quantum phase slip,
	volume = 484,
	copyright = 2012 Nature Publishing Group,
	issn = 1476-4687,
	url = https://www.nature.com/articles/nature10930,
	doi = 10.1038/nature10930,
	abstract = A hundred years after the discovery of superconductivity, one fundamental prediction of the theory, coherent quantum phase slip (CQPS), has not been observed. CQPS is a phenomenon exactly dual1 to the Josephson effect; whereas the latter is a coherent transfer of charges between superconducting leads2,3, the former is a coherent transfer of vortices or fluxes across a superconducting wire. In contrast to previously reported observations4,5,6,7,8 of incoherent phase slip, CQPS has been only a subject of theoretical study9,10,11,12. Its experimental demonstration is made difficult by quasiparticle dissipation due to gapless excitations in nanowires or in vortex cores. This difficulty might be overcome by using certain strongly disordered superconductors near the superconductor–insulator transition. Here we report direct observation of CQPS in a narrow segment of a superconducting loop made of strongly disordered indium oxide; the effect is made manifest through the superposition of quantum states with different numbers of flux quanta13. As with the Josephson effect, our observation should lead to new applications in superconducting electronics and quantum metrology1,10,11.,
	language = en,
	number = 7394,
	urldate = 2018-03-27,
	journal = Nature,
	author = Astafiev, O. V. and Ioffe, L. B. and Kafanov, S. and Pashkin, Yu A. and Arutyunov, K. Yu and Shahar, D. and Cohen, O. and Tsai, J. S.,
	month = apr,
	year = 2012,
	pages = 355–358


@articlematveev_persistent_2002,
	title = Persistent current in superconducting nanorings,
	volume = 89,
	number = 9,
	journal = Physical review letters,
	author = Matveev, K. A. and Larkin, A. I. and Glazman, L. I.,
	year = 2002,
	pages = 096802


@articlemccumber_time_1970,
	title = Time scale of intrinsic resistive fluctuations in thin superconducting wires,
	volume = 1,
	number = 3,
	journal = Physical Review B,
	author = McCumber, D. E. and Halperin, B. I.,
	year = 1970,
	pages = 1054


@articlehriscu_coulomb_2011,
	title = Coulomb blockade due to quantum phase slips illustrated with devices,
	volume = 83,
	url = https://link.aps.org/doi/10.1103/PhysRevB.83.174511,
	doi = 10.1103/PhysRevB.83.174511,
	abstract = To illustrate the emergence of Coulomb blockade from coherent quantum phase-slip processes in thin superconducting wires, we propose and theoretically investigate two elementary setups, or devices. The setups are derived from the Cooper-pair box and Cooper-pair transistor, so we refer to them as the QPS box and QPS transistor, respectively. We demonstrate that the devices exhibit sensitivity to a charge induced by a gate electrode, this being the main signature of Coulomb blockade. Experimental realization of these devices will unambiguously prove the Coulomb blockade as an effect of coherence of phase-slip processes. We analyze the emergence of discrete charging in the limit of strong phase slips. We have found and investigated six distinct regimes that are realized depending on the relation between three characteristic energy scales: inductive energy, charging energy, and phase-slip amplitude. For completeness, we include a brief discussion of dual Josephson-junction devices.,
	number = 17,
	urldate = 2018-03-29,
	journal = Physical Review B,
	author = Hriscu, A. M. and Nazarov, Yu. V.,
	month = may,
	year = 2011,
	pages = 174511


@articleioffe_possible_2002,
	title = Possible realization of an ideal quantum computer in Josephson junction array,
	volume = 66,
	url = https://link.aps.org/doi/10.1103/PhysRevB.66.224503,
	doi = 10.1103/PhysRevB.66.224503,
	abstract = We introduce a class of Josephson arrays which have nontrivial topology and exhibit a novel state at low temperatures. This state is characterized by long-range order in a two Cooper pair condensate and by a discrete topological order parameter. These arrays have degenerate ground states with this degeneracy “protected” from the external perturbations (and noise) by the topological order parameter. We show that in ideal conditions the low order effect of the external perturbations on this degeneracy is exactly zero and that deviations from ideality lead to only exponentially small effects of perturbations. We argue that this system provides a physical implementation of an ideal quantum computer with a built-in error correction and show that even a small array exhibits interesting physical properties such as superconductivity with double charge, 4e, and extremely long decoherence times.,
	number = 22,
	urldate = 2018-03-30,
	journal = Physical Review B,
	author = Ioffe, L. B. and Feigel’man, M. V.,
	month = dec,
	year = 2002,
	pages = 224503


@inproceedingshamilton_new_1844,
	title = On a new species of imaginary quantities connected with a theory of quaternions,
	volume = 2,
	booktitle = Proceedings of the Royal Irish Academy,
	author = Hamilton, William Rowan,
	year = 1844,
	pages = 4–1


@articlehamilton_quaternions;_1844,
	title = On quaternions; or on a new system of imaginaries in algebra,
	volume = 25,
	number = 163,
	journal = Philosophical Magazine Series 3,
	author = Hamilton, William Rowan,
	year = 1844,
	pages = 10–13


@articlevyas_results_2014,
	title = Some results on topological currents in field theory,
	journal = arXiv preprint arXiv:1411.3099,
	author = Vyas, Vivek M. and Panigrahi, Prasanta K.,
	year = 2014


@articlecataliotti_josephson_2001,
	title = Josephson Junction Arrays with Bose-Einstein Condensates,
	volume = 293,
	issn = 0036-8075, 1095-9203,
	url = http://science.sciencemag.org/content/293/5531/843,
	doi = 10.1126/science.1062612,
	abstract = We report on the direct observation of an oscillating atomic current in a one-dimensional array of Josephson junctions realized with an atomic Bose-Einstein condensate. The array is created by a laser standing wave, with the condensates trapped in the valleys of the periodic potential and weakly coupled by the interwell barriers. The coherence of multiple tunneling between adjacent wells is continuously probed by atomic interference. The square of the small-amplitude oscillation frequency is proportional to the microscopic tunneling rate of each condensate through the barriers and provides a direct measurement of the Josephson critical current as a function of the intermediate barrier heights. Our superfluid array may allow investigation of phenomena so far inaccessible to superconducting Josephson junctions and lays a bridge between the condensate dynamics and the physics of discrete nonlinear media.,
	language = en,
	number = 5531,
	urldate = 2018-04-04,
	journal = Science,
	author = Cataliotti, F. S. and Burger, S. and Fort, C. and Maddaloni, P. and Minardi, F. and Trombettoni, A. and Smerzi, A. and Inguscio, M.,
	month = aug,
	year = 2001,
	pmid = 11486083,
	pages = 843–846


@articlegorter_two_1949,
	title = The two fluid model for Helium II,
	volume = 6,
	number = 2,
	journal = Il Nuovo Cimento (1943-1954),
	author = Gorter, C. J.,
	year = 1949,
	pages = 245–250


@articlestrominger_massless_1995,
	title = Massless black holes and conifolds in string theory,
	volume = 451,
	number = 1-2,
	journal = Nuclear Physics B,
	author = Strominger, Andrew,
	year = 1995,
	pages = 96–108


@articleharvey_five-brane_1998,
	title = Five-brane instantons and R 2 couplings in N= 4 string theory,
	volume = 57,
	number = 4,
	journal = Physical Review D,
	author = Harvey, Jeffrey A. and Moore, Gregory,
	year = 1998,
	pages = 2323


@phdthesishoffmann_superfluid_2001,
	type = PhD Thesis,
	title = Superfluid 4He: On sin φ Josephson Weak Links and Dissipation of Third Sound,
	shorttitle = Superfluid 4He,
	school = Ph. D. thesis, University of California at Berkeley,
	author = Hoffmann, Joan A.,
	year = 2001


@articleanderson_radio-frequency_1964,
	title = Radio-frequency effects in superconducting thin film bridges,
	volume = 13,
	number = 6,
	journal = Physical Review Letters,
	author = Anderson, P. W. and Dayem, A. H.,
	year = 1964,
	pages = 195


@articlemaki_creation_1977,
	title = Creation of soliton pairs by electric fields in charge-density—wave condensates,
	volume = 39,
	number = 1,
	journal = Physical Review Letters,
	author = Maki, Kazumi,
	year = 1977,
	pages = 46


@articleatiyah_skyrmions_1989,
	title = Skyrmions from instantons,
	volume = 222,
	number = 3-4,
	journal = Physics Letters B,
	author = Atiyah, Michael Francis and Manton, N. S.,
	year = 1989,
	pages = 438–442


@articleshenoy_static_1985,
	title = Static response of a N×N Josephson junction array,
	volume = 18,
	issn = 0022-3719,
	url = http://stacks.iop.org/0022-3719/18/i=26/a=025,
	doi = 10.1088/0022-3719/18/26/025,
	abstract = Duality and scaling techniques are applied to a N*N Josephson junction array to calculate the static Josephson current response at a junction ij, due to an applied transverse vector potential at kl. The long-wavelength response function vanishes suddenly above a Kosterlitz-Thouless transition temperature T KT , due to the onset of incoherence in the effective Josephson phase. The zero-frequency inverse kinetic inductance and the helicity modulus thus also drop at T KT , consistent with recent Monte Carlo calculations.,
	language = en,
	number = 26,
	urldate = 2018-04-09,
	journal = Journal of Physics C: Solid State Physics,
	author = Shenoy, S. R.,
	year = 1985,
	pages = 5143


@articlesullivan_new_2000,
	title = New tetrahedrally close-packed structures,
	journal = Preprint,
	author = Sullivan, John,
	year = 2000


@articleokeeffe_duals_1998,
	title = Duals of Frank-Kasper structures as C, Si and Ge clathrates: Energetics and structure,
	volume = 78,
	issn = 0950-0839,
	shorttitle = Duals of Frank-Kasper structures as C, Si and Ge clathrates,
	url = https://doi.org/10.1080/095008398178219,
	doi = 10.1080/095008398178219,
	abstract = The four-connected clathrate structures derived as the duals of some of the tetrahedrally close-packed intermetallic structures (Frank-Kasper structures) are considered as possible structures for elemental C, Si and Ge. The minimumenergy structures are found using empirical potentials. The type II structure is found to have the lowest energy, but other clathrate structures have only a slightly higher energy within a few kT of the energy of the diamond form. Explicit coordinates are given for some Si structures.,
	number = 1,
	urldate = 2018-04-11,
	journal = Philosophical Magazine Letters,
	author = O'Keeffe, M. and Adams, G. B. and Sankey, O. F.,
	month = jul,
	year = 1998,
	pages = 21–28


@articlebouligand_distortions_1978,
	title = Distortions with double topological character : the case of cholesterics,
	volume = 39,
	issn = 0302-0738,
	shorttitle = Distortions with double topological character,
	url = http://dx.doi.org/10.1051/jphys:01978003908086300,
	doi = 10.1051/jphys:01978003908086300,
	abstract = Journal de Physique, Journal de Physique Archives représente une mine d informations facile à consulter sur la manière dont la physique a été publiée depuis 1872.,
	language = en,
	number = 8,
	urldate = 2018-04-11,
	journal = Journal de Physique,
	author = Bouligand, Y. and Derrida, B. and Poenaru, V. and Pomeau, Y. and Toulouse, G.,
	month = aug,
	year = 1978,
	pages = 863–867


@articlesachdev_thermally_2000,
	title = Thermally fluctuating superconductors in two dimensions,
	volume = 405,
	number = 6784,
	journal = Nature,
	author = Sachdev, Subir and Starykh, Oleg A.,
	year = 2000,
	pages = 322


@articlepearl_current_1964,
	title = Current distribution in superconducting films carrying quantized fluxoids,
	volume = 5,
	number = 4,
	journal = Applied Physics Letters,
	author = Pearl, J.,
	year = 1964,
	pages = 65–66


@articleonsager_statistical_1949,
	title = Statistical hydrodynamics,
	volume = 6,
	number = 2,
	journal = Il Nuovo Cimento (1943-1954),
	author = Onsager, Lars,
	year = 1949,
	pages = 279–287


@articlegriffiths_dependence_1970,
	title = Dependence of Critical Indices on a Parameter,
	volume = 24,
	url = https://link.aps.org/doi/10.1103/PhysRevLett.24.1479,
	doi = 10.1103/PhysRevLett.24.1479,
	abstract = A number of lattice models of phase transitions and critical points can be related to one another by variation of linear parameters appearing in the Hamiltonian. It is suggested that the critical indices as functions of these parameters remain constant except possibly at points where the nature of the associated first-order phase transition is itself altered by varying a parameter. Several models exhibiting critical phenomena are consistent with this proposal.,
	number = 26,
	urldate = 2018-04-15,
	journal = Physical Review Letters,
	author = Griffiths, Robert B.,
	month = jun,
	year = 1970,
	pages = 1479–1482


@articlebobbert_phase_1990,
	title = Phase transitions in dissipative Josephson chains,
	volume = 41,
	number = 7,
	journal = Physical Review B,
	author = Bobbert, P. A. and Fazio, R. and Schön, Gerd and Zimanyi, G. T.,
	year = 1990,
	pages = 4009


@articlekadanoff_critical_1971,
	title = Critical Phenomena, Proceedings of the International School" Enrico Fermi,",
	author = Kadanoff, L. P.,
	year = 1971


@articlekadanoff_critical_1971-1,
	title = Critical Phenomena, Proceedings of the International School" Enrico Fermi,",
	author = Kadanoff, L. P.,
	year = 1971


@articlebowers_regular_1997,
	title = A “regular” pentagonal tiling of the plane,
	volume = 1,
	number = 5,
	journal = Conformal Geometry and Dynamics of the American Mathematical Society,
	author = Bowers, Philip and Stephenson, Kenneth,
	year = 1997,
	pages = 58–86


@articlepenrose_pentaplexity_1979,
	title = Pentaplexity a class of non-periodic tilings of the plane,
	volume = 2,
	number = 1,
	journal = The mathematical intelligencer,
	author = Penrose, Roger,
	year = 1979,
	pages = 32–37


@booklamb_hydrodynamics_1932,
	title = Hydrodynamics,
	publisher = Cambridge university press,
	author = Lamb, Horace,
	year = 1932


@articlemonastyrskii_concerning_1975,
	title = Concerning the existence of monopoles in gauge field theories,
	volume = 21,
	journal = ZhETF Pisma Redaktsiiu,
	author = Monastyrskii, M. I. and Perelomov, A. M.,
	year = 1975,
	pages = 94


@bookdebye_vortrage_1914,
	title = Vorträge über die kinetische Theorie der Materie und der Elektrizität,
	volume = 6,
	publisher = BG Teubner,
	author = Debye, P. J. W. and Nernst, W. and Smoluchowski, M. and Sommerfeld, A. and Lorentz, H. A.,
	year = 1914


@bookricheson_eulers_2008,
	title = Euler's gem: the polyhedron formula and the birth of topology,
	volume = 6,
	shorttitle = Euler's gem,
	publisher = Springer,
	author = Richeson, D. S.,
	year = 2008,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/LMCZ3SWA/Richeson - 2008 - Euler's gem the polyhedron formula and the birth .pdf:application/pdf


@bookfeynman_quantum_2010,
	title = Quantum mechanics and path integrals,
	publisher = Courier Corporation,
	author = Feynman, R. P. and Hibbs, A. R. and Styer, D. F.,
	year = 2010,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/BRD2RC59/books.html:text/html


@bookfeynman_lectures_1965,
	title = Lectures on Physics, vol. III,
	publisher = Addison-Wesley Reading (Mass),
	author = Feynman, R. P. and Leighton, R. B. and Sands, M.,
	year = 1965


@articlesun_berezinskii-kosterlitz-thouless_2008,
	title = Berezinskii-Kosterlitz-Thouless phase transition for the dilute planar rotator model on a triangular lattice,
	volume = 78,
	number = 15,
	journal = Physical Review B,
	author = Sun, Y-Z and Yi, L. and Wysin, G. M.,
	year = 2008,
	pages = 155409


@articlefazio_condensed-matter_2008,
	title = Condensed-matter physics: Opposite of a superconductor,
	volume = 452,
	shorttitle = Condensed-matter physics,
	number = 7187,
	journal = Nature,
	author = Fazio, Rosario,
	year = 2008,
	pages = 542,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/Y45PPKWP/452542a.html:text/html


@articlemanucharyan_fluxonium:_2009,
	title = Fluxonium: Single cooper-pair circuit free of charge offsets,
	volume = 326,
	shorttitle = Fluxonium,
	number = 5949,
	journal = Science,
	author = Manucharyan, Vladimir E. and Koch, Jens and Glazman, Leonid I. and Devoret, Michel H.,
	year = 2009,
	pages = 113–116,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/Z7G3KFWX/Manucharyan et al. - 2009 - Fluxonium Single cooper-pair circuit free of char.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/L3EIE8CP/113.html:text/html


@bookjones_groups_1998,
	title = Groups, representations and physics,
	publisher = CRC Press,
	author = Jones, Hugh F.,
	year = 1998,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/BVLVX4IL/9781420050295.html:text/html


@miscnoauthor_courses_nodate,
	title = Courses,
	url = http://www.cmth.ph.ic.ac.uk/people/d.vvedensky/courses.html,
	urldate = 2018-07-24,
	file = Courses:/Users/carolinegorham/Zotero/storage/9IZYADSY/courses.html:text/html


@miscrowland_orthogonal_2018,
	title = Orthogonal Transformation,
	url = http://mathworld.wolfram.com/OrthogonalTransformation.html,
	journal = From MathWorld–A Wolfram Web Resource,
	author = Rowland, Todd,
	year = 2018,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/FT9Y5XYS/OrthogonalTransformation.html:text/html


@articlexu_space-time_2018,
	title = Space-Time Crystal and Space-Time Group,
	volume = 120,
	url = https://link.aps.org/doi/10.1103/PhysRevLett.120.096401,
	doi = 10.1103/PhysRevLett.120.096401,
	abstract = Crystal structures and the Bloch theorem play a fundamental role in condensed matter physics. We extend the static crystal to the dynamic “space-time” crystal characterized by the general intertwined space-time periodicities in D+1 dimensions, which include both the static crystal and the Floquet crystal as special cases. A new group structure dubbed a “space-time” group is constructed to describe the discrete symmetries of a space-time crystal. Compared to space and magnetic groups, the space-time group is augmented by “time-screw” rotations and “time-glide” reflections involving fractional translations along the time direction. A complete classification of the 13 space-time groups in one-plus-one dimensions (1+1D) is performed. The Kramers-type degeneracy can arise from the glide time-reversal symmetry without the half-integer spinor structure, which constrains the winding number patterns of spectral dispersions. In 2+1D, nonsymmorphic space-time symmetries enforce spectral degeneracies, leading to protected Floquet semimetal states. We provide a general framework for further studying topological properties of the (D+1)-dimensional space-time crystal.,
	number = 9,
	urldate = 2018-07-23,
	journal = Physical Review Letters,
	author = Xu, Shenglong and Wu, Congjun,
	month = feb,
	year = 2018,
	pages = 096401,
	file = APS Snapshot:/Users/carolinegorham/Zotero/storage/MUXPPNLJ/PhysRevLett.120.html:text/html


@articlechynoweth_internal_1957,
	title = Internal Field Emission in Silicon p-n Junctions,
	volume = 106,
	url = https://link.aps.org/doi/10.1103/PhysRev.106.418,
	doi = 10.1103/PhysRev.106.418,
	number = 3,
	urldate = 2018-06-19,
	journal = Physical Review,
	author = Chynoweth, A. G. and McKay, K. G.,
	month = may,
	year = 1957,
	pages = 418–426,
	file = APS Snapshot:/Users/carolinegorham/Zotero/storage/VXHLY8AP/PhysRev.106.html:text/html


@articlekobayashi_first_1980,
	title = First Chern class and holomorphic tensor fields,
	volume = 77,
	journal = Nagoya Mathematical Journal,
	author = Kobayashi, Shoshichi,
	year = 1980,
	pages = 5–11,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/83QA32V8/6618F649DC57B8CE4314989203070555.html:text/html


@bookfulton_intersection_2013,
	title = Intersection theory,
	volume = 2,
	publisher = Springer Science & Business Media,
	author = Fulton, William,
	year = 2013,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/NIW4FUZB/books.html:text/html


@articlebloch_algebraic_1986,
	title = Algebraic cycles and higher K-theory,
	volume = 61,
	number = 3,
	journal = Advances in Mathematics,
	author = Bloch, Spencer,
	year = 1986,
	pages = 267–304,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/RJTQANKY/Bloch - 1986 - Algebraic cycles and higher K-theory.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/67IGMHM9/Bloch - 1986 - Algebraic cycles and higher K-theory.pdf:application/pdf


@articlefazio_condensed-matter_2008-1,
	title = Condensed-matter physics: Opposite of a superconductor,
	volume = 452,
	shorttitle = Condensed-matter physics,
	number = 7187,
	journal = Nature,
	author = Fazio, Rosario,
	year = 2008,
	pages = 542,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/3NYP7T9P/452542a.html:text/html


@booknoauthor_resistance_nodate,
	title = RESISTANCE IN SUPERCONDUCTORS \textbar BCS: 50 Years,
	url = https://www.worldscientific.com/doi/abs/10.1142/9789814304665_0010,
	urldate = 2018-07-17


@incollectiongrezld_chapter_1972,
	series = Lie Gronps, Principal Bundles, and Characteristic Classes,
	title = Chapter X The Gauss–Bonnet–Chern Theorem,
	volume = 47,
	url = http://www.sciencedirect.com/science/article/pii/S0079816908628809,
	abstract = This chapter consists of an exposition of Chern's proof of the Gauss-Bonnet theorem that asserts that the Pfaffian class of an oriented Riemannian vector bundle (of even rank) coincides with the Euler class of the associated sphere bundle. This theorem implies that the integral of the Pfaffian class of the tangent bundle of a compact oriented manifold of even dimension is equal to the Euler-Poincare characteristic of the manifold.,
	urldate = 2018-07-13,
	booktitle = Pure and Applied Mathematics,
	publisher = Elsevier,
	editor = Grezld, Werner and Halperin, Stephen and Vanstone, Ray,
	month = jan,
	year = 1972,
	doi = 10.1016/S0079-8169(08)62880-9,
	pages = 477–491,
	file = ScienceDirect Snapshot:/Users/carolinegorham/Zotero/storage/5CS4KB9G/S0079816908628809.html:text/html


@articletaylor_mechanism_1934,
	title = The mechanism of plastic deformation of crystals. Part I.—Theoretical,
	volume = 145,
	number = 855,
	journal = Proc. R. Soc. Lond. A,
	author = Taylor, Geoffrey Ingram,
	year = 1934,
	pages = 362–387,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/9HUCXNMM/Taylor - 1934 - The mechanism of plastic deformation of crystals. .pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/3NNFIK82/362.html:text/html


@bookvogel_glass_2012,
	title = Glass chemistry,
	publisher = Springer Science & Business Media,
	author = Vogel, Werner,
	year = 2012,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/DGWX8AT6/books.html:text/html


@booklamb_few_nodate,
	title = A Few of My Favorite Spaces: The Three-Torus,
	shorttitle = A Few of My Favorite Spaces,
	url = https://blogs.scientificamerican.com/roots-of-unity/a-few-of-my-favorite-spaces-the-three-torus/,
	abstract = Living in a three-dimensional torus would be a narcissist's dream.,
	language = en,
	urldate = 2018-07-11,
	author = Lamb, Evelyn,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/C6IG9AVJ/a-few-of-my-favorite-spaces-the-three-torus.html:text/html


@incollectionlee_definitions_1997,
	series = Graduate Texts in Mathematics,
	title = Definitions and Examples of Riemannian Metrics,
	isbn = 978-0-387-98322-6 978-0-387-22726-9,
	url = https://link.springer.com/chapter/10.1007/0-387-22726-1_3,
	abstract = In this chapter we officially define Riemannian metrics and construct some of the elementary objects associated with them. At the end of the chapter, we introduce three classes of highly symmetric “model” Riemannian manifolds—Euclidean spaces, spheres, and hyperbolic spaces—to which we will return repeatedly as our understanding deepens and our tools become more sophisticated.,
	language = en,
	urldate = 2018-07-12,
	booktitle = Riemannian Manifolds,
	publisher = Springer, New York, NY,
	author = Lee, John M.,
	year = 1997,
	doi = 10.1007/0-387-22726-1_3,
	pages = 23–46,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/HCU8SR5Y/10.html:text/html


@articletextbackslashlodziana_negative_2004,
	title = A negative surface energy for alumina,
	volume = 3,
	number = 5,
	journal = Nature materials,
	author = \textbackslashLodziana, Zbigniew and Topsøe, Nan-Yu and Nørskov, Jens K.,
	year = 2004,
	pages = 289,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/WLV8R2V9/nmat1106.html:text/html


@articlehamilton_lvi._1856,
	title = LVI. Memorandum respecting a new system of roots of unity,
	volume = 12,
	number = 81,
	journal = The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science,
	author = Hamilton, William Rowan,
	year = 1856,
	pages = 446–446,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/CM3URFPN/14786445608642212.html:text/html


@articleding_kosterlitz-thouless_1990,
	title = Kosterlitz-Thouless transition in the two-dimensional quantum XY model,
	volume = 42,
	number = 10,
	journal = Physical Review B,
	author = Ding, H.-Q. and Makivić, M. S.,
	year = 1990,
	pages = 6827,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/GXLXMDH4/PhysRevB.42.html:text/html


@articletareyeva_orientation_2008,
	title = Orientation ordering and the transition to the orientational glass state in fullerite C 60,
	volume = 155,
	number = 2,
	journal = Theoretical and Mathematical Physics,
	author = Tareyeva, E. E. and Schelkacheva, T. I. and Chtchelkatchev, N. M.,
	year = 2008,
	pages = 812,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/KXANM4L8/Tareyeva et al. - 2008 - Orientation ordering and the transition to the ori.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/N89GIDKG/s11232-008-0070-3.html:text/html


@articleabriata_third_2004,
	title = The third law of thermodynamics and low temperature phase stability,
	volume = 49,
	number = 3-4,
	journal = Progress in Materials Science,
	author = Abriata, Jose P. and Laughlin, David E.,
	year = 2004,
	pages = 367–387,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/9DY5N6SI/Abriata and Laughlin - 2004 - The third law of thermodynamics and low temperatur.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/D6XAKWUS/S0079642503000306.html:text/html


@articlebaldi_thermal_2008,
	title = Thermal conductivity and terahertz vibrational dynamics of vitreous silica,
	volume = 77,
	number = 21,
	journal = Physical Review B,
	author = Baldi, G. and Giordano, V. M. and Monaco, G. and Sette, F. and Fabiani, E. and Fontana, A. and Ruocco, G.,
	year = 2008,
	pages = 214309,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/4DI2N7LT/PhysRevB.77.html:text/html


@articleabriata_third_2004-1,
	title = The third law of thermodynamics and low temperature phase stability,
	volume = 49,
	number = 3-4,
	journal = Progress in Materials Science,
	author = Abriata, Jose P. and Laughlin, David E.,
	year = 2004,
	pages = 367–387,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/K5YHTBJL/Abriata and Laughlin - 2004 - The third law of thermodynamics and low temperatur.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/RTFCIFLI/S0079642503000306.html:text/html


@articlelaughlin_third_2018,
	title = The Third Law of Thermodynamics: Phase equilibria and phase diagrams at low temperatures,
	volume = 145,
	issn = 1359-6454,
	shorttitle = The Third Law of Thermodynamics,
	url = http://www.sciencedirect.com/science/article/pii/S1359645417309801,
	doi = 10.1016/j.actamat.2017.11.037,
	abstract = Great progress has been made over the recent decades in the application of computational thermodynamics (Calphad) and theoretical methodologies (CVM) including so-called first principles approaches to modeling thermodynamic properties and the calculation of phase diagrams of materials. The aim of this paper is to call attention to considerations of the THIRD LAW OF THERMODYNAMICS when evaluating these results when applied to low temperature phase equilibria. In this effort we call attention to the essential content of the modern version of this third principle of thermodynamics using an historical and pedagogical approach. An appreciation of the constraints of the THIRD LAW is shown to be valuable in projecting possible low temperature phase fields and boundaries and predicting thermodynamically consistent phase diagram configurations as T→0 K. The ideas of Simon regarding aspects or subsystems are shown to be of paramount importance in assessing the thermodynamic properties of materials at low temperatures.,
	urldate = 2018-07-08,
	journal = Acta Materialia,
	author = Laughlin, David E. and Soffa, William A.,
	month = feb,
	year = 2018,
	keywords = Low temperature phase equilibria, Nernst-Planck-Simon statement, Phase equilibria, Third Law of Thermodynamics,
	pages = 49–61,
	file = ScienceDirect Snapshot:/Users/carolinegorham/Zotero/storage/ADG6WZHP/S1359645417309801.html:text/html


@bookwilks_third_1961-1,
	title = The third law of thermodynamics,
	publisher = Clarendon Press,
	author = Wilks, John,
	year = 1961


@bookwilks_third_1961-2,
	title = The third law of thermodynamics,
	publisher = Clarendon Press,
	author = Wilks, John,
	year = 1961


@articlebaez_octonions_2002,
	title = The octonions,
	volume = 39,
	number = 2,
	journal = Bulletin of the American Mathematical Society,
	author = Baez, John,
	year = 2002,
	pages = 145–205,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/UW3M95T9/Baez - 2002 - The octonions.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/8INI7V8A/home.html:text/html


@articleramos_low-temperature_2003,
	title = Low-temperature specific heat of structural and orientational glasses of simple alcohols,
	volume = 15,
	issn = 0953-8984,
	url = http://stacks.iop.org/0953-8984/15/i=11/a=323,
	doi = 10.1088/0953-8984/15/11/323,
	abstract = In this work, we review, extend and discuss low-temperature specific-heat experiments, that we have conducted on different molecular (hydrogen-bonded) solids both in crystalline and glassy (either amorphous or orientationally disordered) phases. In particular, we have measured the low-temperature specific heat C p for a set of simple, well known alcohols: glycerol, propanol and ethanol. For glycerol, we have prepared and measured C p of both glass and crystal phases down to 0.5 K. The same has been done for propanol, in this case comparing the strikingly different values observed for the two chemical isomers, 1-propanol and 2-propanol. Moreover, ethanol exhibits a very interesting polymorphism presenting three different solid phases at low temperature: a fully ordered (monoclinic) crystal, an orientationally disordered (cubic) crystal or 'orientational glass' and the ordinary structural (amorphous) glass. By measuring and comparing the low-temperature specific heat of the three phases, in the boson peak range 2–10 K as well as in the tunnelling-state range below 1 K, we provide a quantitative confirmation that 'glassy behaviour', either concerning low-temperature properties or the glass-transition phenomenon itself, is not directly related to the lack of long-range crystalline order occurring in amorphous solids.,
	language = en,
	number = 11,
	urldate = 2018-07-07,
	journal = Journal of Physics: Condensed Matter,
	author = Ramos, M. A. and Talón, C. and Jiménez-Riobóo, R. J. and Vieira, S.,
	year = 2003,
	pages = S1007


@articlebaldi_contribution_2008,
	title = Contribution of the terahertz vibrations to the high-temperature thermal conductivity of vitreous silica,
	volume = 88,
	number = 33-35,
	journal = Philosophical Magazine,
	author = Baldi, Giacomo and Fabiani, Elisa and Fontana, Aldo and Giordano, V. M. and Monaco, Giulio and Ruocco, Giancarlo and Sette, Francesco,
	year = 2008,
	pages = 3915–3923,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/PERJJP5Z/Baldi et al. - 2008 - Contribution of the terahertz vibrations to the hi.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/EXRD886K/14786430802438192.html:text/html


@articleganesh_signature_2006,
	title = Signature of nearly icosahedral structures in liquid and supercooled liquid copper,
	volume = 74,
	number = 13,
	journal = Physical Review B,
	author = Ganesh, P. and Widom, M.,
	year = 2006,
	pages = 134205,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/HKD4ESAU/Ganesh and Widom - 2006 - Signature of nearly icosahedral structures in liqu.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/2YNY3RWN/PhysRevB.74.html:text/html


@articlesluckin_liquid_2000,
	title = The liquid crystal phases: physics and technology,
	volume = 41,
	shorttitle = The liquid crystal phases,
	number = 1,
	journal = Contemporary physics,
	author = Sluckin, Timothy J.,
	year = 2000,
	pages = 37–56,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/MYFBXTUF/001075100181268.html:text/html


@bookbishop_proceedings_2002,
	title = Proceedings of the 16th International Conference on General Relativity & Gravitation: Durban, South Africa, 15-21 July 2001,
	shorttitle = Proceedings of the 16th International Conference on General Relativity & Gravitation,
	publisher = World Scientific,
	author = Bishop, Nigel and Maharaj, Sunil D.,
	year = 2002


@articlefinkelstein_foundations_1962,
	title = Foundations of Quaternion Quantum Mechanics,
	volume = 3,
	issn = 0022-2488,
	url = https://aip-scitation-org.proxy.library.cmu.edu/doi/abs/10.1063/1.1703794,
	doi = 10.1063/1.1703794,
	number = 2,
	urldate = 2018-06-27,
	journal = Journal of Mathematical Physics,
	author = Finkelstein, David and Jauch, Josef M. and Schiminovich, Samuel and Speiser, David,
	month = mar,
	year = 1962,
	pages = 207–220,
	file = Full Text PDF:/Users/carolinegorham/Zotero/storage/98PYPZ27/Finkelstein et al. - 1962 - Foundations of Quaternion Quantum Mechanics.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/XKCXH2F4/1.html:text/html


@bookt_general_2002,
	title = General Relativity And Gravitation, Proceedings Of The 16th International Conference,
	isbn = 978-981-4487-44-3,
	abstract = The 16th conference of the International Society on General Relativity and Gravitation (GR16), held at the International Convention Centre in Durban, South Africa, from 15 to 21 July, was attended by 450 delegates from around the world. The scientific programme comprised 18 plenary lectures, 1 public lecture and 19 workshops which, excepting 3 plenary lectures, are presented in this proceedings. It was the first major international conference on general relativity and gravitation held on the African continent.,
	language = en,
	publisher = World Scientific,
	author = T, Bishop Nigel and D, Maharaj Sunil,
	month = sep,
	year = 2002,
	keywords = Science / Cosmology, Science / Physics / Astrophysics, Science / Astronomy,
	annote = Google-Books-ID: Tb3UCgAAQBAJ


@articlenernst_ueber_1906,
	title = Ueber die Berechnung chemischer Gleichgewichte aus thermischen Messungen,
	volume = 1906,
	journal = Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse,
	author = Nernst, Walther,
	year = 1906,
	pages = 1–40,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/3EM7SKVW/58630.html:text/html


@bookanderson_basic_2018,
	title = Basic notions of condensed matter physics,
	publisher = CRC Press,
	author = Anderson, Philip W.,
	year = 2018,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/9ZBZE4H8/books.html:text/html


@articleborn_notitle_1912,
	volume = 13,
	abstract = von Karman, Theodore,
	journal = Phys. Zeit,
	author = Born, Max,
	year = 1912,
	pages = 297


@articleahmed_four-dimensional_2018,
	title = A four-dimensional generalization of Misner space in curved spacetime,
	volume = 2,
	issn = 2399-6528,
	url = http://stacks.iop.org/2399-6528/2/i=3/a=035036,
	doi = 10.1088/2399-6528/aab37d,
	abstract = We present a topologically trivial nonvacuum solution of the Einstein’s field equations in curved spacetime with stress-energy tensor Type I fluid, satisfying the energy conditions. The metric admits closed timelike curves which appear after a certain instant of time, and the spacetime is a four-dimensional generalization of flat Misner space in curved spacetime.,
	language = en,
	number = 3,
	urldate = 2018-06-22,
	journal = Journal of Physics Communications,
	author = Ahmed, Faizuddin,
	year = 2018,
	pages = 035036,
	file = IOP Full Text PDF:/Users/carolinegorham/Zotero/storage/BENKT5JL/Ahmed - 2018 - A four-dimensional generalization of Misner space .pdf:application/pdf


@articlecampbell_flux_1972,
	title = Flux vortices and transport currents in type II superconductors,
	volume = 21,
	issn = 0001-8732,
	url = https://doi.org/10.1080/00018737200101288,
	doi = 10.1080/00018737200101288,
	abstract = This article is concerned with the mechanisms by which type II super-conductors can carry currents. The equilibrium properties of the vortex lattice are described and the generalized driving force in gradients of temperature and field is derived using irreversible thermodynamics. This leads to expressions for thermal cross effects which can include pinning forces. The field distributions which occur in a range of situations are derived and a number of useful solutions of the critical state given. In particular, the distribution in a longitudinal field is obtained, and the conditions under which force-free configurations can break down by the cutting of vortices discussed. The effects of lattice rigidity on the summation of pinning forces is considered and it is shown that a summation based on statistical arguments uses the same approximations and leads to the same results as a dissipation argument. Theoretical expressions are derived for the vortex pinning interaction to a number of different metallurgical defects. The theoretical models are compared critically with experimental measurements of pinning forces and other related phenomena, such as flux creep, low amplitude vortex oscillations and vortex lattice defect effects. Finally, the implications for technological materials are assessed.,
	number = 90,
	urldate = 2018-06-20,
	journal = Advances in Physics,
	author = Campbell, A. M. and Evetts, J. E.,
	month = mar,
	year = 1972,
	pages = 199–428,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/EC2HFEAT/00018737200101288.html:text/html


@articlehirata_geometric_2013,
	title = Geometric Frustration of Icosahedron in Metallic Glasses,
	volume = 341,
	copyright = Copyright © 2013, American Association for the Advancement of Science,
	issn = 0036-8075, 1095-9203,
	url = http://science.sciencemag.org/content/341/6144/376,
	doi = 10.1126/science.1232450,
	abstract = Order, Order The structure of glassy materials, which are known to have short-range order but no long-range pattern, continues to be a puzzle. One current theory is that some glassy materials possess icosahedral ordering, a motif that cannot show translational periodicity. Hirata et al. (p. 376, published online 11 July) obtained diffraction patterns from subnanometer volumes in a metallic glass, which show some, but not all, of the expected features of an icosahedron. Simulations suggest that the patterns arise from icosahedrons distorted to include features of the face-centered cubic structure. This observation is different from the predictions of molecular dynamics simulations and provides pivotal information in understanding the competition between the formation of the globally inexpensive long-range order and the locally inexpensive short-range order. Icosahedral order has been suggested as the prevalent atomic motif of supercooled liquids and metallic glasses for more than half a century, because the icosahedron is highly close-packed but is difficult to grow, owing to structure frustration and the lack of translational periodicity. By means of angstrom-beam electron diffraction of single icosahedra, we report experimental observation of local icosahedral order in metallic glasses. All the detected icosahedra were found to be distorted with partially face-centered cubic symmetry, presenting compelling evidence on geometric frustration of local icosahedral order in metallic glasses. Small-volume regions in a bulk metallic glass show icosahedral ordering distorted by partial face-centered cubic symmetry. Small-volume regions in a bulk metallic glass show icosahedral ordering distorted by partial face-centered cubic symmetry.,
	language = en,
	number = 6144,
	urldate = 2018-06-19,
	journal = Science,
	author = Hirata, A. and Kang, L. J. and Fujita, T. and Klumov, B. and Matsue, K. and Kotani, M. and Yavari, A. R. and Chen, M. W.,
	month = jul,
	year = 2013,
	pmid = 23845945,
	pages = 376–379,
	file = Full Text PDF:/Users/carolinegorham/Zotero/storage/6KCU47RU/Hirata et al. - 2013 - Geometric Frustration of Icosahedron in Metallic G.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/WCYTA7QV/376.html:text/html


@articlebohmer_nature_1998,
	title = Nature of the non-exponential primary relaxation in structural glass-formers probed by dynamically selective experiments,
	volume = 235-237,
	issn = 0022-3093,
	url = http://www.sciencedirect.com/science/article/pii/S002230939800581X,
	doi = 10.1016/S0022-3093(98)00581-X,
	abstract = Several experimental methods feature the potential to distinguish between slow and fast contributions to the non-exponential, ensemble averaged primary response in glass-forming materials. Some of these techniques are based on the selection of subensembles using multi-dimensional nuclear magnetic resonance, optical bleaching, and non-resonant spectral hole burning. Others, such as the time-dependent solvation spectroscopy, measure microscopic responses induced by local perturbations. Using several of these methods it could be demonstrated for various glass-forming materials that the non-exponential relaxation results from a superposition of dynamically distinguishable entities. The experimental observation that subensembles can be selected efficiently indicates a large degree of heterogeneity. The intrinsic response is compatible with single exponential relaxation.,
	urldate = 2018-06-19,
	journal = Journal of Non-Crystalline Solids,
	author = Böhmer, R. and Chamberlin, R. V. and Diezemann, G. and Geil, B. and Heuer, A. and Hinze, G. and Kuebler, S. C. and Richert, R. and Schiener, B. and Sillescu, H. and Spiess, H. W. and Tracht, U. and Wilhelm, M.,
	month = aug,
	year = 1998,
	pages = 1–9,
	file = ScienceDirect Snapshot:/Users/carolinegorham/Zotero/storage/QQUF8F8G/S002230939800581X.html:text/html


@articlelilienfeld_rontgenstrahlung_1922,
	title = Die Röntgenstrahlung der Kathode bei der autoelektronischen Entladung (Vortrag auf dem deutschen Physikertag in Leipzig, 17.-24.9. 1922),
	volume = 23,
	number = 22/23,
	journal = Physikalische Zeitschrift,
	author = Lilienfeld, J. E.,
	year = 1922,
	pages = 506–511


@articlefowler_electron_1928,
	title = Electron emission in intense electric fields,
	volume = 119,
	number = 781,
	journal = Proc. R. Soc. Lond. A,
	author = Fowler, Ralph Howard and Nordheim, L.,
	year = 1928,
	pages = 173–181,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/7X6BXFC5/Fowler and Nordheim - 1928 - Electron emission in intense electric fields.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/8YWR9JLS/173.html:text/html


@articleesaki_long_1974,
	title = Long Journey into Tunneling,
	volume = 183,
	issn = 0036-8075,
	url = http://www.jstor.org/stable/1737846,
	number = 4130,
	urldate = 2018-06-19,
	journal = Science,
	author = Esaki, Leo,
	year = 1974,
	pages = 1149–1155


@articleesaki_long_1974-1,
	title = Long Journey into Tunneling,
	volume = 183,
	copyright = 1974 by the American Association for the Advancement of Science,
	issn = 0036-8075, 1095-9203,
	url = http://science.sciencemag.org/content/183/4130/1149,
	doi = 10.1126/science.183.4130.1149,
	abstract = I am, of course, deeply aware of important contributions made by many colleagues and my friends throughout this long journey. The subject of the second section was carried out when I was in Japan and all the rest (35) has been performed in the United States of America. Since my journey into tunneling is still continuing, I do not come to any conclusions in this talk. However, I would like to point out that many high barriers exist in this world: barriers between nations, races, and creeds. Unfortunately, some barriers are thick and strong. But I hope, with determination, we will find a way to tunnel through these barriers easily and freely, to bring the world together so that everyone can share in the legacy of Alfred Nobel.,
	language = en,
	number = 4130,
	urldate = 2018-06-19,
	journal = Science,
	author = Esaki, Leo,
	month = mar,
	year = 1974,
	pmid = 17789212,
	pages = 1149–1155,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/EXFCSDV5/tab-pdf.html:text/html


@articledyre_local_1996,
	title = Local elastic expansion model for viscous-flow activation energies of glass-forming molecular liquids,
	volume = 53,
	url = https://link.aps.org/doi/10.1103/PhysRevB.53.2171,
	doi = 10.1103/PhysRevB.53.2171,
	abstract = A model for the viscosity of glass-forming molecular liquids is proposed in which a ‘‘flow event’’ requires a local volume increase. The activation energy for a flow event is identified with the work done in shoving aside the surrounding liquid; this work is proportional to the high-frequency shear modulus, which increases as the temperature decreases. The model is confirmed by experiments on a number of molecular liquids. © 1996 The American Physical Society.,
	number = 5,
	urldate = 2018-06-19,
	journal = Physical Review B,
	author = Dyre, Jeppe C. and Olsen, Niels Boye and Christensen, Tage,
	month = feb,
	year = 1996,
	pages = 2171–2174,
	file = APS Snapshot:/Users/carolinegorham/Zotero/storage/44WDPZ8U/PhysRevB.53.html:text/html;Full Text PDF:/Users/carolinegorham/Zotero/storage/UXH5WND9/Dyre et al. - 1996 - Local elastic expansion model for viscous-flow act.pdf:application/pdf


@articlebyrne_inner_2008,
	title = Inner Product Spaces and Orthogonal Functions,
	author = Byrne, Charles,
	year = 2008,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/ADAGCK96/Byrne - 2008 - Inner Product Spaces and Orthogonal Functions.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/J6YRGE95/Byrne - 2008 - Inner Product Spaces and Orthogonal Functions.pdf:application/pdf


@articlejosephson_relation_1966,
	title = Relation between the superfluid density and order parameter for superfluid He near Tc,
	volume = 21,
	issn = 0031-9163,
	url = http://www.sciencedirect.com/science/article/pii/0031916366900886,
	doi = 10.1016/0031-9163(66)90088-6,
	abstract = Relations are derived between the superfluid density, the order parameter, and the specific heat singularity for superfluid helium near the lambda point.,
	number = 6,
	urldate = 2018-06-19,
	journal = Physics Letters,
	author = Josephson, B. D.,
	month = jul,
	year = 1966,
	pages = 608–609,
	file = ScienceDirect Snapshot:/Users/carolinegorham/Zotero/storage/XRML7WE9/0031916366900886.html:text/html


@articlejosephson_relation_1966-1,
	title = Relation between the superfluid density and order parameter for superfluid He near Tc,
	volume = 21,
	issn = 0031-9163,
	url = http://www.sciencedirect.com/science/article/pii/0031916366900886,
	doi = 10.1016/0031-9163(66)90088-6,
	abstract = Relations are derived between the superfluid density, the order parameter, and the specific heat singularity for superfluid helium near the lambda point.,
	number = 6,
	urldate = 2018-06-19,
	journal = Physics Letters,
	author = Josephson, B. D.,
	month = jul,
	year = 1966,
	pages = 608–609,
	file = ScienceDirect Snapshot:/Users/carolinegorham/Zotero/storage/943U7EDH/0031916366900886.html:text/html


@bookplanck_vorlesungen_1906,
	title = Vorlesungen über die Theorie der Wärmestrahlung,
	publisher = JA Barth,
	author = Planck, Max,
	year = 1906,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/5QEKHPD4/books.html:text/html;Snapshot:/Users/carolinegorham/Zotero/storage/G9HB82CL/books.html:text/html


@bookpines_theory_1966,
	title = The Theory of Quantum Liquids: Normal Fermi Liquids,
	volume = 1,
	shorttitle = The Theory of Quantum Liquids,
	publisher = WA Benjamin,
	author = Pines, David and Nozieres, Philippe,
	year = 1966


@articlerivier_line_1982,
	title = Line defects and tunnelling modes in glasses,
	volume = 43,
	doi = 10.1051/jphys:01982004302029300,
	number = 2,
	journal = Journal de Physique,
	author = Rivier, N. and Duffy, D.M.,
	year = 1982,
	pages = 293–306


@articleeinstein_elementare_1911,
	title = Elementare Betrachtungen über die thermische Molekularbewegung in festen Körpern,
	journal = Annalen der Physik,
	author = Einstein, A.,
	year = 1911


@bookkittel_introduction_1996,
	title = Introduction to solid state physics,
	volume = 7,
	publisher = Wiley New York,
	author = Kittel, Charles and McEuen, Paul,
	year = 1996,
	keywords = polycrystalline


@articleroberts_cosmic_2010,
	title = Cosmic Strings,
	author = Roberts, Kevin,
	year = 2010


@articleazevedo_wiggly_2017,
	title = Wiggly cosmic string as a waveguide for massless and massive fields,
	volume = 96,
	number = 8,
	journal = Physical Review D,
	author = Azevedo, Frankbelson dos S. and Moraes, Fernando and Mireles, Francisco and Berche, Bertrand and Fumeron, Sébastien,
	year = 2017,
	pages = 084047


@articlebeasley_possibility_1979,
	title = Possibility of vortex-antivortex pair dissociation in two-dimensional superconductors,
	volume = 42,
	number = 17,
	journal = Physical Review Letters,
	author = Beasley, M. R. and Mooij, J. E. and Orlando, T. P.,
	year = 1979,
	pages = 1165


@articleschulte_analysis_2006,
	title = Analysis of localization phenomena in weakly interacting disordered lattice gases,
	volume = 8,
	issn = 1367-2630,
	url = http://stacks.iop.org/1367-2630/8/i=10/a=230,
	doi = 10.1088/1367-2630/8/10/230,
	abstract = Disorder plays a crucial role in many systems particularly in solid state physics. However, the disorder in a particular system cannot usually be chosen or controlled. We show that the unique control available for ultracold atomic gases may be used for the production and observation of disordered quantum degenerate gases. A detailed analysis of localization effects for two possible realizations of a disordered potential is presented. In a theoretical analysis, clear localization effects are observed when a superlattice is used to provide a quasiperiodic disorder. The effects of localization are analysed by investigating the superfluid fraction and the localization length within the system. The theoretical analysis in this paper paves a clear path for the future observation of Anderson-like localization in disordered quantum gases.,
	language = en,
	number = 10,
	urldate = 2018-04-19,
	journal = New Journal of Physics,
	author = Schulte, T. and Drenkelforth, S. and Kruse, J. and Tiemeyer, R. and Sacha, K. and Zakrzewski, J. and Lewenstein, M. and Ertmer, W. and Arlt, J. J.,
	year = 2006,
	pages = 230


@articleyu_equivalent_2011,
	title = Equivalent expression of ${\textbackslashmathbb{Z}}_{2}$ topological invariant for band insulators using the non-Abelian Berry connection,
	volume = 84,
	url = https://link.aps.org/doi/10.1103/PhysRevB.84.075119,
	doi = 10.1103/PhysRevB.84.075119,
	abstract = We introduce an expression for the Z2 topological invariant of band insulators using the non-Abelian Berry connection. Our expression can identify the topological nature of a general band insulator without any of the gauge-fixing problems that plague the concrete implementation of previous invariants. This expression can be derived from the “partner switching” of the Wannier function center during time-reversal pumping and is thus equivalent to the Z2 topological invariant proposed by Kane and Mele. Using our expression, we have recalculated the Z2 topological index for several topological insulator material systems and obtained consistent results with the previous studies.,
	number = 7,
	urldate = 2018-04-19,
	journal = Physical Review B,
	author = Yu, Rui and Qi, Xiao Liang and Bernevig, Andrei and Fang, Zhong and Dai, Xi,
	month = aug,
	year = 2011,
	pages = 075119


@articlemironov_charge_2018,
	title = Charge Berezinskii-Kosterlitz-Thouless transition in superconducting NbTiN films,
	volume = 8,
	copyright = 2018 The Author(s),
	issn = 2045-2322,
	url = https://www.nature.com/articles/s41598-018-22451-1,
	doi = 10.1038/s41598-018-22451-1,
	abstract = Three decades after the prediction of charge-vortex duality in the critical vicinity of the two-dimensional superconductor-insulator transition (SIT), one of the fundamental implications of this duality—the charge Berezinskii-Kosterlitz-Thouless (BKT) transition that should occur on the insulating side of the SIT—has remained unobserved. The dual picture of the process points to the existence of a superinsulating state endowed with zero conductance at finite temperature. Here, we report the observation of the charge BKT transition on the insulating side of the SIT in 10 nm thick NbTiN films, identified by the BKT critical behavior of the temperature and magnetic field dependent resistance, and map out the magnetic-field dependence of the critical temperature of the charge BKT transition. Finally, we ascertain the effects of the finite electrostatic screening length and its divergence at the magnetic field-tuned approach to the superconductor-insulator transition.,
	language = en,
	number = 1,
	urldate = 2018-04-20,
	journal = Scientific Reports,
	author = Mironov, Alexey Yu and Silevitch, Daniel M. and Proslier, Thomas and Postolova, Svetlana V. and Burdastyh, Maria V. and Gutakovskii, Anton K. and Rosenbaum, Thomas F. and Vinokur, Valerii V. and Baturina, Tatyana I.,
	month = mar,
	year = 2018,
	pages = 4082


@articleandersson_thermal_1996,
	title = Thermal conductivity of C 60 at pressures up to 1 GPa and temperatures in the 50–300 K range,
	volume = 54,
	number = 5,
	journal = Physical Review B,
	author = Andersson, Ove and Soldatov, Alexander and Sundqvist, Bertil,
	year = 1996,
	pages = 3093


@articlemorelli_thermal_1985,
	title = Thermal conductivity and thermopower of graphite at very low temperatures,
	volume = 31,
	number = 10,
	journal = Physical Review B,
	author = Morelli, D. T. and Uher, C.,
	year = 1985,
	pages = 6721


@articlemorelli_thermal_1985-1,
	title = Thermal conductivity and thermopower of graphite at very low temperatures,
	volume = 31,
	url = https://link.aps.org/doi/10.1103/PhysRevB.31.6721,
	doi = 10.1103/PhysRevB.31.6721,
	abstract = Measurements of the in-plane thermal conductivity and thermopower of graphite have been performed from 70 mK to 8 K. The thermal conductivity exhibits a crossover from a Tn (n\textgreater2) dependence above 1 K to a T1.14±0.02 law at lower temperatures, behavior attributed to a combination of increasing carrier conduction and a lattice component varying slower than T2 from 1 K down to about 0.3 K. The thermoelectric power is negative throughout the range; below 2 K, it is a linear function of temperature, the magnitude of the slope being proportional to the degree of structural imperfection of the samples.,
	number = 10,
	urldate = 2018-04-20,
	journal = Physical Review B,
	author = Morelli, D. T. and Uher, C.,
	month = may,
	year = 1985,
	pages = 6721–6725


@articlewillart_structural_2000,
	title = Structural signature of the configurational entropy change during the glass formation of plastic crystal cyanoadamantane,
	volume = 112,
	issn = 0021-9606,
	url = https://aip-scitation-org.proxy.library.cmu.edu/doi/abs/10.1063/1.481738,
	doi = 10.1063/1.481738,
	number = 24,
	urldate = 2018-04-20,
	journal = The Journal of Chemical Physics,
	author = Willart, J. F. and Descamps, M. and van Miltenburg, J. C.,
	month = jun,
	year = 2000,
	pages = 10992–10997


@articlemooij_quantum_2005,
	title = Quantum Phase Slip Junctions, Condensed Matter,
	journal = arXiv preprint cond-mat/0511535,
	author = Mooij, J. E. and Nazarov, Yu V.,
	year = 2005


@articlewithers_thermal_1993,
	title = Thermal Diffusivity/Conductivity of Compacts of C60 Buckminsterfullerene and a C60–C70 Mixture,
	volume = 76,
	number = 3,
	journal = Journal of the American Ceramic Society,
	author = Withers, James C. and Loutfy, Raouf O. and Donaldson, Kimberly Y. and Hasselman, D. P. H.,
	year = 1993,
	pages = 754–756


@articleberman_nitrogen_1975,
	title = Nitrogen in diamond: evidence from thermal conductivity,
	volume = 8,
	shorttitle = Nitrogen in diamond,
	number = 21,
	journal = Journal of Physics C: Solid State Physics,
	author = Berman, R. and Hudson, P. R. W. and Martinez, M.,
	year = 1975,
	pages = L430


@articlenihira_thermal_1975,
	title = Thermal resistivity changes in electron-irradiated pyrolytic graphite,
	volume = 14,
	number = 8,
	journal = Japanese Journal of Applied Physics,
	author = Nihira, Takeshi and Iwata, Tadao,
	year = 1975,
	pages = 1099


@bookgriffiths_introduction_1962,
	title = Introduction to electrodynamics,
	publisher = Prentice Hall,
	author = Griffiths, David J.,
	year = 1962


@articlepolyakov_spectrum_1974,
	title = Spectrum of particles in quantum field theory,
	volume = 20,
	journal = JETP Lett,
	author = Polyakov, A. M.,
	year = 1974,
	pages = 430–433


@articlenelson_universal_1977,
	title = Universal jump in the superfluid density of two-dimensional superfluids,
	volume = 39,
	number = 19,
	journal = Physical Review Letters,
	author = Nelson, David R. and Kosterlitz, J. M.,
	year = 1977,
	pages = 1201


@articlecladis_non-singular_1972,
	title = Non-singular disclinations of strength S=+ 1 in nematics,
	volume = 33,
	number = 5-6,
	journal = Journal de Physique,
	author = Cladis, P. E. and Kleman, M.,
	year = 1972,
	pages = 591–598


@articlewilliams_fils_1974,
	title = Fils et disinclinaisons dans un nématique en tube capillaire,
	volume = 35,
	number = 7-8,
	journal = Journal de Physique,
	author = Williams, C. and Bouligand, Y.,
	year = 1974,
	pages = 589–593


@articlekamien_geometry_2002,
	title = The geometry of soft materials: a primer,
	volume = 74,
	shorttitle = The geometry of soft materials,
	number = 4,
	journal = Reviews of Modern physics,
	author = Kamien, Randall D.,
	year = 2002,
	pages = 953


@articlekobayashi_theory_1971,
	title = Theory of Translational and Orientational Melting with Application to Liquid Crystals,
	volume = 13,
	issn = 0026-8941,
	url = https://doi.org/10.1080/15421407108084959,
	doi = 10.1080/15421407108084959,
	abstract = A theory of melting with application to liquid crystals in which both translational and orientational order parameters are taken into account is developed in a manner similar to that of Kirkwood and Monroe.,
	number = 2,
	urldate = 2018-04-22,
	journal = Molecular Crystals and Liquid Crystals,
	author = Kobayashi, Kenji K.,
	month = may,
	year = 1971,
	pages = 137–148


@articlecichocki_electrostatic_1989,
	title = Electrostatic interactions in two-dimensional Coulomb systems with periodic boundary conditions,
	volume = 158,
	number = 3,
	journal = Physica A: Statistical Mechanics and its Applications,
	author = Cichocki, B. and Felderhof, B. U.,
	year = 1989,
	pages = 706–722


@articlepoenaru_crossing_1977,
	title = The crossing of defects in ordered media and the topology of 3-manifolds,
	volume = 38,
	number = 8,
	journal = Journal de Physique,
	author = Poenaru, Valentin and Toulouse, Gérard,
	year = 1977,
	pages = 887–895


@bookrao_field_2002,
	title = Field theories in condensed matter physics,
	publisher = CRC Press,
	author = Rao, Sumathi,
	year = 2002


@bookchen_topological_2012,
	title = Topological defects in nematic and smectic liquid crystals,
	publisher = University of Pennsylvania,
	author = Chen, Bryan Gin-ge,
	year = 2012


@articlecladis_non-singular_1972-1,
	title = Non-singular disclinations of strength S = + 1 in nematics,
	volume = 33,
	issn = 0302-0738,
	url = http://dx.doi.org/10.1051/jphys:01972003305-6059100,
	doi = 10.1051/jphys:01972003305-6059100,
	abstract = Journal de Physique, Journal de Physique Archives représente une mine d informations facile à consulter sur la manière dont la physique a été publiée depuis 1872.,
	language = en,
	number = 5-6,
	urldate = 2018-04-25,
	journal = Journal de Physique,
	author = Cladis, P. E. and Kléman, M.,
	month = may,
	year = 1972,
	pages = 591–598


@articlekleman_topological_2006,
	title = Topological point defects in nematic liquid crystals,
	volume = 86,
	issn = 1478-6435,
	url = https://doi.org/10.1080/14786430600593016,
	doi = 10.1080/14786430600593016,
	abstract = Point defects in nematics, also called hedgehogs, are topological entities that have no equivalent in ordered atomic solids, despite the homonymy. They have been the subject of intense experimental and, above all, theoretical (analytical and computational) investigations in the last thirty years. They are present in bulk specimens and at the specimen boundaries. This review article stresses the importance of the core structure of the defect, the possibility of it splitting into a disclination loop, and boundary conditions, as well as taking stock of the recent advances on point defects in nematic colloidal suspensions. An important topic is the formation of strings between opposite hedgehogs (radial and hyperbolic), and their role in the dynamic properties of nematics.,
	number = 25-26,
	urldate = 2018-04-25,
	journal = Philosophical Magazine,
	author = Kleman, M. and Lavrentovich, O. D.,
	month = sep,
	year = 2006,
	pages = 4117–4137


@articleserra_curvature_2016,
	title = Curvature and defects in nematic liquid crystals,
	volume = 43,
	issn = 0267-8292,
	url = https://doi.org/10.1080/02678292.2016.1209698,
	doi = 10.1080/02678292.2016.1209698,
	abstract = The use of nematic liquid crystals for directed assembly of particles and for the creation of multistable systems depends on the ability to control the topological defects and the distortions of the director field. These are not only driven by topological constraints and by anchoring energies but also by the curvature field created by the bounding surfaces. This review explores the interaction between defects, topology, inclusions and curvature in nematics. I will introduce the relationship between curvature and the Frank elastic energy in nematics, and then I will give an overview of specific examples that show how this coupling can create unexpected behaviours, such as lock-and-key interactions, anchoring transitions on curved surfaces and memory effects.,
	number = 13-15,
	urldate = 2018-04-25,
	journal = Liquid Crystals,
	author = Serra, Francesca,
	month = dec,
	year = 2016,
	keywords = self-assembly, curvature, Nematic liquid crystals (LCs), soft matter, topological defects,
	pages = 1920–1936


@articleskyrme_unified_1962,
	title = A unified field theory of mesons and baryons,
	volume = 31,
	journal = Nuclear Physics,
	author = Skyrme, Tony Hilton Royle,
	year = 1962,
	pages = 556–569


@articlejerome_surface_1991,
	title = Surface effects and anchoring in liquid crystals,
	volume = 54,
	issn = 0034-4885,
	url = http://stacks.iop.org/0034-4885/54/i=3/a=002,
	doi = 10.1088/0034-4885/54/3/002,
	abstract = As their name indicates, liquid crystals simultaneously exhibit some characteristics common to both ordinary isotropic liquids and solid crystals. This ambivalence is also found in the effects of surfaces on these systems which lead to a great diversity of phenomena. These phenomena are reviewed focusing on nematic liquid crystals which have the simplest structure among the many existing types and which have been the most extensively studied. Three main kinds of effects can be distinguished. The first concerns the perturbation of the liquid crystalline structure close to the surface. Beyond this transition region, the bulk liquid crystalline structure is recovered with an orientation which is fixed by the surface: this phenomenon of orientation of liquid crystals by surfaces is the so-called anchoring. Finally, close to bulk phase transitions, critical adsorption or wetting can occur at surfaces as is also seen in isotropic systems.,
	language = en,
	number = 3,
	urldate = 2018-04-25,
	journal = Reports on Progress in Physics,
	author = Jerome, B.,
	year = 1991,
	pages = 391


@articlecopar_quaternions_2013,
	title = Quaternions and hybrid nematic disclinations,
	volume = 469,
	copyright = © 2013 The Author(s) Published by the Royal Society. All rights reserved.,
	issn = 1364-5021, 1471-2946,
	url = http://rspa.royalsocietypublishing.org/content/469/2156/20130204,
	doi = 10.1098/rspa.2013.0204,
	abstract = Disclination lines in nematic liquid crystals can exist in different geometric conformations, characterized by their director profile. In certain confined colloidal suspensions and even more prominently in chiral nematics, the director profile may vary along the disclination line. We construct a robust geometric decomposition of director profile in closed disclination loops and use it to apply topological classification to linked loops with arbitrary variation of the profile, generalizing the self-linking number description of disclination loops with the winding number \textlessimg class="highwire-embed" alt="Embedded Image" src="http://rspa.royalsocietypublishing.org/sites/default/files/highwire/royprsa/469/2156/20130204/embed/inline-graphic-1.gif"/\textgreater. The description bridges the gap between the known abstract classification scheme derived from homotopy theory and the observable local features of disclinations, allowing application of said theory to structures that occur in practice.,
	language = en,
	number = 2156,
	urldate = 2018-04-25,
	journal = Proc. R. Soc. A,
	author = Čopar, Simon and Žumer, Slobodan,
	month = aug,
	year = 2013,
	pages = 20130204


@incollectionwitten_su2_1994,
	title = An su(2) anomaly,
	isbn = 978-981-02-1681-8,
	url = https://www.worldscientific.com/doi/abs/10.1142/9789812794345_0028,
	urldate = 2018-04-25,
	booktitle = Instantons in Gauge Theories,
	publisher = WORLD SCIENTIFIC,
	author = Witten, Edward,
	month = jul,
	year = 1994,
	doi = 10.1142/9789812794345_0028,
	pages = 230–234


@articlekihara_classical_2008,
	title = Classical solution in six-dimensional gauge theory with higher derivative coupling,
	volume = 77,
	url = https://link.aps.org/doi/10.1103/PhysRevD.77.047702,
	doi = 10.1103/PhysRevD.77.047702,
	abstract = We show that the spin connection of the standard metric on a six-dimensional sphere gives an exact solution to the generalized self-duality equations suggested by Tchrakian some years ago. We work on a SO(6) gauge theory with a higher-derivative coupling term. The model consists of vector fields only. The pseudoenergy is bounded from below by a topological charge, which is proportional to the winding number of spatial S5 around the internal space SO(6). The fifth homotopy group of SO(6) is, indeed, Z. The coupling constant of the higher derivative term is quadratic in the radius of the underlying space S6.,
	number = 4,
	urldate = 2018-04-25,
	journal = Physical Review D,
	author = Kihara, Hironobu and Nitta, Muneto,
	month = feb,
	year = 2008,
	pages = 047702


@articlenitta_fractional_2015,
	title = Fractional instantons and bions in the principal chiral model on ℝ2$\textbackslashtimes$ S1 $ $${$$\textbackslashbackslash$mathrm ${$$\textbackslashbackslash$mathbb ${$R$}$$}$$}$ˆ 2$\textbackslashbackslash$times ${$S$}$ˆ 1$ $ with twisted boundary conditions,
	volume = 2015,
	number = 8,
	journal = Journal of High Energy Physics,
	author = Nitta, Muneto,
	year = 2015,
	pages = 63


@booknoauthor_fractional_nodate,
	title = Fractional instantons and bions in the principal chiral model on [equation] with twisted boundary conditions \textbar SpringerLink,
	url = https://link.springer.com/article/10.1007
	urldate = 2018-04-25


@articleskyrme_particle_1961,
	title = Particle states of a quantized meson field,
	volume = 262,
	number = 1309,
	journal = Proc. R. Soc. Lond. A,
	author = Skyrme, T. H. R.,
	year = 1961,
	pages = 237–245


@articlemottram_disclination_1997,
	title = Disclination core structure and induced phase change in nematic liquid crystals,
	volume = 355,
	issn = 1364-503X, 1471-2962,
	url = http://rsta.royalsocietypublishing.org/content/355/1731/2045,
	doi = 10.1098/rsta.1997.0106,
	abstract = Using a continuum theory which allows for changes in variables which represent the phase and biaxiality of the liquid crystal as well as the director field, the core structure of plus or minus one half and plus or minus one strength disclination lines is investigated. Under certain approximations analytical solutions are found near to the centre of the disclination. Good agreement is found with numerical solutions for the full problem. Using a continuation package (AUTO), the changes to these numerical solutions are then considered as various parameters are altered. The model exhibits a first-order phase transition near to the clearing point temperature induced by the presence of the disclination core. If the disclination was not present, this phase transition would occur when the liquid crystalline state loses stability at a higher temperature.,
	language = en,
	number = 1731,
	urldate = 2018-04-26,
	journal = Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences,
	author = Mottram, N. J. and Hogan, S. J.,
	month = oct,
	year = 1997,
	pages = 2045–2064


@articledirac_theory_1948,
	title = The Theory of Magnetic Poles,
	volume = 74,
	url = https://link.aps.org/doi/10.1103/PhysRev.74.817,
	doi = 10.1103/PhysRev.74.817,
	abstract = If one supposes that a particle with a single magnetic pole can exist and that it interacts with charged particles, the laws of quantum mechanics lead to the requirement that the electric charges shall be quantized—all charges must be integral multiples of a unit charge e connected with the pole strength g by the formula eg=12ℏc. Since electric charges are known to be quantized and no reason for this has yet been proposed apart from the existence of magnetic poles, we have here a reason for taking magnetic poles seriously. The fact that they have not yet been observed may be ascribed to the large value of the quantum of pole.,
	number = 7,
	urldate = 2018-04-26,
	journal = Physical Review,
	author = Dirac, P. A. M.,
	month = oct,
	year = 1948,
	pages = 817–830


@articlemajumdar_radial-hedgehog_2012,
	title = The radial-hedgehog solution in Landau–de Gennes' theory for nematic liquid crystals,
	volume = 23,
	number = 1,
	journal = European Journal of Applied Mathematics,
	author = Majumdar, Apala,
	year = 2012,
	pages = 61–97


@articlecollie_partonic_2009,
	title = The partonic nature of instantons,
	volume = 2009,
	number = 08,
	journal = Journal of High Energy Physics,
	author = Collie, Benjamin and Tong, David,
	year = 2009,
	pages = 006


@articlebelavin_quantum_1979,
	title = Quantum fluctuations of multi-instanton solutions,
	volume = 83,
	number = 3-4,
	journal = Physics Letters B,
	author = Belavin, A. A. and Fateev, V. A. and Schwarz, Albert S. and Tyupkin, Yu S.,
	year = 1979,
	pages = 317–320


@incollectionzhitnitsky_confinement-deconfinement_2007,
	title = Confinement-deconfinement phase transition and fractional instanton quarks in dense matter,
	booktitle = Continuous Advances in QCD 2006,
	publisher = World Scientific,
	author = Zhitnitsky, Ariel R.,
	year = 2007,
	pages = 207–213


@articlegross_meron_1978,
	title = Meron configurations in the two-dimensional O (3) σ-model,
	volume = 132,
	number = 5,
	journal = Nuclear Physics B,
	author = Gross, David J.,
	year = 1978,
	pages = 439–456


@articledodd_instantons_1978,
	title = Instantons and the real world,
	volume = 77,
	number = 1096,
	journal = New Scientist (London),
	author = Dodd, J.,
	year = 1978,
	pages = 858–859


@articlecallan_jr_mechanism_1977,
	title = A mechanism for quark confinement,
	volume = 66,
	number = 4,
	journal = Physics Letters B,
	author = Callan Jr, Curtis G. and Dashen, Roger and Gross, David J.,
	year = 1977,
	pages = 375–381


@articlerosner_orbis_1977,
	title = Orbis Scientiae, Deeper Pathways in High Energy Physics,
	author = Rosner, J.,
	year = 1977


@articlenewnham_phase_2012,
	title = Phase diagrams and crystal chemistry,
	volume = 5,
	journal = Phase Diagrams 6-V: Materials Science and Technology,
	author = Newnham, R. E.,
	year = 2012


@incollectioncallan_jr_toward_1994,
	title = Toward a theory of the strong interactions,
	booktitle = Instantons In Gauge Theories,
	publisher = World Scientific,
	author = Callan Jr, Curtis G. and Dashen, Roger and Gross, David J.,
	year = 1994,
	pages = 36–60


@articlebrucker_geometry_1986,
	title = Geometry of the SU (2) Di-Meron Solution,
	volume = 41,
	number = 4,
	journal = Zeitschrift für Naturforschung A,
	author = Brucker, R. and Sorg, M.,
	year = 1986,
	pages = 571–584


@articlegipson_quasi-solitons_1984,
	title = Quasi-solitons in the strongly coupled Higgs sector of the standard model,
	volume = 231,
	number = 3,
	journal = Nuclear Physics B,
	author = Gipson, John M.,
	year = 1984,
	pages = 365–385


@articlepoenaru_crossing_1977-1,
	title = The crossing of defects in ordered media and the topology of 3-manifolds,
	volume = 38,
	number = 8,
	journal = Journal de Physique,
	author = Poenaru, Valentin and Toulouse, Gérard,
	year = 1977,
	pages = 887–895


@articleoh_yang-mills_2011,
	title = Yang-Mills instantons from gravitational instantons,
	volume = 2011,
	issn = 1029-8479,
	url = https://link.springer.com/article/10.1007/JHEP04(2011)087,
	doi = 10.1007/JHEP04(2011)087,
	abstract = We show that every gravitational instantons are SU(2) Yang-Mills instantons on a Ricci-flat four manifold although the reverse is not necessarily true. It is shown that gravitational instantons satisfy exactly the same self-duality equation of SU(2) Yang-Mills instantons on the Ricci-flat manifold determined by the gravitational instantons themselves. We explicitly check the correspondence with several examples and discuss their topological properties.,
	language = en,
	number = 4,
	urldate = 2018-04-30,
	journal = Journal of High Energy Physics,
	author = Oh, John J. and Park, Chanyong and Yang, Hyun Seok,
	month = apr,
	year = 2011,
	pages = 87


@articlemeiboom_lattice_1983,
	title = Lattice of disclinations: The structure of the blue phases of cholesteric liquid crystals,
	volume = 27,
	shorttitle = Lattice of disclinations,
	url = https://link.aps.org/doi/10.1103/PhysRevA.27.438,
	doi = 10.1103/PhysRevA.27.438,
	abstract = We argue that the basic mechanism stabilizing the blue phases is the appearance of double cholesteric twist. The free-energy cost of the disclination lattice that inevitably accompanies double twist becomes small near the clearing point. We use the director picture and the Oseen-Frank equations in a computer calculation of the free energy for three specific models, with O5, O2, and O8 symmetry. Disclinations are treated as having an isotropic core. Comparison of the results of the computation with a number of experimental quantities is given. In a final section, a mean-field theory of disclinations is presented. It is argued there that the biaxiality, which is a characteristic of Landau theories of the blue phase, can be considered as an "escape" of the core of the disclination, forced by the implicit requirement of analyticity.,
	number = 1,
	urldate = 2018-04-30,
	journal = Physical Review A,
	author = Meiboom, S. and Sammon, M. and Brinkman, W. F.,
	month = jan,
	year = 1983,
	pages = 438–454


@articleforkel_infrared_2006,
	title = Infrared degrees of freedom of Yang-Mills theory in the Schr\textbackslash"odinger representation,
	volume = 73,
	url = https://link.aps.org/doi/10.1103/PhysRevD.73.105002,
	doi = 10.1103/PhysRevD.73.105002,
	abstract = We set up a new calculational framework for the Yang-Mills vacuum transition amplitude in the Schrödinger representation. After integrating out hard-mode contributions perturbatively and performing a gauge-invariant gradient expansion of the ensuing soft-mode action, a manageable saddle-point expansion for the vacuum overlap can be formulated. In combination with the squeezed approximation to the vacuum wave functional this allows for an essentially analytical treatment of physical amplitudes. Moreover, it leads to the identification of dominant and gauge-invariant classes of gauge field orbits which play the role of gluonic infrared (IR) degrees of freedom. The latter emerge as a diverse set of saddle-point solutions and are represented by unitary matrix fields. We discuss their scale stability, the associated virial theorem and other general properties including topological quantum numbers and action bounds. We then find important saddle-point solutions (most of them solitons) explicitly and examine their physical impact. While some are related to tunneling solutions of the classical Yang-Mills equation, i.e. to instantons and merons, others appear to play unprecedented roles. A remarkable new class of IR degrees of freedom consists of Faddeev-Niemi type link and knot solutions, potentially related to glueballs.,
	number = 10,
	urldate = 2018-04-30,
	journal = Physical Review D,
	author = Forkel, Hilmar,
	month = may,
	year = 2006,
	pages = 105002


@articlekobayashi_abe_2012,
	title = Abe homotopy classification of topological excitations under the topological influence of vortices,
	volume = 856,
	number = 2,
	journal = Nuclear Physics B,
	author = Kobayashi, Shingo and Kobayashi, Michikazu and Kawaguchi, Yuki and Nitta, Muneto and Ueda, Masahito,
	year = 2012,
	pages = 577–606


@incollectionfazio_charges_2013,
	title = Charges and Vortices in Josephson Junction Arrays,
	booktitle = 40 Years of Berezinskii–Kosterlitz–Thouless Theory,
	publisher = World Scientific,
	author = Fazio, Rosario and Schön, Gerd,
	year = 2013,
	pages = 237–254


@articlebruder_superconductormott-insulator_1993-1,
	title = Superconductor–Mott-insulator transition in Bose systems with finite-range interactions,
	volume = 47,
	url = https://link.aps.org/doi/10.1103/PhysRevB.47.342,
	doi = 10.1103/PhysRevB.47.342,
	abstract = We study the superconductor-insulator transition of Bose-Hubbard models with finite-range interactions. Commensurability of the charge distribution with the underlying lattice leads to a richly structured phase diagram. In addition to the lobes of insulating phase characterized by integer fillings, we find–for finite-range interactions–lobes with rational filling factors. At low temperatures we can investigate the phase transition by mapping the model onto a XXZ spin-1/2 Heisenberg model.,
	number = 1,
	urldate = 2018-05-01,
	journal = Physical Review B,
	author = Bruder, C. and Fazio, Rosario and Schön, Gerd,
	month = jan,
	year = 1993,
	pages = 342–347


@articlefisher_presence_1990,
	title = Presence of quantum diffusion in two dimensions: Universal resistance at the superconductor-insulator transition,
	volume = 64,
	shorttitle = Presence of quantum diffusion in two dimensions,
	number = 5,
	journal = Physical review letters,
	author = Fisher, Matthew PA and Grinstein, G. and Girvin, S. M.,
	year = 1990,
	pages = 587


@articlefisher_quantum_1990,
	title = Quantum phase transitions in disordered two-dimensional superconductors,
	volume = 65,
	number = 7,
	journal = Physical Review Letters,
	author = Fisher, Matthew PA,
	year = 1990,
	pages = 923


@articlebahri_uncertainty_2008,
	title = An uncertainty principle for quaternion Fourier transform,
	volume = 56,
	number = 9,
	journal = Computers & Mathematics with Applications,
	author = Bahri, Mawardi and Hitzer, Eckhard SM and Hayashi, Akihisa and Ashino, Ryuichi,
	year = 2008,
	pages = 2398–2410


@incollectionheisenberg_uber_1985,
	title = Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik,
	booktitle = Original Scientific Papers Wissenschaftliche Originalarbeiten,
	publisher = Springer,
	author = Heisenberg, Werner,
	year = 1985,
	pages = 478–504


@bookwheeler_quantum_2014,
	title = Quantum theory and measurement,
	publisher = Princeton University Press,
	author = Wheeler, John Archibald and Zurek, Wojciech Hubert,
	year = 2014


@articlekalnins_group_1976,
	title = The Group O(4), Separation of Variables and the Hydrogen Atom,
	volume = 30,
	number = 4,
	journal = SIAM Journal on Applied Mathematics,
	author = Kalnins, E. G. and Miller, W. and Winternitz, P.,
	year = 1976,
	pages = 630–664


@incollectionisacker_o4_1991,
	title = O(4) Symmetry and Angular Momentum Theory in Four Dimensions,
	isbn = 978-1-4613-6643-0 978-1-4615-3696-3,
	url = https://link.springer.com/chapter/10.1007/978-1-4615-3696-3_16,
	abstract = The theory of angular momentum in four-dimensional space is developed by studying in detail the properties of O(4), the group of rotations in four dimensions. Properties of O(4) Clebsch-Gordan coefficients are reviewed. Making use of the isomorphism O(4) ≈ O(3) ⊗ O(3), general expressions are derived for O(4) recoupling coefficients in terms of the corresponding ones in O(3) (6j-, 9j-,… symbols). The Wigner-Eckart theorem is discussed for O(4) and explicit formulas are given for the associated tensor calculus. The Pauli principle is generalized to four-dimensional space by establishing a connection between O(4) tensor character and statistics (Bose or Fermi). The equations for computing coefficients of fractional parentage in O(4) are derived. The applicability of this formalism to atomic and molecular physics problems is discussed.,
	language = en,
	urldate = 2018-05-02,
	booktitle = Symmetries in Science V,
	publisher = Springer, Boston, MA,
	author = Isacker, P. Van,
	year = 1991,
	doi = 10.1007/978-1-4615-3696-3_16,
	pages = 323–340


@articlefranz_vortex-lattice_1995,
	title = Vortex-lattice melting in two-dimensional superconducting networks and films,
	volume = 51,
	number = 10,
	journal = Physical Review B,
	author = Franz, M. and Teitel, S.,
	year = 1995,
	pages = 6551


@articleseung_defects_1988,
	title = Defects in flexible membranes with crystalline order,
	volume = 38,
	number = 2,
	journal = Physical Review A,
	author = Seung, H. S. and Nelson, David R.,
	year = 1988,
	pages = 1005


@articleolsson_kink-antikink_2005,
	title = Kink-antikink unbinding transition in the two-dimensional fully frustrated $XY$ model,
	volume = 71,
	url = https://link.aps.org/doi/10.1103/PhysRevB.71.104423,
	doi = 10.1103/PhysRevB.71.104423,
	abstract = We carry out numerical simulations to directly confirm the existence of a kink-antikink unbinding transition along Ising-like domain walls in the two-dimensional fully frustrated XY model. We comment on the possible implications of kink-antikink unbinding for the bulk phase transition of the model.,
	number = 10,
	urldate = 2018-05-09,
	journal = Physical Review B,
	author = Olsson, Peter and Teitel, S.,
	month = mar,
	year = 2005,
	pages = 104423


@articlehermele_fate_2005,
	title = Fate of the Josephson effect in thin-film superconductors,
	volume = 1,
	number = 2,
	journal = Nature Physics,
	author = Hermele, Michael and Refael, Gil and Fisher, Matthew PA and Goldbart, Paul M.,
	year = 2005,
	pages = 117


@articlemosseri_frustration_2014,
	series = Quasicristaux / Quasicrystals,
	title = Frustration and defects in non-periodic solids,
	volume = 15,
	doi = 10.1016/j.crhy.2013.09.006,
	number = 1,
	journal = Comptes Rendus Physique,
	author = Mosseri, Rémy and Sadoc, Jean-François,
	month = jan,
	year = 2014,
	keywords = Aperiodicity, Complex intermetallic phases, Défauts, Defects, Frustrations, Périodicité, Phases intermétalliques complexes,
	pages = 90–99


@booksetton_carbon_2002,
	title = Carbon molecules and materials,
	publisher = CRC Press,
	author = Setton, Ralph and Bernier, Patrick and Lefrant, Serge,
	year = 2002


@articlesteinhardt_icosahedral_1981,
	title = Icosahedral Bond Orientational Order in Supercooled Liquids,
	volume = 47,
	doi = 10.1103/PhysRevLett.47.1297,
	number = 18,
	journal = Physical Review Letters,
	author = Steinhardt, Paul J. and Nelson, David R. and Ronchetti, Marco,
	month = nov,
	year = 1981,
	pages = 1297–1300


@articletisza_theory_1947,
	title = The Theory of Liquid Helium,
	volume = 72,
	doi = 10.1103/PhysRev.72.838,
	number = 9,
	journal = Physical Review,
	author = Tisza, Laszlo,
	month = nov,
	year = 1947,
	pages = 838–854


@bookannett_superconductivity_2004,
	title = Superconductivity, superfluids and condensates,
	volume = 5,
	publisher = Oxford University Press,
	author = Annett, James F.,
	year = 2004


@articlekirby_eight_1982,
	title = Eight faces of the Poincaré homology 3-sphere,
	volume = 37,
	number = 5,
	journal = Uspekhi Matematicheskikh Nauk,
	author = Kirby, R. C. and Scharlemann, M. G.,
	year = 1982,
	pages = 139–159


@articlelamoen_crystal_1994,
	title = Crystal field, orientational order, and lattice contraction in solid C60,
	volume = 101,
	issn = 0021-9606,
	url = http://aip.scitation.org/doi/abs/10.1063/1.467768,
	doi = 10.1063/1.467768,
	number = 2,
	urldate = 2018-01-27,
	journal = The Journal of Chemical Physics,
	author = Lamoen, D. and Michel, K. H.,
	month = jul,
	year = 1994,
	pages = 1435–1443


@articleleaf_combined_2016,
	title = A Combined Monte Carlo and Hückel Theory Simulation of Orientational Ordering in C60 Assemblies,
	volume = 120,
	issn = 1932-7447,
	url = http://dx.doi.org/10.1021/acs.jpcc.6b00638,
	doi = 10.1021/acs.jpcc.6b00638,
	abstract = Orientational ordering of C60 molecules within monolayer and multilayer islands is a regularly observed phenomenon in scanning tunneling microscopy (STM) studies. Here we simulate the orientational ordering seen in STM images via a novel combination of Monte Carlo and Hückel theory methods and compare to experimental data. A measure of the repulsive interaction energy between two adjacent C60 molecules is precalculated by estimating and processing the electron density distribution between them. Many combinations of molecular orientations are considered to encompass all the details of the molecular orbitals. Precalculated intermolecular interaction energies are inputted into a simulated C60 island. Here, the center position of each molecule is fixed, but the molecules are allowed to rotate freely around their centers. A minimum in the total island free energy is sought by sequentially picking molecules at random and rotating them according to their neighbors. Results show significant correlation with experimentally observed features in both mono- and multilayered islands on a variety of different substrates.,
	number = 15,
	urldate = 2018-01-27,
	journal = The Journal of Physical Chemistry C,
	author = Leaf, Jeremy and Stannard, Andrew and Jarvis, Samuel P. and Moriarty, Philip and Dunn, Janette L.,
	month = apr,
	year = 2016,
	pages = 8139–8147


@articlelitvin_icosahedral_1991,
	title = The icosahedral point groups,
	volume = 47,
	number = 2,
	journal = Acta Crystallographica Section A: Foundations of Crystallography,
	author = Litvin, Daniel B.,
	year = 1991,
	pages = 70–73


@articlekorkinge_sur_1877,
	title = Sur les formes quadratiques positives,
	volume = 11,
	number = 2,
	journal = Mathematische Annalen,
	author = Korkinge, A. and Zolotareff, G.,
	year = 1877,
	pages = 242–292


@articlekorkinge_sur_1877-1,
	title = Sur les formes quadratiques positives,
	volume = 11,
	issn = 0025-5831, 1432-1807,
	url = https://link.springer.com/article/10.1007/BF01442667,
	doi = 10.1007/BF01442667,
	language = fr,
	number = 2,
	urldate = 2018-01-28,
	journal = Mathematische Annalen,
	author = Korkinge, A. and Zolotareff, G.,
	month = jun,
	year = 1877,
	pages = 242–292


@bookcheng_phase_2008,
	title = Phase transitions in polymers: the role of metastable states,
	shorttitle = Phase transitions in polymers,
	publisher = Elsevier,
	author = Cheng, Stephen ZD,
	year = 2008


@bookweisstein_hypersphere_2017,
	title = Hypersphere Packing,
	copyright = Copyright 1999-2018 Wolfram Research, Inc. See http://mathworld.wolfram.com/about/terms.html for a full terms of use statement.,
	url = http://mathworld.wolfram.com/HyperspherePacking.html,
	abstract = In two dimensions, there are two periodic circle packings for identical circles: square lattice and hexagonal lattice. In 1940, Fejes Tóth proved that the hexagonal lattice is the densest of all possible plane packings (Conway and Sloane 1993, pp. 8-9). The analog of face-centered cubic packing is the densest lattice packing in four and five dimensions. In eight dimensions, the densest lattice packing is made up of two copies of face-centered cubic. In six and seven dimensions, the...,
	language = en,
	urldate = 2018-01-28,
	author = Weisstein, Eric W.,
	year = 2017


@articlelord_sphere_2001-1,
	title = Sphere packing, helices and the polytope (3, 3, 5),
	volume = 15,
	number = 3,
	journal = The European Physical Journal D-Atomic, Molecular, Optical and Plasma Physics,
	author = Lord, E. A. and Ranganathan, S.,
	year = 2001,
	pages = 335–343


@articleheinekamp_spin-correlation_1985,
	title = Spin-correlation function in the two-dimensional XY model,
	volume = 32,
	url = https://link.aps.org/doi/10.1103/PhysRevB.32.4528,
	doi = 10.1103/PhysRevB.32.4528,
	abstract = We study the two-spin correlation function in the high-temperature phase of the two-dimensional XY model. We derive a roughening representation of this function in the generalized Villain model, which is useful for high-temperature analysis. In the ordinary Villain model, we use duality to show that the correlation function is identical at high temperatures to the spin-correlation function in the two-dimensional Ising model. We use this result, together with spin-wave analysis, to perform a Nelson-Rudnick matching calculation of the spin-correlation function in the ordinary Villain model, thereby obtaining an approximate expression for this function at all length scales and temperatures above Tc.,
	number = 7,
	urldate = 2018-02-02,
	journal = Physical Review B,
	author = Heinekamp, Scott W. and Pelcovits, Robert A.,
	month = oct,
	year = 1985,
	pages = 4528–4538


@articlerice_superconductivity_1965,
	title = Superconductivity in One and Two Dimensions,
	volume = 140,
	url = https://link.aps.org/doi/10.1103/PhysRev.140.A1889,
	doi = 10.1103/PhysRev.140.A1889,
	abstract = The effect of thermodynamic fluctuations on off-diagonal long-range order (ODLRO) is discussed. The two-particle Yang correlation function is calculated using the Ginzburg-Landau theory allowing such fluctuations. The behavior of the correlation function at large separation is examined and it is found to be consistent with Yang's criterion for ODLRO only in three dimensions. In one and two dimensions Yang's criterion is not satisfied.,
	number = 6A,
	urldate = 2018-02-05,
	journal = Physical Review,
	author = Rice, T. M.,
	month = dec,
	year = 1965,
	pages = A1889–A1891


@articlecanali_spin-spin_1993,
	title = Spin-spin correlation functions for the square-lattice Heisenberg antiferromagnet at zero temperature,
	volume = 48,
	url = https://link.aps.org/doi/10.1103/PhysRevB.48.3264,
	doi = 10.1103/PhysRevB.48.3264,
	abstract = We have calculated the dynamical transverse and longitudinal spin-correlation functions for the two-dimensional Heisenberg antiferromagnet at zero temperature, by the Dyson-Maleev spin-wave theory to second order in perturbation theory. The transverse correlation function is characterized by a dominant one-magnon peak and a broad three-magnon continuum. For spin 1/2 the contribution of the three-magnon excitations is small but not negligible, and might be detected in highly sensitive neutron-scattering experiments in the undoped layered cuprates. We have also computed the transverse equal-time correlations and compared the results with recent series-expansion estimates. The good agreement between the two formalisms reinforces the validity of spin-wave theory. The longitudinal structure factor, to leading order, displays a two-peak structure similar to that obtained by the Schwinger-boson mean-field formalism. The magnon interaction reduces the second peak, in some cases substantially. We discuss how umklapp processes affect the multiple-magnon excitations. We have finally computed the staggered magnetization and transverse susceptibility corrected to second order. For spin 1/2 we find m=0.3069±0.00020 for the staggered magnetization, and Zχ=0.4844±0.00010 for the susceptibility renormalization constant, in agreement with the results obtained by other techniques.,
	number = 5,
	urldate = 2018-02-06,
	journal = Physical Review B,
	author = Canali, C. M. and Wallin, Mats,
	month = aug,
	year = 1993,
	pages = 3264–3280


@articlesadoc_orientational_1985,
	title = Orientational order in disordered systems,
	volume = 46,
	number = C9,
	journal = Le Journal de Physique Colloques,
	author = Sadoc, J. F.,
	year = 1985,
	pages = C9–79


@booklipcshutz_linear_2009,
	title = Linear Algebra. Schaum’s Outlines,
	publisher = McGraw Hill, USA,
	author = Lipcshutz, S. and Lipson, M.,
	year = 2009


@articlesondhi_continuous_1997,
	title = Continuous quantum phase transitions,
	volume = 69,
	number = 1,
	journal = Reviews of modern physics,
	author = Sondhi, S. L. and Girvin, S. M. and Carini, J. P. and Shahar, D.,
	year = 1997,
	pages = 315


@articleteo_topological_2010,
	title = Topological defects and gapless modes in insulators and superconductors,
	volume = 82,
	number = 11,
	journal = Physical Review B,
	author = Teo, Jeffrey CY and Kane, Charles L.,
	year = 2010


@articlekapikranian_spin-spin_2012,
	title = Spin-spin correlation function of the two-dimensional XY model with weak site or bond dilution,
	volume = 85,
	number = 9,
	journal = Physical Review B,
	author = Kapikranian, Oleksandr,
	year = 2012,
	pages = 094405


@articlekapikranian_spin-spin_2012-1,
	title = Spin-spin correlation function of the two-dimensional XY model with weak site or bond dilution,
	volume = 85,
	url = https://link.aps.org/doi/10.1103/PhysRevB.85.094405,
	doi = 10.1103/PhysRevB.85.094405,
	number = 9,
	urldate = 2018-02-05,
	journal = Physical Review B,
	author = Kapikranian, Oleksandr,
	month = mar,
	year = 2012


@bookadler_physics_2012,
	title = Physics of Disordered Materials,
	publisher = Springer Science & Business Media,
	author = Adler, David,
	year = 2012,
	keywords = Science / Physics / Condensed Matter, Science / Physics / Atomic & Molecular, Science / Chemistry / Analytic, Science / Spectroscopy & Spectrum Analysis


@articlejensen_kosterlitz-thouless_2003,
	title = The Kosterlitz-Thouless Transition,
	journal = Lecture notes on Kosterlitz-Thouless transition in the XY model, Imperial College,
	author = Jensen, Henrik Jeldtoft,
	year = 2003


@articleramirez-santiago_correlation_1992,
	title = Correlation Functions in the Fully Frustrated 2D XY Model,
	volume = 68,
	url = https://link.aps.org/doi/10.1103/PhysRevLett.68.1224,
	doi = 10.1103/PhysRevLett.68.1224,
	abstract = We present a detailed analysis of the critical properties of the two-dimensional XY model at full frustration. We calculate U(1) and Z2 gauge-invariant correlation functions, as well as the chiral magnetization and susceptibility, by using extensive Monte Carlo simulations in lattices up to 240×240. The best fits to our results give νU(1)=0.3069, ηU(1)(TcU(1)=0.446)=0.1915, while νZ2=0.875, 2βZ2=0.1936, 2γZ2=1.82, 2γ′Z2=1.025. These novel results are quantitatively different from those expected for separate 2D XY and 2D Ising models.,
	number = 8,
	urldate = 2018-02-24,
	journal = Physical Review Letters,
	author = Ramirez-Santiago, Guillermo and José, Jorge V.,
	month = feb,
	year = 1992,
	pages = 1224–1227


@articleshirahama_localized_2008,
	title = Localized Bose–Einstein Condensation of 4He Confined in Nanoporous Media,
	volume = 77,
	number = 11,
	journal = Journal of the Physical Society of Japan,
	author = Shirahama, Keiya and Yamamoto, Keiichi and Shibayama, Yoshiyuki,
	year = 2008,
	pages = 111011


@articleeucken_uber_1911,
	title = Über die temperaturabhängigkeit der wärmeleitfähigkeit fester nichtmetalle,
	volume = 339,
	number = 2,
	journal = Annalen der Physik,
	author = Eucken, A.,
	year = 1911,
	pages = 185–221


@articleschrodinger_stetige_1926,
	title = Der stetige Übergang von der Mikro-zur Makromechanik,
	volume = 14,
	number = 28,
	journal = Naturwissenschaften,
	author = Schrödinger, Erwin,
	year = 1926,
	pages = 664–666


@articlekeesom_heat_1936,
	title = On the heat conductivity of liquid helium,
	volume = 3,
	issn = 0031-8914,
	doi = 10.1016/S0031-8914(36)80312-7,
	number = 5,
	journal = Physica,
	author = Keesom, W. H. and Keesom, A. P.,
	month = may,
	year = 1936,
	pages = 359–360


@booksachdev_quantum_2011,
	title = Quantum phase transitions,
	publisher = Cambridge University Press, New York,
	author = Sachdev, Subir,
	year = 2011


@bookkleinert_gauge_1989,
	title = Gauge Fields in Condensed Matter: Vol. 1: Superflow and Vortex Lines (Disorder Fields, Phase Transitions) Vol. 2: Stresses and Defects (Differential Geometry, Crystal Melting),
	shorttitle = Gauge Fields in Condensed Matter,
	publisher = World Scientific,
	author = Kleinert, Hagen,
	year = 1989


@incollectionfazio_charges_1992,
	title = Charges and Vortices in Josephson Junction Arrays,
	booktitle = Single-Electron Tunneling and Mesoscopic Devices,
	publisher = Springer,
	author = Fazio, Rosario and Schön, Gerd,
	year = 1992,
	pages = 105–120


@bookherbut_modern_2007,
	title = A modern approach to critical phenomena,
	publisher = Cambridge University Press,
	author = Herbut, Igor,
	year = 2007


@articlemermin_crystalline_1968,
	title = Crystalline order in two dimensions,
	volume = 176,
	number = 1,
	journal = Physical Review,
	author = Mermin, N. David,
	year = 1968,
	pages = 250


@bookkauffman_knots_2001,
	title = Knots and physics,
	volume = 1,
	publisher = World scientific,
	author = Kauffman, Louis H.,
	year = 2001


@articlevolovik_investigation_1977,
	title = Investigation of singularities in superfluid He3 in liquid crystals by the homotopic topology methods,
	volume = 72,
	journal = Zh. Eksp. Teor. Fiz,
	author = Volovik, G. E. and Mineev, V. P.,
	year = 1977,
	pages = 22562274


@incollectionangell_relaxation_1990,
	title = Relaxation, Glass Formation, Nucleation, & Rupture in Normal and “Water-Like” Liquids at Low Temperatures and/or Negative Pressures,
	booktitle = Correlations and Connectivity,
	publisher = Springer,
	author = Angell, C. Austen,
	year = 1990,
	pages = 133–160


@incollectionrobert_monte_2014,
	title = Monte Carlo Methods,
	copyright = Copyright © 2014 John Wiley & Sons, Ltd. All rights reserved.,
	abstract = With the prevalence of high-powered computing, Monte Carlo methods are increasingly used in a wide range of disciplines. In this article, we review some of the principles behind these methods, note the relationship with other techniques used in systems reliability, and demonstrate some methods in practice. In particular, the accept–reject algorithm, the importance sampler, and the method of composition are highlighted here. While this is not the central topic of the introduction, we also mention the connections with Markov chain Monte Carlo (MCMC) methods.,
	language = en,
	booktitle = Wiley StatsRef: Statistics Reference Online,
	publisher = John Wiley & Sons, Ltd,
	author = Robert, Christian P.,
	year = 2014,
	keywords = Monte Carlo, antithetic variables, composition, correlation, ensemble methods, importance sampling, Markov chain Monte Carlo methods, rejection


@articleabrikosov_type_2003,
	title = Type II superconductors and the vortex lattice,
	volume = 5,
	journal = Nobel Lecture,
	author = Abrikosov, Alexei A.,
	year = 2003


@articleavenel_observation_1985,
	title = Observation of Singly Quantized Dissipation Events Obeying the Josephson Frequency Relation in the Critical Flow of Superfluid 4-He through an Aperture,
	volume = 55,
	doi = 10.1103/PhysRevLett.55.2704,
	number = 24,
	journal = Physical Review Letters,
	author = Avenel, O. and Varoquaux, E.,
	month = dec,
	year = 1985,
	pages = 2704–2707


@articleavenel_josephson_1988,
	title = Josephson effect and quantum phase slippage in superfluids,
	volume = 60,
	doi = 10.1103/PhysRevLett.60.416,
	abstract = We describe the operation of a hydromechanical resonator immersed in 4He and 3B superfluids and opened on the main bath by two holes, a micro-orifice acting as a weak link and a long parallel channel. Transitions between adjacent quantum states differing by one hydrodynamic circulation quantum can be induced coherently, yielding a succession of steps arranged in a staircase pattern. In 3He at about 0.8 mK and 0 bar, a nearly ideal, nondissipative hydrodynamic Josephson effect can be observed.,
	number = 5,
	journal = Physical Review Letters,
	author = Avenel, O. and Varoquaux, E.,
	month = feb,
	year = 1988,
	pages = 416–419


@articlesadoc_e8_1993-1,
	title = The E8 lattice and quasicrystals,
	volume = 153,
	journal = Journal of non-crystalline solids,
	author = Sadoc, J. F. and Mosseri, R.,
	year = 1993,
	pages = 247–252


@articledavid_crystal_1991,
	title = Crystal structure and bonding of ordered C60,
	volume = 353,
	url = https://www.researchgate.net/profile/T_J_S_Dennis/publication/232753712_Crystal_Structure_and_Bonding_of_Ordered_C60/links/0deec527aa364a2bdd000000/Crystal-Structure-and-Bonding-of-Ordered-C60.pdf,
	number = 6340,
	journal = Nature,
	author = David, William IF and Ibberson, Richard M. and Matthewman, Judy C. and Prassides, Kosmas and Dennis, T. John S. and Hare, Jonathan P. and Kroto, Harold W. and Taylor, Roger and Walton, David RM,
	year = 1991,
	pages = 147–149


@articlephillips_t3_1985,
	title = T3 specific-heat anomaly in network solids,
	volume = 32,
	url = http://link.aps.org/doi/10.1103/PhysRevB.32.5356,
	doi = 10.1103/PhysRevB.32.5356,
	number = 8,
	author = Phillips, J. C.,
	year = 1985,
	keywords = fractal, fracton, tunneling, network, heat capacity,
	pages = 5356–5361


@bookreeves_introduction_2014,
	title = An introduction to topological defects in field theories,
	author = Reeves, Daniel B,
	year = 2014


@articlemilsted_matrix_2016,
	title = Matrix product states and the non-Abelian rotor model,
	volume = 93,
	url = https://link.aps.org/doi/10.1103/PhysRevD.93.085012,
	doi = 10.1103/PhysRevD.93.085012,
	abstract = We use uniform matrix product states to study the (1+1)D O(2) and O(4) rotor models, which are equivalent to the Kogut-Susskind formulation of matter-free non-Abelian lattice gauge theory on a “Hawaiian earring” graph for U(1) and SU(2), respectively. Applying tangent space methods to obtain ground states and determine the mass gap and the β function, we find excellent agreement with known results, locating the Berezinskii-Kosterlitz-Thouless transition for O(2) and successfully entering the asymptotic weak-coupling regime for O(4). To obtain a finite local Hilbert space, we truncate in the space of generalized Fourier modes of the gauge group, comparing the effects of different cutoff values. We find that higher modes become important in the crossover and weak-coupling regimes of the non-Abelian theory, where entanglement also suddenly increases. This could have important consequences for tensor network state studies of Yang-Mills on higher-dimensional graphs.,
	number = 8,
	journal = Physical Review D,
	author = Milsted, Ashley,
	month = apr,
	year = 2016,
	pages = 085012


@articlephillips_two-level_1987,
	title = Two-level states in glasses,
	volume = 50,
	issn = 0034-4885,
	url = http://stacks.iop.org/0034-4885/50/i=12/a=003,
	doi = 10.1088/0034-4885/50/12/003,
	abstract = This review covers a wide range of experimental and theoretical studies of two-level or tunnelling states in glasses. Emphasis is on fundamental physics rather than a detailed comparison of experiment and theory. Sections cover the static and dynamic properties of tunnelling states, their contribution to thermal properties and their response to weak and strong electric and acoustic fields, both steady state and pulsed. A section on metallic glasses focuses on the importance of electron tunnelling-state interactions, and a final section illustrates approaches to a microscopic description by means of selected examples.,
	language = en,
	number = 12,
	urldate = 2016-10-11,
	journal = Reports on Progress in Physics,
	author = Phillips, W. A.,
	year = 1987,
	pages = 1657


@bookhanson_visualizing_2006,
	title = Visualizing Quaternions,
	publisher = San Francisco: The Morgan Kaufmann Series in Interactive 3D Technology,
	author = Hanson, A. J.,
	year = 2006


@articleskyrme_non-linear_1961,
	title = A Non-Linear Field Theory,
	volume = 260,
	issn = 1364-5021, 1471-2946,
	url = http://rspa.royalsocietypublishing.org/content/260/1300/127,
	doi = 10.1098/rspa.1961.0018,
	abstract = A unified field theory of mesons and their particle sources is proposed and considered in its classical aspects. The theory has static solutions of a singular nature, but finite energy, characterized by spin directions; the number of such entities is a rigorously conserved constant of motion; they interact with an external meson field through a derivative-type coupling with the spins, akin to the formalism of strong-coupling meson theory. There is a conserved current identifiable with isobaric spin, and another that may be related to hypercharge. The postulates include one constant of the dimensions of length, and another that is conjectured necessarily to have the value $\textbackslashhslas{h}$c, or perhaps $\textbackslashfrac{1}{2}\textbackslashhslas{h}$c, in the quantized theory.,
	language = en,
	number = 1300,
	urldate = 2016-08-04,
	journal = Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences,
	author = Skyrme, T. H. R.,
	month = feb,
	year = 1961,
	pages = 127–138


@bookkittel_introduction_1996-1,
	title = Introduction to solid state physics,
	volume = 7,
	publisher = Wiley New York,
	author = Kittel, C. and McEuen, P.,
	year = 1996,
	keywords = polycrystalline


@articlephillips_tunneling_1972,
	title = Tunneling states in amorphous solids,
	volume = 7,
	issn = 0022-2291,
	number = 3,
	journal = Journal of Low Temperature Physics,
	author = Phillips, W. A.,
	year = 1972,
	keywords = amorphous, fractal, fracton, tunneling,
	pages = 351–360


@bookdove_introduction_1993,
	title = Introduction to lattice dynamics,
	volume = 4,
	url = https://books.google.com/books?hl=en   lr=   id=jpe2aYwF3v0C   oi=fnd   pg=PR13   dq=dove+lattice+dynamics   ots=NQe2yBL_rO   sig=tfHVOeQTUOQmMPPQlq3U_H1XAyA,
	urldate = 2016-06-01,
	publisher = Cambridge university press,
	author = Dove, M. T.,
	year = 1993


@articlekittel_interpretation_1949,
	title = Interpretation of the Thermal Conductivity of Glasses,
	volume = 75,
	url = http://link.aps.org/doi/10.1103/PhysRev.75.972,
	doi = 10.1103/PhysRev.75.972,
	number = 6,
	journal = Phys. Rev.,
	author = Kittel, C.,
	year = 1949,
	keywords = localization, (amorphous) glass,
	pages = 972–974


@articlezeller_thermal_1971,
	title = Thermal Conductivity and Specific Heat of Noncrystalline Solids,
	volume = 4,
	url = http://link.aps.org/doi/10.1103/PhysRevB.4.2029,
	doi = 10.1103/PhysRevB.4.2029,
	number = 6,
	journal = Phys. Rev. B,
	author = Zeller, R. C. and Pohl, R. O.,
	year = 1971,
	keywords = amorphous, fractal, fracton, thermal conductivity, heat capacity, model,
	pages = 2029–2041


@bookkleman_soft_2007,
	title = Soft Matter Physics: An Introduction,
	isbn = 978-0-387-21759-8,
	publisher = Springer Science & Business Media,
	author = Kleman, Maurice and Laverntovich, Oleg D.,
	month = may,
	year = 2007,
	keywords = Science / Physics / General, Science / Chemistry / Organic, Science / Physics / Condensed Matter, Technology & Engineering / Materials Science, Science / Physics / Atomic & Molecular, Technology & Engineering / Textiles & Polymers, Science / Chemistry / Analytic


@articlepereira_metric_2013,
	title = Metric approach for sound propagation in nematic liquid crystals,
	volume = 87,
	url = https://journals.aps.org/pre/abstract/10.1103/PhysRevE.87.022506,
	number = 2,
	urldate = 2017-06-03,
	journal = Physical Review E,
	author = Pereira, E. and Fumeron, Sébastien and Moraes, F.,
	year = 2013,
	pages = 022506


@articlecahill_heat_1989,
	title = Heat flow and lattice vibrations in glasses,
	volume = 70,
	issn = 0038-1098,
	doi = 10.1016/0038-1098(89)90630-3,
	number = 10,
	journal = Solid State Commun.,
	author = Cahill, David G. and Pohl, R. O.,
	year = 1989,
	keywords = amorphous,
	pages = 927 – 930


@articlenelson_order_1983,
	title = Order, frustration, and defects in liquids and glasses,
	volume = 28,
	url = http://link.aps.org/doi/10.1103/PhysRevB.28.5515,
	doi = 10.1103/PhysRevB.28.5515,
	abstract = A defect description of liquids and metallic glasses is developed. In two dimensions, surfaces of constant negative curvature contain an irreducible density of point disclinations in a hexatic order parameter. Analogous defect lines in an icosahedral order parameter appear in three-dimensional flat space. Frustration in tetrahedral particle packings forces disclination lines into the medium in a way reminiscent of Abrikosov flux lines in a type-II superconductor and of uniformly frustrated spin-glasses. The defect density is determined by an isotropic curvature mismatch, and the resulting singular lines run in all directions. The Frank-Kasper phases of transition-metal alloys are ordered networks of these lines, which, when disordered, provide an appealing model for structure in metallic glasses.,
	number = 10,
	urldate = 2016-01-19,
	journal = Physical Review B,
	author = Nelson, David R.,
	month = nov,
	year = 1983,
	pages = 5515–5535


@articlesethna_frustration_1983,
	title = Frustration and Curvature: Glasses and the Cholesteric Blue Phase,
	volume = 51,
	shorttitle = Frustration and Curvature,
	url = http://link.aps.org/doi/10.1103/PhysRevLett.51.2198,
	doi = 10.1103/PhysRevLett.51.2198,
	abstract = An analogy is drawn between continuum elastic theories of the blue phase of cholesteric liquid crystals and recent theories of frustration in configurational glasses. Both involve the introduction of a lattice of disclination lines to relieve frustration; the frustration is due to an intrinsic curvature in the natural form of parallel transport. A continuum theory of configurational glasses is proposed.,
	number = 24,
	urldate = 2016-01-19,
	journal = Physical Review Letters,
	author = Sethna, James P.,
	month = dec,
	year = 1983,
	pages = 2198–2201


@articlestillwell_story_2001,
	title = The story of the 120-cell,
	volume = 48,
	url = http://davidsenouf.com/wp-content/uploads/2012/02/The-Story-of-the-120-Cell.pdf,
	number = 1,
	urldate = 2016-03-13,
	journal = Notices of the AMS,
	author = Stillwell, John,
	year = 2001


@articlestuart_reactive_2000,
	title = A reactive potential for hydrocarbons with intermolecular interactions,
	volume = 112,
	issn = 0021-9606, 1089-7690,
	url = http://scitation.aip.org/content/aip/journal/jcp/112/14/10.1063/1.481208,
	doi = 10.1063/1.481208,
	abstract = A potential function is presented that can be used to model both chemical reactions and intermolecular interactions in condensed-phase hydrocarbon systems such as liquids,graphite, and polymers. This potential is derived from a well-known dissociable hydrocarbon force field, the reactive empirical bond-order potential. The extensions include an adaptive treatment of the nonbonded and dihedral-angle interactions, which still allows for covalent bonding interactions. Torsional potentials are introduced via a novel interaction potential that does not require a fixed hybridization state. The resulting model is intended as a first step towards a transferable, empirical potential capable of simulating chemical reactions in a variety of environments. The current implementation has been validated against structural and energetic properties of both gaseous and liquid hydrocarbons, and is expected to prove useful in simulations of hydrocarbon liquids,thin films, and other saturated hydrocarbon systems.,
	number = 14,
	urldate = 2014-08-20,
	journal = The Journal of Chemical Physics,
	author = Stuart, Steven J. and Tutein, Alan B. and Harrison, Judith A.,
	month = apr,
	year = 2000,
	keywords = Thin film structure, Intermolecular forces, Liquid structure simulation, Chemical reactions, Liquid thin films,
	pages = 6472–6486


@articlesteinhardt_bond-orientational_1983,
	title = Bond-orientational order in liquids and glasses,
	volume = 28,
	doi = 10.1103/PhysRevB.28.784,
	number = 2,
	journal = Physical Review B,
	author = Steinhardt, Paul J. and Nelson, David R. and Ronchetti, Marco,
	month = jul,
	year = 1983,
	keywords = polycrystalline, (polycrystalline), tetrahedral, unread,
	pages = 784–805


@articleslack_thermal_1964,
	title = Thermal Conductivity of Pure and Impure Silicon, Silicon Carbide, and Diamond,
	volume = 35,
	url = http://link.aip.org/link/?JAP/35/3460/1,
	doi = 10.1063/1.1713251,
	number = 12,
	author = Slack, Glen A.,
	year = 1964,
	pages = 3460–3466


@articleorbach_phonon_1993,
	title = Phonon localization and transport in disordered systems,
	volume = 164–166, Part 2,
	issn = 0022-3093,
	doi = 10.1016/0022-3093(93)91147-U,
	number = 0,
	journal = Journal of Non-Crystalline Solids,
	author = Orbach, R.,
	year = 1993,
	keywords = fractal, fracton, localization, disordered, amorphous theory, theory,
	pages = 917 – 922


@articletea_thermal_1993,
	title = Thermal conductivity of C60 and C70 crystals,
	volume = 56,
	issn = 0947-8396,
	doi = 10.1007/BF00539478,
	language = English,
	number = 3,
	journal = Applied Physics A,
	author = Tea, N.H. and Yu, R.-C. and Salamon, M.B. and Lorents, D.C. and Malhotra, R. and Ruoff, R.S.,
	year = 1993,
	keywords = unread, c60, fullerene, 66.70.+f, 61.50.−f, 64.70.Pf,
	pages = 219–225


@articlerandall_x-ray_1930,
	title = X-ray Diffraction and the Structure of Vitreous Solids — I,
	volume = 75,
	issn = 2196-7105,
	url = http://www.degruyter.com/view/j/zkri.1930.75.issue-1/zkri-1930-0114/zkri-1930-0114.xml,
	doi = 10.1515/zkri-1930-0114,
	number = 1,
	urldate = 2016-05-27,
	journal = Zeitschrift für Kristallographie - Crystalline Materials,
	author = Randall, J. T. and Rooksby, H. P. and Cooper, B. S.,
	year = 1930,
	pages = 196–214


@articlenakayama_increase_1999,
	title = On the increase of thermal conductivity in glasses above the plateau region,
	volume = 263–264,
	issn = 0921-4526,
	doi = 10.1016/S0921-4526(98)01472-0,
	number = 0,
	journal = Physica B: Condensed Matter,
	author = Nakayama, T. and Orbach, R. L.,
	year = 1999,
	keywords = fractal, fracton, (amorphous) glass,
	pages = 261 – 263


@articlevenkataraman_curved_1985,
	title = Curved space and amorphous structures part I Geometric models,
	volume = 26,
	issn = 0010-7514,
	url = http://www.tandfonline.com/doi/abs/10.1080/00107518508210992,
	doi = 10.1080/00107518508210992,
	abstract = Abstract This paper offers (in two parts) a broad overview of recent developments concerning the use of curved space concepts in amorphous structures. Keeping particularly in mind nonspecialist readers, expository background material is included, wherever appropriate. Part I deals essentially with geometrical modelling, and starts with a brief recapitualtion of the famous model-building exercise due to Bernal. We then discuss the Kleman-Sadoc prescription for realizing amorphous structures as mappings of spherical polytopes (the four-dimensional analogue of spherical polyhedra) onto Euclidean space. Such an approach has not only provided a fast and convenient algorithm, but more importantly, has focused attention on the line defects (disclinations) in amorphous structures. As a result, one is now able to relate these disclinations to the Frank-Kasper lines present in complex alloy structures. In turn, this has led to a qualitative scenario for the transformation of the liquid during a cool-down, into the crystalline or the amorphous state. Part II deals with attempts to provide a quantitative structure to this scenario via gauge theories. ‘One geometry cannot be more true than another; it can only be more convenient’. Poincaré (quoted by Coxeter),
	number = 6,
	urldate = 2014-06-25,
	journal = Contemporary Physics,
	author = Venkataraman, G. and Sahoo, Debendranath,
	year = 1985,
	pages = 579–615


@articletisza_transport_1938,
	title = Transport phenomena in helium II,
	volume = 141,
	number = 3577,
	journal = Nature,
	author = Tisza, Laszlo,
	year = 1938,
	pages = 913


@bookdresselhaus_group_2007,
	title = Group theory: application to the physics of condensed matter,
	shorttitle = Group theory,
	publisher = Springer Science & Business Media,
	author = Dresselhaus, Mildred S. and Dresselhaus, Gene and Jorio, Ado,
	year = 2007


@bookjose_40_2013,
	title = 40 years of Berezinskii-Kosterlitz-Thouless theory,
	publisher = World Scientific,
	author = Jose, Jorge V.,
	year = 2013


@articlesugawa_second_2018,
	title = Second Chern number of a quantum-simulated non-Abelian Yang monopole,
	volume = 360,
	number = 6396,
	journal = Science,
	author = Sugawa, Seiji and Salces-Carcoba, Francisco and Perry, Abigail R. and Yue, Yuchen and Spielman, I. B.,
	year = 2018,
	pages = 1429–1434,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/T3PYZXR3/Sugawa et al. - 2018 - Second Chern number of a quantum-simulated non-Abe.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/C545SIQW/1429.html:text/html


@articleprice_measurement_2016,
	title = Measurement of Chern numbers through center-of-mass responses,
	volume = 93,
	number = 24,
	journal = Physical Review B,
	author = Price, Hannah M. and Zilberberg, Oded and Ozawa, Tomoki and Carusotto, Iacopo and Goldman, Nathan,
	year = 2016,
	pages = 245113,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/5BEGC3C2/PhysRevB.93.html:text/html


@articlestajic_going_2018,
	title = Going beyond the first Chern number,
	volume = 360,
	copyright = Copyright © 2018 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works. http://www.sciencemag.org/about/science-licenses-journal-article-reuse,
	issn = 0036-8075, 1095-9203,
	url = http://science.sciencemag.org/content/360/6396/1416.13,
	doi = 10.1126/science.360.6396.1416-m,
	abstract = Quantum Simulation
Topological properties of physical systems are reflected in so-called Chern numbers: A nonzero Chern number typically means that a system is topologically nontrivial. Sugawa et al. engineered a cold atom system with a nonzero second Chern number, in contrast to condensed matter physics, where only the first Chern number is usually invoked. The exotic topology relates to the emergence of a type of magnetic monopole called the Yang monopole (known from theoretical high-energy physics) in a five-dimensional space of internal degrees of freedom in a rubidium Bose-Einstein condensate. The results illustrate the potential of cold atoms physics to simulate high-energy phenomena.

Science , this issue p. [1429][1]

 [1]: /lookup/doi/10.1126/science.aam9031,
	language = en,
	number = 6396,
	urldate = 2018-10-09,
	journal = Science,
	author = Stajic, Jelena,
	month = jun,
	year = 2018,
	pages = 1416–1418,
	file = Full Text PDF:/Users/carolinegorham/Zotero/storage/KKY9FVI3/Stajic - 2018 - Going beyond the first Chern number.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/SIZSSQIF/1416.html:text/html


@articlejiang_skyrmions_2017,
	title = Skyrmions in magnetic multilayers,
	journal = Physics Reports,
	author = Jiang, Wanjun and Chen, Gong and Liu, Kai and Zang, Jiadong and te Velthuis, Suzanne GE and Hoffmann, Axel,
	year = 2017,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/7V93I6WG/S0370157317302934.html:text/html;Snapshot:/Users/carolinegorham/Zotero/storage/PMFDKUMX/S0370157317302934.html:text/html


@articlejiang_skyrmions_2017-1,
	series = Skyrmions in Magnetic Multilayers,
	title = Skyrmions in magnetic multilayers,
	volume = 704,
	issn = 0370-1573,
	url = http://www.sciencedirect.com/science/article/pii/S0370157317302934,
	doi = 10.1016/j.physrep.2017.08.001,
	abstract = Symmetry breaking together with strong spin–orbit interaction gives rise to many exciting phenomena within condensed matter physics. A recent example is the existence of chiral spin textures, which are observed in magnetic systems lacking inversion symmetry. These chiral spin textures, including domain walls and magnetic skyrmions, are both fundamentally interesting and technologically promising. For example, they can be driven very efficiently by electrical currents, and exhibit many new physical properties determined by their real-space topological characteristics. Depending on the details of the competing interactions, these spin textures exist in different parameter spaces. However, the governing mechanism underlying their physical behaviors remains essentially the same. In this review article, the fundamental topological physics underlying these chiral spin textures, the key factors for materials optimization, and current developments and future challenges will be discussed. In the end, a few promising directions that will advance the development of skyrmion based spintronics will be highlighted.,
	urldate = 2018-10-09,
	journal = Physics Reports,
	author = Jiang, Wanjun and Chen, Gong and Liu, Kai and Zang, Jiadong and te Velthuis, Suzanne G. E. and Hoffmann, Axel,
	month = aug,
	year = 2017,
	keywords = Chiral spin textures, Dzyaloshinskii–Moriya interaction, Inversion symmetry breaking, Magnetic heterostructures, Magnetic skyrmion, Nanomagnetism, Race-track memory, Spin Hall effects, Spin sensitive imaging, Spin–orbit torques, Topological transport,
	pages = 1–49,
	file = ScienceDirect Full Text PDF:/Users/carolinegorham/Zotero/storage/KW7LLJIB/Jiang et al. - 2017 - Skyrmions in magnetic multilayers.pdf:application/pdf;ScienceDirect Snapshot:/Users/carolinegorham/Zotero/storage/4M4RKX7Z/S0370157317302934.html:text/html


@articlemanucharyan_fluxonium:_2009-1,
	title = Fluxonium: Single cooper-pair circuit free of charge offsets,
	volume = 326,
	shorttitle = Fluxonium,
	number = 5949,
	journal = Science,
	author = Manucharyan, Vladimir E. and Koch, Jens and Glazman, Leonid I. and Devoret, Michel H.,
	year = 2009,
	pages = 113–116,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/IUPVZLH2/Manucharyan et al. - 2009 - Fluxonium Single cooper-pair circuit free of char.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/MZJ8MGM5/113.html:text/html


@articlekoshibae_memory_2015,
	title = Memory functions of magnetic skyrmions,
	volume = 54,
	issn = 1347-4065,
	url = http://iopscience.iop.org/article/10.7567/JJAP.54.053001/meta,
	doi = 10.7567/JJAP.54.053001,
	language = en,
	number = 5,
	urldate = 2018-10-09,
	journal = Japanese Journal of Applied Physics,
	author = Koshibae, Wataru and Kaneko, Yoshio and Iwasaki, Junichi and Kawasaki, Masashi and Tokura, Yoshinori and Nagaosa, Naoto,
	month = apr,
	year = 2015,
	pages = 053001


@articlelaughlin_anomalous_1983,
	title = Anomalous quantum Hall effect: an incompressible quantum fluid with fractionally charged excitations,
	volume = 50,
	shorttitle = Anomalous quantum Hall effect,
	number = 18,
	journal = Physical Review Letters,
	author = Laughlin, Robert B.,
	year = 1983,
	pages = 1395,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/5ILH4M9G/Laughlin - 1983 - Anomalous quantum Hall effect an incompressible q.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/ZDHR22JI/PhysRevLett.50.html:text/html


@articleroy_disordered_2016,
	title = Disordered Chern insulator with a two-step Floquet drive,
	volume = 94,
	number = 21,
	journal = Physical Review B,
	author = Roy, Sthitadhi and Sreejith, G. J.,
	year = 2016,
	pages = 214203,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/72VWTBUH/Roy and Sreejith - 2016 - Disordered Chern insulator with a two-step Floquet.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/9H2ID7PW/PhysRevB.94.html:text/html


@incollectionlaughlin_elementary_1987-1,
	title = Elementary theory: the incompressible quantum fluid,
	shorttitle = Elementary theory,
	booktitle = The quantum Hall effect,
	publisher = Springer,
	author = Laughlin, Robert B.,
	year = 1987,
	pages = 233–301,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/KHUKMQC7/978-1-4684-0499-9_7.html:text/html


@articlezwerger_global_1989,
	title = Global and Local Phase Coherence in Dissipative Josephson-Junction Arrays,
	volume = 9,
	issn = 0295-5075,
	url = http://stacks.iop.org/0295-5075/9/i=5/a=003,
	doi = 10.1209/0295-5075/9/5/003,
	abstract = It is shown that at zero temperature a regular network of Josephson junctions in one or two dimensions including quantum fluctuations and dissipation has three different phases: a nonsuperconducting one with no order in the phases of locally superconducting grains and two different superconducting ones showing either long-range spatial phase coherence and a Meissner effect or local phase coherence only. The latter phase occurs for normal state sheet resistances smaller than 6.5 kΩ and may explain the corresponding observed threshold for superconductivity in thin granular films.,
	language = en,
	number = 5,
	urldate = 2018-10-06,
	journal = EPL (Europhysics Letters),
	author = Zwerger, W.,
	year = 1989,
	pages = 421,
	file = IOP Full Text PDF:/Users/carolinegorham/Zotero/storage/9C6ARAE2/Zwerger - 1989 - Global and Local Phase Coherence in Dissipative Jo.pdf:application/pdf


@articlebobbert_phase_1990-1,
	title = Phase transitions in dissipative Josephson chains,
	volume = 41,
	url = https://link.aps.org/doi/10.1103/PhysRevB.41.4009,
	doi = 10.1103/PhysRevB.41.4009,
	abstract = We study the zero-temperature phase transitions of a chain of Josephson junctions, taking into account the quantum fluctuations due to the charging energy and the effects of an Ohmic dissipation. We map the problem onto a generalized Coulomb gas model, which then is transformed into a sine-Gordon field theory. Apart from the expected dipole unbinding transition, which describes a transition between globally superconducting and resistive behavior, we find a quadrupole unbinding transition at a critical strength of the dissipation. This transition separates two superconducting states characterized by different local properties.,
	number = 7,
	urldate = 2018-10-06,
	journal = Physical Review B,
	author = Bobbert, P. A. and Fazio, R. and Schön, Gerd and Zimanyi, G. T.,
	month = mar,
	year = 1990,
	pages = 4009–4016,
	file = APS Snapshot:/Users/carolinegorham/Zotero/storage/SKRD5FYD/PhysRevB.41.html:text/html


@articlebobbert_phase_1990-2,
	title = Phase transitions in dissipative Josephson chains,
	volume = 41,
	number = 7,
	journal = Physical Review B,
	author = Bobbert, P. A. and Fazio, R. and Schön, Gerd and Zimanyi, G. T.,
	year = 1990,
	pages = 4009,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/FDLP25LE/PhysRevB.41.html:text/html


@articlekorshunov_effect_1989,
	title = Effect of dissipation on the low-temperature properties of a tunnel-junction chain,
	volume = 95,
	journal = Zh. Eksp. Teor. Fiz,
	author = Korshunov, S. E.,
	year = 1989,
	pages = 1058–1075,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/M9WBBIZB/Korshunov - 1989 - Effect of dissipation on the low-temperature prope.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/FAJRPTIA/Korshunov - 1989 - Effect of dissipation on the low-temperature prope.pdf:application/pdf


@miscnoauthor_korshunov_nodate,
	title = korshunov 1989 - Google Scholar,
	url = https://scholar.google.com/scholar?hl=en   as_sdt=0
	urldate = 2018-10-06,
	file = korshunov 1989 - Google Scholar:/Users/carolinegorham/Zotero/storage/CNCBLQ3J/scholar.html:text/html


@articlezwerger_global_1989-1,
	title = Global and local phase coherence in dissipative Josephson-junction arrays,
	volume = 9,
	number = 5,
	journal = EPL (Europhysics Letters),
	author = Zwerger, W.,
	year = 1989,
	pages = 421,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/29AWWDNS/meta.html:text/html


@articlebobbert_phase_1992,
	title = Phase transitions in dissipative Josephson chains: Monte Carlo results and response functions,
	volume = 45,
	shorttitle = Phase transitions in dissipative Josephson chains,
	url = https://link.aps.org/doi/10.1103/PhysRevB.45.2294,
	doi = 10.1103/PhysRevB.45.2294,
	abstract = A chain of Josephson junctions shunted by Ohmic resistors undergoes phase transitions at zero temperature that result from the interplay between quantum fluctuations induced by charging effects and the dissipation. The quantum-mechanical partition function expressed in terms of phase slips in space-time can be mapped onto that of a two-dimensional Coulomb gas. Due to the dissipation the interaction is anisotropic. Despite the simplicity of the model, there is no general agreement about the phase diagram and the response functions. We have performed Monte Carlo simulations to determine the zero-temperature phase boundaries. We find four phases with the absence or presence of global or local order, in all combinations. We discuss the response functions in the different phases and find interesting transport properties.,
	number = 5,
	urldate = 2018-10-06,
	journal = Physical Review B,
	author = Bobbert, P. A. and Fazio, Rosario and Schön, Gerd and Zaikin, A. D.,
	month = feb,
	year = 1992,
	pages = 2294–2304,
	file = APS Snapshot:/Users/carolinegorham/Zotero/storage/E38SEWY9/PhysRevB.45.html:text/html


@incollectiongirvin_spin_2010,
	title = Spin and Isospin: Exotic Order in Quantum Hall Ferromagnets: Spin and a peculiar kind of isospin in two-dimensional electron gases can exhibit novel counterintuitive ordering phenomena,
	shorttitle = Spin and Isospin,
	booktitle = The Multifaceted Skyrmion,
	publisher = World Scientific,
	author = Girvin, Steven M.,
	year = 2010,
	pages = 217–231,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/C3ILDRF9/Girvin - 2010 - Spin and Isospin Exotic Order in Quantum Hall Fer.pdf:application/pdf


@articlenoether_invarianten_1918,
	title = Invarianten beliebiger Differentialausdrücke,
	volume = 1918,
	journal = Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, mathematisch-physikalische Klasse,
	author = Noether, Emmy,
	year = 1918,
	pages = 37–44,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/P6R8EMWH/59011.html:text/html


@articlegobel_family_2018,
	title = The family of topological Hall effects for electrons in skyrmion crystals,
	journal = arXiv preprint arXiv:1806.06958,
	author = Göbel, Börge and Mook, Alexander and Henk, Jürgen and Mertig, Ingrid,
	year = 2018,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/XCUFANTL/Göbel et al. - 2018 - The family of topological Hall effects for electro.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/9KUGLFH9/1806.html:text/html


@articlebosma_identification_2018,
	title = Identification and tunable optical coherent control of transition-metal spins in silicon carbide,
	volume = 4,
	copyright = 2018 The Author(s),
	issn = 2056-6387,
	url = https://www.nature.com/articles/s41534-018-0097-8,
	doi = 10.1038/s41534-018-0097-8,
	abstract = A study of defects in silicon carbide could enable the integration of quantum and standard telecommunications technologies. Defects in semiconductors are attractive systems for quantum technologies as quantum states can be prepared that have both long lifetimes and bright optical properties. Their optical transitions often lie outside of telecommunication wavelengths, however, which limit their potential use in and integration with standard communication technology. Tom Bosma from the University of Groningen and an international team of collaborators now show that they can optically control molybdenum defects in silicon carbide, which have transitions at the technologically important near-infrared wavelengths, showing that this is a promising platform for interfacing quantum and telecommunications technologies.,
	language = en,
	number = 1,
	urldate = 2018-10-04,
	journal = npj Quantum Information,
	author = Bosma, Tom and Lof, Gerrit J. J. and Gilardoni, Carmem M. and Zwier, Olger V. and Hendriks, Freddie and Magnusson, Björn and Ellison, Alexandre and Gällström, Andreas and Ivanov, Ivan G. and Son, N. T. and Havenith, Remco W. A. and Wal, Caspar H. van der,
	month = oct,
	year = 2018,
	pages = 48,
	file = Full Text PDF:/Users/carolinegorham/Zotero/storage/46ESWBX6/Bosma et al. - 2018 - Identification and tunable optical coherent contro.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/7WX8YRJ3/s41534-018-0097-8.html:text/html


@articledzyaloshinsky_thermodynamic_1958,
	title = A thermodynamic theory of “weak” ferromagnetism of antiferromagnetics,
	volume = 4,
	number = 4,
	journal = Journal of Physics and Chemistry of Solids,
	author = Dzyaloshinsky, Igor,
	year = 1958,
	pages = 241–255,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/F5KJLKCZ/0022369758900763.html:text/html


@articlemuhlbauer_skyrmion_2009,
	title = Skyrmion lattice in a chiral magnet,
	volume = 323,
	number = 5916,
	journal = Science,
	author = Mühlbauer, Sebastian and Binz, Benedikt and Jonietz, F. and Pfleiderer, Christian and Rosch, Achim and Neubauer, Anja and Georgii, Robert and Böni, Peter,
	year = 2009,
	pages = 915–919,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/PS88C59J/Mühlbauer et al. - 2009 - Skyrmion lattice in a chiral magnet.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/PTT2N2NT/915.html:text/html


@bookheisenberg_einfuhrung_1967,
	title = Einführung in die einheitliche Feldtheorie der Elementarteilchen,
	publisher = Hirzel Stuttgart,
	author = Heisenberg, Werner,
	year = 1967,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/P6MRW8EG/print.html:text/html


@articlemuhlbauer_s._2009,
	title = S. Mühlbauer, B. Binz, F. Jonietz, C. Pfleiderer, A. Rosch, A. Neubauer, R. Georgii, and P. Böni, Science 323, 915 (2009).,
	volume = 323,
	journal = Science,
	author = Mühlbauer, S.,
	year = 2009,
	pages = 915


@articlebowick_cosmological_1994,
	title = The Cosmological Kibble Mechanism in the Laboratory: String Formation in Liquid Crystals,
	volume = 263,
	copyright = 1994 by the American Association for the Advancement of Science,
	issn = 0036-8075, 1095-9203,
	shorttitle = The Cosmological Kibble Mechanism in the Laboratory,
	url = http://science.sciencemag.org/content/263/5149/943,
	doi = 10.1126/science.263.5149.943,
	abstract = The production of strings (disclination lines and loops) has been observed by means of the Kibble mechanism of domain (bubble) formation in the isotropic-nematic phase transition of the uniaxial nematic liquid crystal 4-cyano-4'-n-pentylbiphenyl. The number of strings formed per bubble is about 0.6. This value is in reasonable agreement with a numerical simulation of the experiment in which the Kibble mechanism is used for the order parameter space of a uniaxial nematic liquid crystal.,
	language = en,
	number = 5149,
	urldate = 2018-10-03,
	journal = Science,
	author = Bowick, Mark J. and Chandar, L. and Schiff, E. A. and Srivastava, Ajit M.,
	month = feb,
	year = 1994,
	pmid = 17758635,
	pages = 943–945,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/H4GX8FMC/943.html:text/html


@bookabbot_flatland_1884,
	title = Flatland,
	publisher = Domaine public,
	author = Abbot, Edwin,
	year = 1884,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/2PLLTUWB/Abbot - 1884 - Flatland.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/6IQ9W7NW/Abbot - 1884 - Flatland.pdf:application/pdf


@articleboulle_room-temperature_2016,
	title = Room-temperature chiral magnetic skyrmions in ultrathin magnetic nanostructures,
	volume = 11,
	number = 5,
	journal = Nature nanotechnology,
	author = Boulle, Olivier and Vogel, Jan and Yang, Hongxin and Pizzini, Stefania and de Souza Chaves, Dayane and Locatelli, Andrea and Menteş, Tevfik Onur and Sala, Alessandro and Buda-Prejbeanu, Liliana D. and Klein, Olivier,
	year = 2016,
	pages = 449,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/47BJPK2K/Boulle et al. - 2016 - Room-temperature chiral magnetic skyrmions in ultr.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/4ILEAAHE/nnano.2015.html:text/html


@articlefert_skyrmions_2013,
	title = Skyrmions on the track,
	volume = 8,
	number = 3,
	journal = Nature nanotechnology,
	author = Fert, Albert and Cros, Vincent and Sampaio, Joao,
	year = 2013,
	pages = 152,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/GAIQ3NUF/Fert et al. - 2013 - Skyrmions on the track.pdf:application/pdf


@articlenagaosa_topological_2013,
	title = Topological properties and dynamics of magnetic skyrmions,
	volume = 8,
	number = 12,
	journal = Nature nanotechnology,
	author = Nagaosa, Naoto and Tokura, Yoshinori,
	year = 2013,
	pages = 899,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/T6R7Q9UP/Nagaosa and Tokura - 2013 - Topological properties and dynamics of magnetic sk.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/JTSW8MUI/nnano.2013.html:text/html


@articlenagaosa_topological_2013-1,
	title = Topological properties and dynamics of magnetic skyrmions,
	volume = 8,
	number = 12,
	journal = Nature nanotechnology,
	author = Nagaosa, Naoto and Tokura, Yoshinori,
	year = 2013,
	pages = 899,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/QYYSXK79/Nagaosa and Tokura - 2013 - Topological properties and dynamics of magnetic sk.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/Y5C6Z9KS/nnano.2013.html:text/html


@articlerosler_spontaneous_2006,
	title = Spontaneous skyrmion ground states in magnetic metals,
	volume = 442,
	copyright = 2006 Nature Publishing Group,
	issn = 1476-4687,
	url = https://www.nature.com/articles/nature05056,
	doi = 10.1038/nature05056,
	abstract = Since the 1950s, Heisenberg and others have addressed the problem of how to explain the appearance of countable particles in continuous fields1. Stable localized field configurations were searched for an ingredient for a general field theory of elementary particles, but the majority of nonlinear field models were unable to predict them. As an exception, Skyrme succeeded in describing nuclear particles as localized states, so-called ‘skyrmions’2. Skyrmions are a characteristic of nonlinear continuum models ranging from microscopic to cosmological scales3,4,5,6. Skyrmionic states have been found under non-equilibrium conditions, or when stabilized by external fields or the proliferation of topological defects. Examples are Turing patterns in classical liquids7, spin textures in quantum Hall magnets8, or the blue phases in liquid crystals9. However, it has generally been assumed that skyrmions cannot form spontaneous ground states, such as ferromagnetic or antiferromagnetic order, in magnetic materials. Here, we show theoretically that this assumption is wrong and that skyrmion textures may form spontaneously in condensed-matter systems with chiral interactions without the assistance of external fields or the proliferation of defects. We show this within a phenomenological continuum model based on a few material-specific parameters that can be determined experimentally. Our model has a condition not considered before: we allow for softened amplitude variations of the magnetization, characteristic of, for instance, metallic magnets. Our model implies that spontaneous skyrmion lattice ground states may exist generally in a large number of materials, notably at surfaces and in thin films, as well as in bulk compounds, where a lack of space inversion symmetry leads to chiral interactions.,
	language = en,
	number = 7104,
	urldate = 2018-10-01,
	journal = Nature,
	author = Rößler, U. K. and Bogdanov, A. N. and Pfleiderer, C.,
	year = 2006,
	pages = 797–801,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/VQFSPIH7/nature05056.html:text/html


@articleromming_writing_2013,
	title = Writing and deleting single magnetic skyrmions,
	volume = 341,
	number = 6146,
	journal = Science,
	author = Romming, Niklas and Hanneken, Christian and Menzel, Matthias and Bickel, Jessica E. and Wolter, Boris and von Bergmann, Kirsten and Kubetzka, André and Wiesendanger, Roland,
	year = 2013,
	pages = 636–639,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/G2LQ8E42/Romming et al. - 2013 - Writing and deleting single magnetic skyrmions.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/8LVLJVGB/636.html:text/html


@articledupe_tailoring_2014,
	title = Tailoring magnetic skyrmions in ultra-thin transition metal films,
	volume = 5,
	journal = Nature communications,
	author = Dupé, Bertrand and Hoffmann, Markus and Paillard, Charles and Heinze, Stefan,
	year = 2014,
	pages = 4030,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/2DP5ZV4R/ncomms5030.html:text/html;Snapshot:/Users/carolinegorham/Zotero/storage/JLLKTXPU/ncomms5030.html:text/html


@articlerozsa_complex_2016,
	title = Complex magnetic phase diagram and skyrmion lifetime in an ultrathin film from atomistic simulations,
	volume = 93,
	number = 2,
	journal = Physical Review B,
	author = Rózsa, Levente and Simon, Eszter and Palotás, Krisztián and Udvardi, László and Szunyogh, László,
	year = 2016,
	pages = 024417,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/AXVXYENT/Rózsa et al. - 2016 - Complex magnetic phase diagram and skyrmion lifeti.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/7IP3EVTC/PhysRevB.93.html:text/html


@articlechoi_quantum_1998,
	title = Quantum phase transitions in Josephson-junction chains,
	volume = 57,
	number = 2,
	journal = Physical Review B,
	author = Choi, M.-S. and Yi, J. and Choi, M. Y. and Choi, J. and Lee, S.-I.,
	year = 1998,
	pages = R716,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/WMJJY9W6/Choi et al. - 1998 - Quantum phase transitions in Josephson-junction ch.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/69E6RWIB/PhysRevB.57.html:text/html


@bookkaku_quantum_1993,
	title = Quantum field theory: a modern introduction,
	shorttitle = Quantum field theory,
	publisher = Oxford Univ. Press,
	author = Kaku, Michio,
	year = 1993,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/63JP7RI5/Kaku - 1993 - Quantum field theory a modern introduction.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/DSNK49RQ/Kaku - 1993 - Quantum field theory a modern introduction.pdf:application/pdf


@articlezhang_magnetic_2016,
	title = Magnetic bilayer-skyrmions without skyrmion Hall effect,
	volume = 7,
	journal = Nature communications,
	author = Zhang, Xichao and Zhou, Yan and Ezawa, Motohiko,
	year = 2016,
	pages = 10293,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/P7RVPK6A/ncomms10293.html:text/html;Snapshot:/Users/carolinegorham/Zotero/storage/QKRNY68T/ncomms10293.html:text/html


@articlemoriya_anisotropic_1960,
	title = Anisotropic superexchange interaction and weak ferromagnetism,
	volume = 120,
	number = 1,
	journal = Physical Review,
	author = Moriya, Tôru,
	year = 1960,
	pages = 91,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/LT5LICA6/PhysRev.120.html:text/html


@articlemilde_unwinding_2013,
	title = Unwinding of a skyrmion lattice by magnetic monopoles,
	volume = 340,
	number = 6136,
	journal = Science,
	author = Milde, Peter and Köhler, Denny and Seidel, Joachim and Eng, L. M. and Bauer, Andreas and Chacon, Alfonso and Kindervater, Jonas and Mühlbauer, Sebastian and Pfleiderer, Christian and Buhrandt, Stefan,
	year = 2013,
	pages = 1076–1080,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/ZN8N5GWP/Milde et al. - 2013 - Unwinding of a skyrmion lattice by magnetic monopo.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/HPGTY59S/1076.html:text/html


@articleackerman_squirming_2017,
	title = Squirming motion of baby skyrmions in nematic fluids,
	volume = 8,
	copyright = 2017 The Author(s),
	issn = 2041-1723,
	url = https://www.nature.com/articles/s41467-017-00659-5,
	doi = 10.1038/s41467-017-00659-5,
	abstract = A skyrmion is a topological object originally introduced to model elementary particles and a baby skyrmion is its two-dimensional counterpart which can be realized as a defect in liquid crystals. Here the authors show that an electric field can drive uniform motion of baby skyrmions in liquid crystals.,
	language = en,
	number = 1,
	urldate = 2018-09-27,
	journal = Nature Communications,
	author = Ackerman, Paul J. and Boyle, Timothy and Smalyukh, Ivan I.,
	month = sep,
	year = 2017,
	pages = 673,
	file = Full Text PDF:/Users/carolinegorham/Zotero/storage/DQQYEQ5T/Ackerman et al. - 2017 - Squirming motion of baby skyrmions in nematic flui.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/XVBRM7J6/s41467-017-00659-5.html:text/html


@articleqi_symmetry_2012,
	title = Symmetry Meets Topology,
	volume = 338,
	copyright = Copyright © 2012, American Association for the Advancement of Science,
	issn = 0036-8075, 1095-9203,
	url = http://science.sciencemag.org/content/338/6114/1550,
	doi = 10.1126/science.1232394,
	abstract = A unified theory may describe both the persistent spin of electrons and the design of novel materials.
A unified theory may describe both the persistent spin of electrons and the design of novel materials.,
	language = en,
	number = 6114,
	urldate = 2018-09-27,
	journal = Science,
	author = Qi, Xiao-Liang,
	month = dec,
	year = 2012,
	pmid = 23258881,
	pages = 1550–1551,
	file = Full Text PDF:/Users/carolinegorham/Zotero/storage/RTVKCYRZ/Qi - 2012 - Symmetry Meets Topology.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/L3AP2CTR/1550.html:text/html


@bookcage_quantum_2012,
	title = The quantum Hall effect,
	publisher = Springer Science & Business Media,
	author = Cage, Marvin E. and Klitzing, Kv and Chang, A. M. and Duncan, F. and Haldane, M. and Laughlin, Robert B. and Pruisken, A. M. M. and Thouless, D. J.,
	year = 2012,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/VTN64ASU/books.html:text/html


@articlestormer_quantized_1983,
	title = The Quantized Hall Effect,
	volume = 220,
	copyright = © 1983,
	issn = 0036-8075, 1095-9203,
	url = http://science.sciencemag.org/content/220/4603/1241,
	doi = 10.1126/science.220.4603.1241,
	abstract = Quantization of the Hall effect is one of the most surprising discoveries in recent experimental solid-state research. At low temperatures and high magnetic fields the ratio of the Hall voltage to the electric current in a two-dimensional system is quantized in units of h/e2, where h is Planck's constant and e is the electronic charge. Concomitantly, the electrical resistance of the specimen drops to values far below the resistances of the best normal metals.,
	language = en,
	number = 4603,
	urldate = 2018-09-27,
	journal = Science,
	author = Stormer, H. L. and Tsui, D. C.,
	month = jun,
	year = 1983,
	pmid = 17769353,
	pages = 1241–1246,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/5992QHML/1241.html:text/html


@articlebernevig_eight-dimensional_2003,
	title = Eight-dimensional quantum Hall effect and “octonions”,
	volume = 91,
	number = 23,
	journal = Physical review letters,
	author = Bernevig, Bogdan A. and Hu, Jiangping and Toumbas, Nicolaos and Zhang, Shou-Cheng,
	year = 2003,
	pages = 236803,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/QRL6WTDY/PhysRevLett.91.html:text/html


@miscnoauthor_zhang_nodate,
	title = zhang four-dimensional generalization of - Google Scholar,
	url = https://scholar.google.com/scholar?hl=en   as_sdt=0
	urldate = 2018-09-26,
	file = zhang four-dimensional generalization of - Google Scholar:/Users/carolinegorham/Zotero/storage/GYWU9FFZ/scholar.html:text/html


@articlezhang_four-dimensional_2001,
	title = A four-dimensional generalization of the quantum Hall effect,
	volume = 294,
	number = 5543,
	journal = Science,
	author = Zhang, Shou-Cheng and Hu, Jiangping,
	year = 2001,
	pages = 823–828,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/3F3YZZWK/Zhang and Hu - 2001 - A four-dimensional generalization of the quantum H.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/J43HJGVL/823.html:text/html


@articlestern_topological_2013,
	title = Topological Quantum Computation—From Basic Concepts to First Experiments,
	volume = 339,
	copyright = Copyright © 2013, American Association for the Advancement of Science,
	issn = 0036-8075, 1095-9203,
	url = http://science.sciencemag.org/content/339/6124/1179,
	doi = 10.1126/science.1231473,
	abstract = Quantum computation requires controlled engineering of quantum states to perform tasks that go beyond those possible with classical computers. Topological quantum computation aims to achieve this goal by using non-Abelian quantum phases of matter. Such phases allow for quantum information to be stored and manipulated in a nonlocal manner, which protects it from imperfections in the implemented protocols and from interactions with the environment. Recently, substantial progress in this field has been made on both theoretical and experimental fronts. We review the basic concepts of non-Abelian phases and their topologically protected use in quantum information processing tasks. We discuss different possible realizations of these concepts in experimentally available solid-state systems, including systems hosting Majorana fermions, their recently proposed fractional counterparts, and non-Abelian quantum Hall states.,
	language = en,
	number = 6124,
	urldate = 2018-09-26,
	journal = Science,
	author = Stern, Ady and Lindner, Netanel H.,
	month = mar,
	year = 2013,
	pmid = 23471401,
	pages = 1179–1184,
	file = Full Text PDF:/Users/carolinegorham/Zotero/storage/VG5D35NV/Stern and Lindner - 2013 - Topological Quantum Computation—From Basic Concept.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/2CHZ98UJ/1179.html:text/html


@articlechoi_quantum_1994,
	title = Quantum Hall effect in ideal superconducting arrays at zero temperature,
	volume = 50,
	number = 14,
	journal = Physical Review B,
	author = Choi, M. Y.,
	year = 1994,
	pages = 10088,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/SK829REI/PhysRevB.50.html:text/html


@articlenazarov_incompressible_1994,
	title = Incompressible quantum states in Josephson junction arrays,
	volume = 194-196,
	issn = 0921-4526,
	url = http://www.sciencedirect.com/science/article/pii/0921452694913684,
	doi = 10.1016/0921-4526(94)91368-4,
	abstract = We consider arrays of small Josephson junctions (Ec ∼ Ej) in the case of small and uniform charge and flux frustrations. The dynamics of this system can be described in terms of interacting quantum particles-charges (for small Ej) or vortices (for large Ej). We show that at low concentrations of the particles, i.e. in the limit of a short range interaction, the system is intimately related to the hard core bosons in the fractional quantum Hall regime. In particular, the ground state can be described by the Laughlin type wave function Ψ(f)m = IIijf(zi−zj)(2i−zj)mexp(−σkzk2/4) with even powers m = 2,4,… As a result, the Hall conductance of an array σxy shows quantization (at least) at the universal values (2e)2/hm (for small Ej).,
	urldate = 2018-09-25,
	journal = Physica B: Condensed Matter,
	author = Nazarov, Yu. V. and Odintsov, A. A.,
	month = feb,
	year = 1994,
	pages = 1737–1738,
	file = ScienceDirect Snapshot:/Users/carolinegorham/Zotero/storage/7IPRJCQ8/0921452694913684.html:text/html


@articlestern_quantum_1994,
	title = Quantum Hall fluid of vortices in a two-dimensional array of Josephson junctions,
	volume = 50,
	number = 14,
	journal = Physical Review B,
	author = Stern, Ady,
	year = 1994,
	pages = 10092,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/JAT8NGX8/PhysRevB.50.html:text/html


@articlechoi_quantum_1994-1,
	title = Quantum Hall effect in ideal superconducting arrays at zero temperature,
	volume = 50,
	number = 14,
	journal = Physical Review B,
	author = Choi, M. Y.,
	year = 1994,
	pages = 10088,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/7WXTIBWS/PhysRevB.50.html:text/html


@articlehasebe_higher_2017,
	title = Higher (odd) dimensional quantum Hall effect and extended dimensional hierarchy,
	volume = 920,
	issn = 0550-3213,
	url = http://www.sciencedirect.com/science/article/pii/S0550321317301074,
	doi = 10.1016/j.nuclphysb.2017.03.017,
	abstract = We demonstrate dimensional ladder of higher dimensional quantum Hall effects by exploiting quantum Hall effects on arbitrary odd dimensional spheres. Non-relativistic and relativistic Landau models are analyzed on S2k−1 in the SO(2k−1) monopole background. The total sub-band degeneracy of the odd dimensional lowest Landau level is shown to be equal to the winding number from the base-manifold S2k−1 to the one-dimension higher SO(2k) gauge group. Based on the chiral Hopf maps, we clarify the underlying quantum Nambu geometry for odd dimensional quantum Hall effect and the resulting quantum geometry is naturally embedded also in one-dimension higher quantum geometry. An origin of such dimensional ladder connecting even and odd dimensional quantum Hall effects is illuminated from a viewpoint of the spectral flow of Atiyah–Patodi–Singer index theorem in differential topology. We also present a BF topological field theory as an effective field theory in which membranes with different dimensions undergo non-trivial linking in odd dimensional space. Finally, an extended version of the dimensional hierarchy for higher dimensional quantum Hall liquids is proposed, and its relationship to quantum anomaly and D-brane physics is discussed.,
	urldate = 2018-09-25,
	journal = Nuclear Physics B,
	author = Hasebe, Kazuki,
	month = jul,
	year = 2017,
	pages = 475–520,
	file = ScienceDirect Full Text PDF:/Users/carolinegorham/Zotero/storage/WPQTB8GK/Hasebe - 2017 - Higher (odd) dimensional quantum Hall effect and e.pdf:application/pdf;ScienceDirect Snapshot:/Users/carolinegorham/Zotero/storage/PNX4W2Z8/S0550321317301074.html:text/html


@incollectiontinkham_physical_1989,
	title = Physical properties of the new superconductors,
	volume = 42,
	booktitle = Solid State Physics,
	publisher = Elsevier,
	author = Tinkham, M. and Lobb, C. J.,
	year = 1989,
	pages = 91–134,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/8MNXFWPF/S0081194708600806.html:text/html


@articlemanton_topology_1983,
	title = Topology in the Weinberg-Salam theory,
	volume = 28,
	url = https://link.aps.org/doi/10.1103/PhysRevD.28.2019,
	doi = 10.1103/PhysRevD.28.2019,
	abstract = We show that the configuration space of the classical, bosonic Weinberg-Salam theory has a non-contractible loop. This probably implies that there is an unstable, static, finite-energy solution of the field equations. Its energy is the height of the barrier for tunneling between "topologically distinct" vacuums. We establish an upper bound on this energy of order 10 TeV.,
	number = 8,
	urldate = 2018-09-18,
	journal = Physical Review D,
	author = Manton, N. S.,
	month = oct,
	year = 1983,
	pages = 2019–2026,
	file = APS Snapshot:/Users/carolinegorham/Zotero/storage/BJ46MFFN/PhysRevD.28.html:text/html


@articleactor_classical_1979,
	title = Classical solutions of $\mathrm{SU}(2)$ Yang—Mills theories,
	volume = 51,
	url = https://link.aps.org/doi/10.1103/RevModPhys.51.461,
	doi = 10.1103/RevModPhys.51.461,
	abstract = A comprehensive review of the known classical solutions of SU(2) gauge theories is presented. The author follows the historical development of this subject from its beginning (the first explicit solution found was an imbedded Abelian static Coulomb solution) up to the most recent work in the field (in particular the solutions which represent monopoles, instantons, and merons). As well as being a detailed survey, this article is intended to serve as a self-contained introduction to the subject.,
	number = 3,
	urldate = 2018-09-18,
	journal = Reviews of Modern Physics,
	author = Actor, Alfred,
	month = jul,
	year = 1979,
	pages = 461–525,
	file = APS Snapshot:/Users/carolinegorham/Zotero/storage/4EFYNG8Z/RevModPhys.51.html:text/html


@articlejanich_topological_1987,
	title = Topological properties of ordinary nematics in 3-space,
	volume = 8,
	number = 1,
	journal = Acta Applicandae Mathematica,
	author = Jänich, Klaus,
	year = 1987,
	pages = 65–74,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/539JCCVP/BF00046687.html:text/html


@articleovidko_topological_1987,
	title = Topological excitations (defects, solitons, textures, frustrations) in condensed media,
	volume = 104,
	copyright = Copyright © 1987 WILEY‐VCH Verlag GmbH & Co. KGaA,
	issn = 1521-396X,
	url = http://onlinelibrary.wiley.com/doi/abs/10.1002/pssa.2211040102,
	doi = 10.1002/pssa.2211040102,
	language = en,
	number = 1,
	urldate = 2018-09-17,
	journal = physica status solidi (a),
	author = Ovidko, I. A. and Romanov, A. E.,
	month = nov,
	year = 1987,
	pages = 13–45,
	file = Full Text PDF:/Users/carolinegorham/Zotero/storage/9P76CBSU/Ovidko and Romanov - 1987 - Topological excitations (defects, solitons, textur.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/ZPG2PUU8/pssa.html:text/html


@articlehalperin_theory_1978,
	title = Theory of two-dimensional melting,
	volume = 41,
	number = 2,
	journal = Physical Review Letters,
	author = Halperin, B. I. and Nelson, David R.,
	year = 1978,
	pages = 121,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/G8HYQAMD/PhysRevLett.41.html:text/html


@articlenambu_quasi-particles_1960,
	title = Quasi-Particles and Gauge Invariance in the Theory of Superconductivity,
	volume = 117,
	url = https://link.aps.org/doi/10.1103/PhysRev.117.648,
	doi = 10.1103/PhysRev.117.648,
	abstract = Ideas and techniques known in quantum electrodynamics have been applied to the Bardeen-Cooper-Schrieffer theory of superconductivity. In an approximation which corresponds to a generalization of the Hartree-Fock fields, one can write down an integral equation defining the self-energy of an electron in an electron gas with phonon and Coulomb interaction. The form of the equation implies the existence of a particular solution which does not follow from perturbation theory, and which leads to the energy gap equation and the quasi-particle picture analogous to Bogoliubov's.,
	number = 3,
	urldate = 2018-09-14,
	journal = Physical Review,
	author = Nambu, Yoichiro,
	month = feb,
	year = 1960,
	pages = 648–663,
	file = APS Snapshot:/Users/carolinegorham/Zotero/storage/DRFCXCKN/PhysRev.117.html:text/html


@articlejakubczyk_thermodynamics_2016,
	title = Thermodynamics of the two-dimensional XY model from functional renormalization,
	volume = 93,
	number = 6,
	journal = Physical Review E,
	author = Jakubczyk, Pawel and Eberlein, Andreas,
	year = 2016,
	pages = 062145,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/6Y5ZMT4Z/Jakubczyk and Eberlein - 2016 - Thermodynamics of the two-dimensional XY model fro.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/QTZB7TNS/PhysRevE.93.html:text/html


@bookrao_field_2002-1,
	title = Field theories in condensed matter physics,
	publisher = CRC Press,
	author = Rao, Sumathi,
	year = 2002,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/E768KM23/books.html:text/html


@articlegriffin_relationship_2017,
	title = On the relationship between topological and geometric defects,
	volume = 29,
	number = 34,
	journal = Journal of Physics: Condensed Matter,
	author = Griffin, Sinéad M. and Spaldin, Nicola A.,
	year = 2017,
	pages = 343001,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/BDIJ3W35/Griffin and Spaldin - 2017 - On the relationship between topological and geomet.pdf:application/pdf


@articlegraaf_charge_2018,
	title = Charge quantum interference device,
	volume = 14,
	copyright = 2018 The Author(s),
	issn = 1745-2481,
	url = https://www.nature.com/articles/s41567-018-0097-9,
	doi = 10.1038/s41567-018-0097-9,
	abstract = The charge–phase duality in superconductors implies that the well-known SQUID has an analogue based on the interference of fluxons. Such a ‘charge quantum interference device’ (or CQUID) has now been experimentally demonstrated.,
	language = en,
	number = 6,
	urldate = 2018-08-09,
	journal = Nature Physics,
	author = Graaf, S. E. de and Skacel, S. T. and Hönigl-Decrinis, T. and Shaikhaidarov, R. and Rotzinger, H. and Linzen, S. and Ziegler, M. and Hübner, U. and Meyer, H.-G. and Antonov, V. and Il’ichev, E. and Ustinov, A. V. and Tzalenchuk, A. Ya and Astafiev, O. V.,
	month = jun,
	year = 2018,
	pages = 590–594,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/GKSNGL5E/s41567-018-0097-9.html:text/html


@articleelion_aharonov-casher_1994,
	title = The Aharonov-Casher effect for vortices in Josephson-junction arrays,
	volume = 203,
	issn = 0921-4526,
	url = http://www.sciencedirect.com/science/article/pii/0921452694901023,
	doi = 10.1016/0921-4526(94)90102-3,
	abstract = We report on an experiment where we observe quantum mechanical interference of vortices around an induced charge. In a specially designed sample, vortices cross along a doubly connected path. On the superconducting island enclosed by the two paths a charge can be induced by capacitive coupling to a gate. In the resistance that arises from the moving vortices we find clear oscillations as a function of gate voltage. The period of the oscillation corresponds to the single electron charge e, due to the presence of a finite amount of quasiparticles. The oscillations demonstrate quantum interference of vortices which is a manifestation of the generalized Aharonov-Casher effect.,
	number = 3,
	urldate = 2018-08-09,
	journal = Physica B: Condensed Matter,
	author = Elion, W. J. and Wachters, J. J. and Sohn, L. L. and Mooij, J. E.,
	month = dec,
	year = 1994,
	pages = 497–503,
	file = ScienceDirect Snapshot:/Users/carolinegorham/Zotero/storage/AMR546EI/0921452694901023.html:text/html


@articlefriedman_aharonov-casher-effect_2002,
	title = Aharonov-Casher-effect suppression of macroscopic tunneling of magnetic flux,
	volume = 88,
	number = 5,
	journal = Physical review letters,
	author = Friedman, Jonathan R. and Averin, Dmitri V.,
	year = 2002,
	pages = 050403,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/LX6VBAI3/Friedman and Averin - 2002 - Aharonov-Casher-effect suppression of macroscopic .pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/T6MB73Y5/PhysRevLett.88.html:text/html


@articleivanov_interference_2001,
	title = Interference effects in isolated Josephson junction arrays with geometric symmetries,
	volume = 65,
	number = 2,
	journal = Physical Review B,
	author = Ivanov, Dmitri A. and Ioffe, Lev B. and Geshkenbein, Vadim B. and Blatter, Gianni,
	year = 2001,
	pages = 024509,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/UTNYLWI2/Ivanov et al. - 2001 - Interference effects in isolated Josephson junctio.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/TVF2JAVY/PhysRevB.65.html:text/html


@articlereznik_question_1989,
	title = Question of the nonlocality of the Aharonov-Casher effect,
	volume = 40,
	url = https://link.aps.org/doi/10.1103/PhysRevD.40.4178,
	doi = 10.1103/PhysRevD.40.4178,
	abstract = The Aharanov-Casher effect is manifested in a (2+1)-dimensional model that screens the electromagnetic fields, in order to demonstrate that the effect is essentially nonlocal in its nature. The question of nonlocality is discussed by means of a nonrelativistic model for a superconductor. It is demonstrated that although the superconductor screens the electric field generated by an external charge it does not screen the modular electric field which is a constant of motion of the system. Consequently, a magnetic fluxon will accumulate the same phase as if the electric field were unscreened and the Aharonov-Casher effect will exist even in a force-free region.,
	number = 12,
	urldate = 2018-08-09,
	journal = Physical Review D,
	author = Reznik, B. and Aharonov, Y.,
	month = dec,
	year = 1989,
	pages = 4178–4183,
	file = APS Snapshot:/Users/carolinegorham/Zotero/storage/TC6ML39T/PhysRevD.40.html:text/html


@articleaharonov_topological_1984,
	title = Topological quantum effects for neutral particles,
	volume = 53,
	number = 4,
	journal = Physical Review Letters,
	author = Aharonov, Yakir and Casher, Aharon,
	year = 1984,
	pages = 319,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/HQYHBLBW/PhysRevLett.53.html:text/html


@articleaharonov_significance_1959,
	title = Significance of electromagnetic potentials in the quantum theory,
	volume = 115,
	number = 3,
	journal = Physical Review,
	author = Aharonov, Yakir and Bohm, David,
	year = 1959,
	pages = 485,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/CLNWL7N7/Aharonov and Bohm - 1959 - Significance of electromagnetic potentials in the .pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/DDHW34BG/PhysRev.115.html:text/html


@articlevan_wees_quantized_1988,
	title = Quantized conductance of point contacts in a two-dimensional electron gas,
	volume = 60,
	url = https://link.aps.org/doi/10.1103/PhysRevLett.60.848,
	doi = 10.1103/PhysRevLett.60.848,
	abstract = Ballistic point contacts, defined in the two-dimensional electron gas of a GaAs-AlGaAs heterostructure, have been studied in zero magnetic field. The conductance changes in quantized steps of e2/πħ when the width, controlled by a gate on top of heterojunction, is varied. Up to sixteen steps are observed when the point contact is widened from 0 to 360 nm. An explanation is proposed, which assumes quantized transverse momentum in the point-contact region.,
	number = 9,
	urldate = 2018-08-09,
	journal = Physical Review Letters,
	author = van Wees, B. J. and van Houten, H. and Beenakker, C. W. J. and Williamson, J. G. and Kouwenhoven, L. P. and van der Marel, D. and Foxon, C. T.,
	month = feb,
	year = 1988,
	pages = 848–850,
	file = APS Snapshot:/Users/carolinegorham/Zotero/storage/V326ZBXQ/PhysRevLett.60.html:text/html


@articleschwab_measurement_2000,
	title = Measurement of the quantum of thermal conductance,
	volume = 404,
	copyright = 2000 Nature Publishing Group,
	issn = 1476-4687,
	url = https://www.nature.com/articles/35010065,
	doi = 10.1038/35010065,
	abstract = The physics of mesoscopic electronic systems has been explored for more than 15 years. Mesoscopic phenomena in transport processes occur when the wavelength or the coherence length of the carriers becomes comparable to, or larger than, the sample dimensions. One striking result in this domain is the quantization of electrical conduction, observed in a quasi-one-dimensional constriction formed between reservoirs of two-dimensional electron gas1,2. The conductance of this system is determined by the number of participating quantum states or ‘channels’ within the constriction; in the ideal case, each spin-degenerate channel contributes a quantized unit of 2e2/h to the electrical conductance. It has been speculated that similar behaviour should be observable for thermal transport3,4 in mesoscopic phonon systems. But experiments attempted in this regime have so far yielded inconclusive results5,6,7,8,9. Here we report the observation of a quantized limiting value for the thermal conductance, Gth, in suspended insulating nanostructures at very low temperatures. The behaviour we observe is consistent with predictions10,11 for phonon transport in a ballistic, one-dimensional channel: at low temperatures, Gth approaches a maximum value of g0 = π2k 2BT/3h, the universal quantum of thermal conductance.,
	language = en,
	number = 6781,
	urldate = 2018-08-09,
	journal = Nature,
	author = Schwab, K. and Henriksen, E. A. and Worlock, J. M. and Roukes, M. L.,
	month = apr,
	year = 2000,
	pages = 974–977,
	file = Full Text PDF:/Users/carolinegorham/Zotero/storage/3C5UPKMA/Schwab et al. - 2000 - Measurement of the quantum of thermal conductance.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/YHR6RGWL/35010065.html:text/html


@articlecui_quantized_2017,
	title = Quantized thermal transport in single-atom junctions,
	volume = 355,
	copyright = Copyright © 2017, American Association for the Advancement of Science,
	issn = 0036-8075, 1095-9203,
	url = http://science.sciencemag.org/content/355/6330/1192,
	doi = 10.1126/science.aam6622,
	abstract = Calorimetry reaches an atomic junction
Electrical and thermal conductivity in metals are linked at the macroscopic length scale because electrons carry both heat and current. Cui et al. found that this relationship, the Wiedemann-Franz law, holds down to the atomic scale in gold and platinum (see the Perspective by Segal). They made thermal and electrical conductance measurements through a point contact only one atom thick. In gold, the thermal and electrical conductance was quantized, owing to the electronic band structure of the metal. The experiments pave the way for high-resolution calorimetry and other thermal measurements at the nanoscale.
Science, this issue p. 1192; see also p. 1125
Thermal transport in individual atomic junctions and chains is of great fundamental interest because of the distinctive quantum effects expected to arise in them. By using novel, custom-fabricated, picowatt-resolution calorimetric scanning probes, we measured the thermal conductance of gold and platinum metallic wires down to single-atom junctions. Our work reveals that the thermal conductance of gold single-atom junctions is quantized at room temperature and shows that the Wiedemann-Franz law relating thermal and electrical conductance is satisfied even in single-atom contacts. Furthermore, we quantitatively explain our experimental results within the Landauer framework for quantum thermal transport. The experimental techniques reported here will enable thermal transport studies in atomic and molecular chains, which will be key to investigating numerous fundamental issues that thus far have remained experimentally inaccessible.
Thermal and electrical conductance remain tightly connected across gold and platinum single-atom junctions.
Thermal and electrical conductance remain tightly connected across gold and platinum single-atom junctions.,
	language = en,
	number = 6330,
	urldate = 2018-08-09,
	journal = Science,
	author = Cui, Longji and Jeong, Wonho and Hur, Sunghoon and Matt, Manuel and Klöckner, Jan C. and Pauly, Fabian and Nielaba, Peter and Cuevas, Juan Carlos and Meyhofer, Edgar and Reddy, Pramod,
	month = mar,
	year = 2017,
	pmid = 28209640,
	pages = 1192–1195,
	file = Full Text PDF:/Users/carolinegorham/Zotero/storage/8BKCSJAV/Cui et al. - 2017 - Quantized thermal transport in single-atom junctio.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/4G3GLKXX/1192.html:text/html


@articlejezouin_quantum_2013,
	title = Quantum Limit of Heat Flow Across a Single Electronic Channel,
	volume = 342,
	copyright = Copyright © 2013, American Association for the Advancement of Science,
	issn = 0036-8075, 1095-9203,
	url = http://science.sciencemag.org/content/342/6158/601,
	doi = 10.1126/science.1241912,
	abstract = Quantum Heating
Mesoscopic wires exhibit peculiar properties at low temperatures. Their electric conductance can show plateaus at evenly spaced values, which reflects the sequential opening of “quantum transport channels,” each of which can only carry a finite amount of charge or heat. Whereas the step size for the electric conductance depends on the type of the particle carrying the charge, for heat conduction this “quantum” is universal. Jezouin et al. (p. 601, published online 3 October; see the Perspective by Sothmann and Flindt) measured the quantum of heat conduction through a single electronic channel by comparing the amount of heat needed to heat a small metal plate to a constant temperature, while varying the number of electronic channels through which the heat was dissipated from the plate. Encouragingly, the measurement was in agreement with the theoretical prediction.
Quantum physics predicts that there is a fundamental maximum heat conductance across a single transport channel and that this thermal conductance quantum, GQ, is universal, independent of the type of particles carrying the heat. Such universality, combined with the relationship between heat and information, signals a general limit on information transfer. We report on the quantitative measurement of the quantum-limited heat flow for Fermi particles across a single electronic channel, using noise thermometry. The demonstrated agreement with the predicted GQ establishes experimentally this basic building block of quantum thermal transport. The achieved accuracy of below 10% opens access to many experiments involving the quantum manipulation of heat.
The unit of heat carried by electrons is measured using noise thermometry and found to be consistent with predictions. [Also see Perspective by Sothmann and Flindt]
The unit of heat carried by electrons is measured using noise thermometry and found to be consistent with predictions. [Also see Perspective by Sothmann and Flindt],
	language = en,
	number = 6158,
	urldate = 2018-08-09,
	journal = Science,
	author = Jezouin, S. and Parmentier, F. D. and Anthore, A. and Gennser, U. and Cavanna, A. and Jin, Y. and Pierre, F.,
	month = nov,
	year = 2013,
	pmid = 24091707,
	pages = 601–604,
	file = Full Text PDF:/Users/carolinegorham/Zotero/storage/SBLVUNUF/Jezouin et al. - 2013 - Quantum Limit of Heat Flow Across a Single Electro.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/8VA9B3NC/601.html:text/html


@articlecammarota_ideal_2012,
	title = Ideal glass transitions by random pinning,
	volume = 109,
	issn = 0027-8424, 1091-6490,
	url = http://www.pnas.org/content/109/23/8850,
	doi = 10.1073/pnas.1111582109,
	abstract = We study the effect of freezing the positions of a fraction c of particles from an equilibrium configuration of a supercooled liquid at a temperature T. We show that within the random first-order transition theory pinning particles leads to an ideal glass transition for a critical fraction c = cK(T) even for moderate supercooling; e.g., close to the Mode-Coupling transition temperature. First we derive the phase diagram in the T - c plane by mean field approximations. Then, by applying a real-space renormalization group method, we obtain the critical properties for c - cK(T) → 0, in particular the divergence of length and time scales, which are dominated by two zero-temperature fixed points. We also show that for c = cK(T) the typical distance between frozen particles is related to the static point-to-set length scale of the unconstrained liquid. We discuss what are the main differences when particles are frozen in other geometries and not from an equilibrium configuration. Finally, we explain why the glass transition induced by freezing particles provides a new and very promising avenue of research to probe the glassy state and ascertain, or disprove, the validity of the theories of the glass transition.,
	language = en,
	number = 23,
	urldate = 2018-08-03,
	journal = Proceedings of the National Academy of Sciences,
	author = Cammarota, Chiara and Biroli, Giulio,
	month = jun,
	year = 2012,
	pmid = 22623524,
	keywords = slow dynamics, amorphous order, glass materials, ideal glass phase, thermodynamic phase transition,
	pages = 8850–8855,
	file = Full Text PDF:/Users/carolinegorham/Zotero/storage/PBRK8ZYI/Cammarota and Biroli - 2012 - Ideal glass transitions by random pinning.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/N6AJKHM5/8850.html:text/html


@articleginzburg_vl_1950,
	title = VL Ginzburg and LD Landau, J. Exptl. Theoret. Phys.(USSR) 20, 1064 (1950),
	volume = 20,
	journal = J. Exptl. Theoret. Phys.(USSR),
	author = Ginzburg, V. L.,
	year = 1950,
	pages = 1064


@articlehopkins_introduction_2011,
	title = Introduction to Nanoscale Thermal Conduction,
	url = https://www.intechopen.com/books/heat-transfer-mathematical-modelling-numerical-methods-and-information-technology/introduction-to-nanoscale-thermal-conduction/,
	doi = 10.5772/13590,
	urldate = 2018-07-29,
	journal = Heat Transfer - Mathematical Modelling, Numerical Methods and Information Technology,
	author = Hopkins, P. E. and Duda, J. C.,
	year = 2011,
	file = Full Text PDF:/Users/carolinegorham/Zotero/storage/KSUKUZYT/Duda - 2011 - Introduction to Nanoscale Thermal Conduction.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/A8QWTBHR/introduction-to-nanoscale-thermal-conduction.html:text/html


@articlecahill_lattice_1988,
	title = Lattice Vibrations and Heat Transport in Crystals and Glasses,
	volume = 39,
	doi = 10.1146/annurev.pc.39.100188.000521,
	number = 1,
	journal = Annual Review of Physical Chemistry,
	author = Cahill, D. G. and Pohl, R. O.,
	year = 1988,
	keywords = polycrystalline, fractal, fracton, (amorphous) glass, heat transport, crystal


@articleweinberg_quantum_2011,
	title = Quantum Field Theory III,
	volume = 1,
	journal = Mij,
	author = Weinberg, S.,
	year = 2011,
	pages = 3,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/5B43VFMN/Weinberg - 2011 - Quantum Field Theory III.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/5KZ2DB6E/Weinberg - 2011 - Quantum Field Theory III.pdf:application/pdf


@articlemilnor_curvatures_1976,
	title = Curvatures of left invariant metrics on lie groups,
	volume = 21,
	issn = 0001-8708,
	url = http://www.sciencedirect.com/science/article/pii/S0001870876800023,
	doi = 10.1016/S0001-8708(76)80002-3,
	number = 3,
	urldate = 2018-07-29,
	journal = Advances in Mathematics,
	author = Milnor, J.,
	year = 1976,
	file = ScienceDirect Full Text PDF:/Users/carolinegorham/Zotero/storage/ZTNCH4J5/Milnor - 1976 - Curvatures of left invariant metrics on lie groups.pdf:application/pdf;ScienceDirect Snapshot:/Users/carolinegorham/Zotero/storage/8GBA3HM6/S0001870876800023.html:text/html


@articlevan_wees_duality_1991,
	title = Duality between Cooper-pair and vortex dynamics in two-dimensional Josephson-junction arrays,
	volume = 44,
	doi = 10.1103/PhysRevB.44.2264,
	number = 5,
	journal = Physical Review B,
	author = Van Wees, B. J.,
	year = 1991,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/QEG2IVLQ/PhysRevB.44.html:text/html


@articlefradkin_chern-simons_1998,
	title = A Chern-Simons effective field theory for the Pfaffian quantum Hall state,
	volume = 516,
	doi = 10.1016/S0550-3213(98)00111-4,
	number = 3,
	journal = Nuclear Physics B,
	author = Fradkin, E. and Nayak, C. and Tsvelik, A. and Wilczek, F.,
	year = 1998,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/4NKKARGB/Fradkin et al. - 1998 - A Chern-Simons effective field theory for the Pfaf.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/EENYQETL/S0550321398001114.html:text/html


@articlechern_characteristic_1946,
	title = Characteristic Classes of Hermitian Manifolds,
	volume = 47,
	issn = 0003-486X,
	url = http://www.jstor.org/stable/1969037,
	doi = 10.2307/1969037,
	number = 1,
	urldate = 2018-07-15,
	journal = Annals of Mathematics,
	author = Chern, S-S,
	year = 1946,
	file = JSTOR Full Text PDF:/Users/carolinegorham/Zotero/storage/X2FI2K6W/Chern - 1946 - Characteristic Classes of Hermitian Manifolds.pdf:application/pdf


@articlechern_curvatura_1945,
	title = On the Curvatura Integra in a Riemannian Manifold,
	volume = 46,
	issn = 0003-486X,
	url = http://www.jstor.org/stable/1969203,
	doi = 10.2307/1969203,
	number = 4,
	urldate = 2018-07-24,
	journal = Annals of Mathematics,
	author = Chern, S-S,
	year = 1945


@incollectionchern_simple_1996,
	series = Series in 20th Century Mathematics,
	title = A simple intrinsic proof of the gauss-bonnet formula for closed riemannin manifolds,
	volume = 4,
	url = https://www.worldscientific.com/doi/abs/10.1142/9789812812834_0009,
	urldate = 2018-07-15,
	booktitle = A Mathematician and His Mathematical Work,
	publisher = World Scientific,
	author = Chern, S-S,
	year = 1996,
	doi = 10.1142/9789812812834_0009,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/MQ85CHQ7/9789812812834_0009.html:text/html


@articleallendoerfer_gauss-bonnet_1943,
	title = The gauss-bonnet theorem for riemannian polyhedra,
	volume = 53,
	doi = 10.2307/1990134,
	number = 1,
	journal = Transactions of the American Mathematical Society,
	author = Allendoerfer, C. B. and Weil, A.,
	year = 1943,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/63NWMV42/Allendoerfer and Weil - 1943 - The gauss-bonnet theorem for riemannian polyhedra.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/RASKA9FJ/1990134.html:text/html


@articleachim_stability_2011,
	title = Stability of liquid crystalline phases in the phase-field-crystal model,
	volume = 83,
	doi = 10.1103/PhysRevE.83.061712,
	number = 6,
	journal = Physical Review E,
	author = Achim, C. V. and Wittkowski, R. and Löwen, H.,
	year = 2011


@articlelubensky_topological_1998,
	title = Topological defects and interactions in nematic emulsions,
	volume = 57,
	doi = 10.1103/PhysRevE.57.610,
	number = 1,
	journal = Physical Review E,
	author = Lubensky, T. C. and Pettey, David and Currier, Nathan and Stark, Holger,
	year = 1998


@articledavid_structural_1992,
	title = Structural Phase Transitions in the Fullerene C60,
	volume = 18,
	issn = 0295-5075,
	url = http://iopscience.iop.org/0295-5075/18/3/006,
	doi = 10.1209/0295-5075/18/3/006,
	abstract = High-resolution powder neutron diffraction has been used to study the crystal structure of the fullerence C60 in the temperature range 5 K to 320 K. Solid C60 adopts a cubic structure at all temperatures. The experimental data provide clear evidence of a continuous phase transition at ca. 90 K and confirm the existence of a first-order phase transition at 260 K. In the high-temperature face-centred-cubic phase (T \textgreater 260 K), the C60 molecules are completely orientationally disordered, undergoing continuous reorientation. Below 260 K, interpretation of the diffraction data is consistent with uniaxial jump reorientation principally about a single 111 direction. In the lowest-temperature phase (T \textless 90 K), rotational motion is frozen although a small amount of static disorder still persists.,
	language = en,
	number = 3,
	urldate = 2014-08-08,
	journal = EPL (Europhysics Letters),
	author = David, W. I. F. and Ibberson, R. M. and Dennis, T. J. S. and Hare, J. P. and Prassides, K.,
	year = 1992


@articlekroto_c60:_1985,
	title = C60: Buckminsterfullerene,
	volume = 318,
	copyright = 1985 Nature Publishing Group,
	issn = 1476-4687,
	shorttitle = C60,
	url = https://www.nature.com/articles/318162a0,
	doi = 10.1038/318162a0,
	abstract = During experiments aimed at understanding the mechanisms by which long-chain carbon molecules are formed in interstellar space and circumstellar shells1, graphite has been vaporized by laser irradiation, producing a remarkably stable cluster consisting of 60 carbon atoms. Concerning the question of what kind of 60-carbon atom structure might give rise to a superstable species, we suggest a truncated icosahedron, a polygon with 60 vertices and 32 faces, 12 of which are pentagonal and 20 hexagonal. This object is commonly encountered as the football shown in Fig. 1. The C60 molecule which results when a carbon atom is placed at each vertex of this structure has all valences satisfied by two single bonds and one double bond, has many resonance structures, and appears to be aromatic.,
	language = en,
	number = 6042,
	urldate = 2018-04-27,
	journal = Nature,
	author = Kroto, H. W. and Heath, J. R. and O'Brien, S. C. and Curl, R. F. and Smalley, R. E.,
	year = 1985


@articlestaveley_phase_1962,
	title = Phase transitions in plastic crystals,
	volume = 13,
	doi = 10.1146/annurev.pc.13.100162.002031,
	number = 1,
	journal = Annual Review of Physical Chemistry,
	author = Staveley, L. A. K.,
	year = 1962


@articletimmermans_plastic_1961,
	title = Plastic crystals: a historical review,
	volume = 18,
	doi = 10.1016/0022-3697(61)90076-2,
	number = 1,
	journal = Journal of Physics and Chemistry of solids,
	author = Timmermans, J.,
	year = 1961


@articlereinitzer_contributions_1989,
	title = Contributions to the knowledge of cholesterol,
	volume = 5,
	doi = 10.1080/02678298908026349,
	number = 1,
	journal = Liquid Crystals,
	author = Reinitzer, F.,
	year = 1989


@articlehawking_gravitational_1977,
	title = Gravitational instantons,
	volume = 60,
	doi = 10.1016/0375-9601(77)90386-3,
	number = 2,
	journal = Physics Letters A,
	author = Hawking, S. W.,
	year = 1977


@articlecharap_space-time_1977,
	title = Space-time topology and a new class of Yang-Mills instanton,
	volume = 71,
	doi = 10.1016/0370-2693(77)90782-1,
	number = 1,
	journal = Physics Letters B,
	author = Charap, J. M. and Duff, M. J.,
	year = 1977


@articlegoswami_dissipation_2006-1,
	title = Dissipation, topology, and quantum phase transition in a one-dimensional Josephson junction array,
	volume = 73,
	doi = 10.1103/PhysRevB.73.094516,
	number = 9,
	journal = Physical Review B,
	author = Goswami, P. and Chakravarty, S.,
	year = 2006


@articlechoi_cotunneling_1998,
	title = Cotunneling Transport and Quantum Phase Transitions in Coupled Josephson-Junction Chains with Charge Frustration,
	volume = 81,
	url = https://link.aps.org/doi/10.1103/PhysRevLett.81.4240,
	doi = 10.1103/PhysRevLett.81.4240,
	number = 19,
	urldate = 2018-03-23,
	journal = Physical Review Letters,
	author = Choi, M-S and Choi, M. Y. and Choi, T. and Lee, S-I,
	year = 1998


@articlekerman_fluxcharge_2013,
	title = Flux–charge duality and topological quantum phase fluctuations in quasi-one-dimensional superconductors,
	volume = 15,
	issn = 1367-2630,
	doi = 10.1088/1367-2630/15/10/105017,
	abstract = It has long been thought that macroscopic phase coherence breaks down in effectively lower-dimensional superconducting systems even at zero temperature due to enhanced topological quantum phase fluctuations. In quasi-one-dimensional wires, these fluctuations are described in terms of ‘quantum phase-slip’ (QPS): tunneling of the superconducting order parameter for the wire between states differing by ±2 π in their relative phase between the wire's ends. Over the last several decades, many deviations from conventional bulk superconducting behavior have been observed in ultra-narrow superconducting nanowires, some of which have been identified with QPS. While at least some of the observations are consistent with existing theories for QPS, other observations in many cases point to contradictory conclusions or cannot be explained by these theories. Hence, our understanding of the nature of QPS, and its relationship to the various observations, has remained imcomplete. In this paper we present a new model for QPS which takes as its starting point an idea originally postulated by Mooij and Nazarov (2006 Nature Phys. 2 169): that flux–charge duality , a classical symmetry of Maxwell's equations, can be used to relate QPS to the well-known Josephson tunneling of Cooper pairs. Our model provides an alternative, and qualitatively different, conceptual basis for QPS and the phenomena which arise from it in experiments, and it appears to permit for the first time a unified understanding of observations across several different types of experiments and materials systems.,
	language = en,
	number = 10,
	urldate = 2018-03-25,
	journal = New Journal of Physics,
	author = Kerman, A. J.,
	year = 2013


@articlekorshunov_effect_1989-1,
	title = Effect of dissipation on the low-temperature properties of a tunnel-junction chain,
	volume = 95,
	journal = Zh. Eksp. Teor. Fiz,
	author = Korshunov, S. E.,
	year = 1989


@articlejosephson_discovery_1974,
	title = The Discovery of Tunnelling Supercurrent,
	volume = 184,
	url = https://www.jstor.org/stable/1738909,
	number = 4136,
	journal = Science,
	author = Josephson, B. D.,
	year = 1974,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/DNH7NQHV/Josephson - 1974 - The Discovery of Tunnelling Supercurrents-Nobel Le.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/IRB4PFX8/Josephson - 1974 - The Discovery of Tunnelling Supercurrents-Nobel Le.pdf:application/pdf


@articlejosephson_possible_1962,
	title = Possible new effects in superconductive tunnelling,
	volume = 1,
	doi = 10.1016/0031-9163(62)91369-0,
	number = 7,
	journal = Physics letters,
	author = Josephson, B. D.,
	year = 1962


@articlepeng_curl_1999,
	title = The curl in seven dimensional space and its applications,
	volume = 15,
	doi = 10.1007/BF02837124,
	language = en,
	number = 3,
	journal = Approximation Theory and its Applications,
	author = Peng, L. and Yang, L.,
	year = 1999


@articleguilleumas_generating_2002,
	title = Generating vortex rings in Bose-Einstein condensates in the line-source approximation,
	volume = 65,
	doi = 10.1103/PhysRevA.65.053609,
	number = 5,
	journal = Physical Review A,
	author = Guilleumas, M. and Jezek, D. M. and Mayol, R. and Pi, M. and Barranco, M.,
	year = 2002,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/R4ZPQY6U/PhysRevA.65.html:text/html


@articlehess_calculation_1967,
	title = Calculation of potential flow about arbitrary bodies,
	volume = 8,
	doi = 10.1016/0376-0421(67)90003-6,
	journal = Progress in Aerospace Sciences,
	author = Hess, J. L. and Smith, A. M. O.,
	year = 1967,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/26879A9F/Hess and Smith - 1967 - Calculation of potential flow about arbitrary bodi.pdf:application/pdf


@bookkowalewski_determinantentheorie_1948,
	title = Determinantentheorie,
	volume = 39,
	publisher = American Mathematical Soc.,
	author = Kowalewski, G.,
	year = 1948,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/GXCBDQB6/books.html:text/html


@articlezachariasen_atomic_1932,
	title = The atomic arrangement in glass,
	volume = 54,
	doi = 10.1021/ja01349a006,
	number = 10,
	journal = Journal of the American Chemical Society,
	author = Zachariasen, W. H.,
	year = 1932,
	keywords = polycrystalline, random network model


@articlethorpe_continuous_1983,
	title = Continuous deformations in random networks,
	volume = 57,
	doi = 10.1016/0022-3093(83)90424-6,
	number = 3,
	journal = Journal of Non-Crystalline Solids,
	author = Thorpe, M. F.,
	year = 1983,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/MM8E67DS/0022309383904246.html:text/html


@articlebell_properties_1966,
	title = Properties of vitreous silica: Analysis of random network models,
	volume = 212,
	shorttitle = Properties of vitreous silica,
	doi = 10.1038/2121354a0,
	number = 5068,
	journal = Nature,
	author = Bell, R. J. and Dean, P.,
	year = 1966,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/Z53223KJ/2121354a0.html:text/html


@articlewarren_summary_1941,
	title = Summary of work on atomic arrangement in glass,
	volume = 24,
	doi = 10.1111/j.1151-2916.1941.tb14858.x,
	number = 8,
	journal = Journal of the American Ceramic Society,
	author = Warren, B. E.,
	year = 1941,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/KV772H8L/j.1151-2916.1941.tb14858.html:text/html


@articlepeierls_zur_1929,
	title = Zur kinetischen theorie der wärmeleitung in kristallen,
	volume = 395,
	url = http://onlinelibrary.wiley.com/doi/10.1002/andp.19293950803/abstract,
	doi = 10.1002/andp.19293950803,
	number = 8,
	urldate = 2016-06-01,
	journal = Annalen der Physik,
	author = Peierls, R.,
	year = 1929


@articlewarren_x-ray_1937,
	title = X-Ray Determination of the Structure of Liquids and Glass,
	volume = 8,
	issn = 0021-8979, 1089-7550,
	url = http://scitation.aip.org/content/aip/journal/jap/8/10/10.1063/1.1710241,
	doi = 10.1063/1.1710241,
	abstract = Scitation is the online home of leading journals and conference proceedings from AIP Publishing and AIP Member Societies,
	number = 10,
	urldate = 2016-05-27,
	journal = Journal of Applied Physics,
	author = Warren, B. E.,
	year = 1937,
	keywords = Liquid structure


@articlekleman_disclinations_2008,
	title = Disclinations, dislocations, and continuous defects: A reappraisal,
	volume = 80,
	shorttitle = Disclinations, dislocations, and continuous defects,
	url = https://link.aps.org/doi/10.1103/RevModPhys.80.61,
	doi = 10.1103/RevModPhys.80.61,
	abstract = Disclinations were first observed in mesomorphic phases. They were later found relevant to a number of ill-ordered condensed-matter media involving continuous symmetries or frustrated order. Disclinations also appear in polycrystals at the edges of grain boundaries; but they are of limited interest in solid single crystals, where they can move only by diffusion climb and, owing to their large elastic stresses, mostly appear in close pairs of opposite signs. The relaxation mechanisms associated with a disclination in its creation, motion, and change of shape involve an interplay with continuous or quantized dislocations and/or continuous disclinations. These are attached to the disclinations or are akin to Nye’s dislocation densities, which are particularly well suited for consideration here. The notion of an extended Volterra process is introduced, which takes these relaxation processes into account and covers different situations where this interplay takes place. These concepts are illustrated by a variety of applications in amorphous solids, mesomorphic phases, and frustrated media in their curved habit space. These often involve disclination networks with specific node conditions. The powerful topological theory of line defects considers only defects stable against any change of boundary conditions or relaxation processes compatible with the structure considered. It can be seen as a simplified case of the approach considered here, particularly suited for media of high plasticity or/and complex structures. It cannot analyze the dynamical properties of defects nor the elastic constants involved in their static properties; topological stability cannot guarantee energetic stability, and sometimes cannot distinguish finer details of the structure of defects.,
	number = 1,
	urldate = 2018-07-15,
	journal = Reviews of Modern Physics,
	author = Kleman, M. and Friedel, J.,
	year = 2008,
	file = APS Snapshot:/Users/carolinegorham/Zotero/storage/ZFCW4PDV/RevModPhys.80.html:text/html


@inproceedingsvolterra_sur_1907,
	title = Sur l'équilibre des corps élastiques multiplement connexes,
	volume = 24,
	booktitle = Annales scientifiques de l'École normale supérieure,
	author = Volterra, V.,
	year = 1907,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/HCIFY5AF/Volterra - 1907 - Sur l'équilibre des corps élastiques multiplement .pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/KA3CZH3F/Volterra - 1907 - Sur l'équilibre des corps élastiques multiplement .pdf:application/pdf


@articletoulouse_pour_1977,
	title = Pour les nématiques biaxes,
	volume = 38,
	doi = 10.1051/jphyslet:0197700380206700,
	number = 2,
	journal = Journal de Physique Lettres,
	author = Toulouse, G.,
	year = 1977


@incollectionerdos_phonons_1993,
	series = Springer Series in Solid-State Sciences,
	title = Phonons in Crystals, Quasicrystals and Topologically Disordered Lattices,
	copyright = ©1993 Springer-Verlag Berlin Heidelberg,
	language = en,
	urldate = 2014-02-18,
	booktitle = Phonon Scattering in Condensed Matter VII,
	publisher = Springer Berlin Heidelberg,
	author = Erdös, P. and Michalski, J.,
	editor = Meissner, M. and Pohl, R. O.,
	year = 1993,
	keywords = thermodynamics, Physical Chemistry, Surfaces and Interfaces, Thin Films, Phase Transitions and Multiphase Systems,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/Q32WQ7JD/978-3-642-84888-9_8.html:text/html


@articlemichalski_thermal_1992,
	title = Thermal conductivity of amorphous solids above the plateau: Molecular-dynamics study,
	volume = 45,
	doi = 10.1103/PhysRevB.45.7054,
	number = 13,
	journal = Phys. Rev. B,
	author = Michalski, J.,
	year = 1992,
	keywords = polycrystalline, fractal, unread, md


@articlemichalski_comparison_1989,
	title = Comparison of the thermal properties of two-dimensional periodic and aperiodic lattice models,
	volume = 72,
	issn = 0038-1098,
	url = http://www.sciencedirect.com/science/article/pii/0038109889906091,
	doi = 10.1016/0038-1098(89)90609-1,
	abstract = The classical dynamics of two lattice models, periodic and aperiodic, are simulated numerically to compare their thermal properties. The periodic model is a periodic approximation of the Penrose pattern. The aperiodic model is obtained from the periodic one by shifting randomly a small fraction of the atoms in such a way that the local bond orientational order is preserved. We found that the densities of states of both models are almost identical, while their thermal conductivities as functions of temperature differ dramatically. We explain this difference by the presence of localized modes found in the aperiodic model.,
	number = 10,
	urldate = 2014-02-18,
	journal = Solid State Communications,
	author = Michalski, J and Erdös, P,
	year = 1989,
	file = ScienceDirect Full Text PDF:/Users/carolinegorham/Zotero/storage/CE49RGC6/Michalski and Erdös - 1989 - Comparison of the thermal properties of two-dimens.pdf:application/pdf;ScienceDirect Snapshot:/Users/carolinegorham/Zotero/storage/7WIJHNHR/0038109889906091.html:text/html


@articleklemens_thermal_1958,
	title = Thermal conductivity and lattice vibrational modes,
	volume = 7,
	doi = 10.1016/S0081-1947(08)60551-2,
	journal = Solid state physics,
	author = Klemens, P. G.,
	year = 1958,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/DEI68QHN/S0081194708605512.html:text/html


@articleyu_thermal_1992,
	title = Thermal conductivity of single crystal C60,
	volume = 68,
	doi = 10.1103/PhysRevLett.68.2050,
	journal = Physical Review Letters,
	author = Yu, R. C. and Tea, N. and Salamon, M. B. and Lorents, D. and Malhotra, R.,
	year = 1992


@articlestillinger_supercooled_1988,
	title = Supercooled liquids, glass transitions, and the Kauzmann paradox,
	volume = 88,
	doi = 10.1063/1.454295,
	number = 12,
	journal = The Journal of chemical physics,
	author = Stillinger, F. H.,
	year = 1988,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/SR8J2INH/Stillinger - 1988 - Supercooled liquids, glass transitions, and the Ka.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/Z4UQTG6G/1.html:text/html


@articlejaric_long-range_1985,
	title = Long-Range Icosahedral Orientational Order and Quasicrystals,
	volume = 55,
	url = https://link.aps.org/doi/10.1103/PhysRevLett.55.607,
	doi = 10.1103/PhysRevLett.55.607,
	abstract = It is shown that a quartic orientational free energy leads to long-range icosahedral bond-orientational order which, through a coupling with a translational order parameter, stabilizes the icosahedral quasicrystalline phase. The bond-orientational order selects the wave vectors which point into vertices or faces of an icosahedron.,
	number = 6,
	urldate = 2018-07-18,
	journal = Physical Review Letters,
	author = Jarić, M. V.,
	year = 1985,
	file = APS Snapshot:/Users/carolinegorham/Zotero/storage/C97YPM9L/PhysRevLett.55.html:text/html


@articledebenedetti_supercooled_2001,
	title = Supercooled liquids and the glass transition,
	volume = 410,
	doi = 10.1038/35065704,
	number = 6825,
	journal = Nature,
	author = Debenedetti, P. G. and Stillinger, F. H.,
	year = 2001,
	keywords = unread


@articlekauzmann_nature_1948,
	title = The Nature of the Glassy State and the Behavior of Liquids at Low Temperatures.,
	volume = 43,
	issn = 0009-2665,
	url = http://dx.doi.org/10.1021/cr60135a002,
	doi = 10.1021/cr60135a002,
	number = 2,
	urldate = 2015-02-21,
	journal = Chemical Reviews,
	author = Kauzmann, W.,
	year = 1948


@booksadoc_geometry_1990,
	title = Geometry in condensed matter physics,
	volume = 9,
	publisher = World Scientific,
	author = Sadoc, J.-F.,
	year = 1990,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/3SXXYE2F/books.html:text/html


@articlelanger_mysterious_2007,
	title = The mysterious glass transition,
	volume = 60,
	doi = 10.1063/1.2711621,
	number = 2,
	journal = Physics Today,
	author = Langer, J.,
	year = 2007


@articleberthier_facets_2016,
	title = Facets of glass physics,
	volume = 69,
	doi = 10.1063/PT.3.3052,
	number = 1,
	journal = Physics today,
	author = Berthier, L. and Ediger, M.,
	year = 2016,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/8S95IJQ3/articulo.html:text/html


@articleprzedborski_absence_2014,
	title = Absence of phase transition in the XY-model on Menger sponge,
	volume = 399,
	doi = 10.1016/j.physa.2013.10.023,
	journal = Physica A: Statistical Mechanics and its Applications,
	author = Przedborski, M. A. and Mitrović, B.,
	year = 2014,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/PA99882R/Przedborski and Mitrović - 2014 - Absence of phase transition in the XY-model on Men.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/6MLJEYYX/S0378437113009953.html:text/html


@articlehall_metropolis_2014,
	title = The Metropolis Monte Carlo method with CUDA enabled Graphic Processing Units,
	volume = 258,
	issn = 0021-9991,
	doi = 10.1016/j.jcp.2013.11.012,
	urldate = 2018-07-01,
	journal = Journal of Computational Physics,
	author = Hall, C. and Ji, W. and Blaisten-Barojas, E.,
	year = 2014,
	keywords = Atomistic & molecular simulation, CUDA, GPU, Graphic Processing Units, Metropolis Monte Carlo parallelization,
	file = ScienceDirect Snapshot:/Users/carolinegorham/Zotero/storage/3KFDHFNS/S0021999113007626.html:text/html


@articlealerstam_parallel_2008,
	title = Parallel computing with graphics processing units for high-speed Monte Carlo simulation of photon migration,
	volume = 13,
	doi = 10.1117/1.3041496,
	number = 6,
	journal = Journal of Biomedical Optics,
	author = Alerstam, E. and Svensson, T. and Andersson-Engels, S.,
	year = 2008,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/7HRC9ZRV/1.3041496.html:text/html


@articlemassey_surfaces_1962,
	title = Surfaces of Gaussian curvature zero in Euclidean 3-space,
	volume = 14,
	doi = 10.2748/tmj/1178244205,
	number = 1,
	journal = Tohoku Mathematical Journal, Second Series,
	author = Massey, W. S.,
	year = 1962,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/FDKF2L7F/Massey - 1962 - Surfaces of Gaussian curvature zero in Euclidean 3.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/JQIBX3MC/ja.html:text/html


@articleyazyev_polycrystalline_2014,
	title = Polycrystalline graphene and other two-dimensional materials,
	volume = 9,
	issn = 1748-3387, 1748-3395,
	url = http://www.nature.com/articles/nnano.2014.166,
	doi = 10.1038/nnano.2014.166,
	language = en,
	number = 10,
	urldate = 2018-06-13,
	journal = Nature Nanotechnology,
	author = Yazyev, O. V. and Chen, Y. P.,
	year = 2014,
	file = Yazyev and Chen - 2014 - Polycrystalline graphene and other two-dimensional.pdf:/Users/carolinegorham/Zotero/storage/DDITZQ5E/Yazyev and Chen - 2014 - Polycrystalline graphene and other two-dimensional.pdf:application/pdf


@articlepretko_fracton-elasticity_2018,
	title = Fracton-Elasticity Duality,
	volume = 120,
	doi = 10.1103/PhysRevLett.120.195301,
	number = 19,
	journal = Physical Review Letters,
	author = Pretko, M. and Radzihovsky, L.,
	year = 2018,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/IIZBQKEN/Pretko and Radzihovsky - 2018 - Fracton-Elasticity Duality.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/2FSVJQP6/PhysRevLett.120.html:text/html


@articlelandau_theory_1986,
	title = Theory of Elasticity, vol. 7,
	volume = 3,
	journal = Course of Theoretical Physics,
	author = Landau, L. D. and Lifshitz, E. M.,
	year = 1986


@articleshimshoni_duality_1997,
	title = Duality near quantum Hall transitions,
	volume = 55,
	doi = 10.1103/PhysRevB.55.13730,
	number = 20,
	journal = Physical Review B,
	author = Shimshoni, E. and Sondhi, S. L. and Shahar, D.,
	year = 1997,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/I248YKNU/Shimshoni et al. - 1997 - Duality near quantum Hall transitions.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/IGKXXS2W/PhysRevB.55.html:text/html


@articlehamer_strong-coupling_1979,
	title = Strong-coupling expansions and phase diagrams for the O(2), O(3), and O(4) Heisenberg spin systems in two dimensions,
	volume = 19,
	url = https://link.aps.org/doi/10.1103/PhysRevD.19.3091,
	doi = 10.1103/PhysRevD.19.3091,
	abstract = The Ising and O(n), 2≤n≤4, models in two dimensions are studied using a quantum-mechanical Hamiltonian formalism in which a "time" axis is continuous and a spatial axis is discrete. Strong-coupling series for the theory's mass gaps and β (Callan-Symanzik) functions are computed and are used to search for phase transitions. The critical point and critical index ν of the Ising model are found exactly. The critical point of the O(2) model is found (g∗=1.08), and the series suggest that the theory's correlation length possesses an essential singularity with the behavior predicted by Kosterlitz. The critical points of the O(3) and O(4) models are predicted to be at zero coupling, i.e., no evidence for a phase transition at nonzero g is found for the non-Abelian models. Interpolating forms (two-point Padé approximants) for these theories' β (Callan-Symanzik) functions are computed for all g. The transition regions between weak and strong coupling are seen to be quite narrow.,
	number = 10,
	urldate = 2018-05-02,
	journal = Physical Review D,
	author = Hamer, C. J. and Kogut, John B. and Susskind, L.,
	year = 1979


@articlehooft_symmetry_1994,
	title = Symmetry breaking through Bell-Jackiw anomalies,
	doi = 10.1142/9789812794345_0027,
	journal = Instantons In Gauge Theories,
	author = Hooft, G.'t,
	year = 1994


@articlemoore_lattice_1997,
	title = Lattice Chern-Simons number without ultraviolet problems,
	volume = 56,
	doi = 10.1103/PhysRevD.56.6533,
	number = 10,
	journal = Physical Review D,
	author = Moore, Guy D. and Turok, Neil,
	year = 1997


@booksethna_statistical_2006,
	title = Statistical mechanics: entropy, order parameters, and complexity,
	volume = 14,
	shorttitle = Statistical mechanics,
	publisher = Oxford University Press,
	author = Sethna, J.,
	year = 2006


@articlespring_euler_1986,
	title = Euler parameters and the use of quaternion algebra in the manipulation of finite rotations: A review,
	volume = 21,
	issn = 0094-114X,
	shorttitle = Euler parameters and the use of quaternion algebra in the manipulation of finite rotations,
	url = http://www.sciencedirect.com/science/article/pii/0094114X86900844,
	doi = 10.1016/0094-114X(86)90084-4,
	number = 5,
	urldate = 2018-06-19,
	journal = Mechanism and Machine Theory,
	author = Spring, K. W.,
	year = 1986,
	file = ScienceDirect Snapshot:/Users/carolinegorham/Zotero/storage/QKCS924A/0094114X86900844.html:text/html


@incollectionbenfatto_berezinskiikosterlitzthouless_2013,
	title = Berezinskii–Kosterlitz–Thouless Transition within the Sine-Gordon Approach: The Role of the Vortex-Core Energy,
	shorttitle = Berezinskii–Kosterlitz–Thouless Transition within the Sine-Gordon Approach,
	booktitle = 40 Years of Berezinskii–Kosterlitz–Thouless Theory,
	publisher = World Scientific,
	author = Benfatto, L and Castellani, C. and Giamarchi, T.,
	year = 2013,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/I6P28VGL/Benfatto et al. - 2013 - Berezinskii–Kosterlitz–Thouless Transition within .pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/K5SUWJ76/9789814417648_0005.html:text/html


@articlebradley_quantum_1984-1,
	title = Quantum fluctuations in chains of Josephson junctions,
	volume = 30,
	doi = 10.1103/PhysRevB.30.1138,
	number = 3,
	journal = Physical Review B,
	author = Bradley, R. M. and Doniach, S.,
	year = 1984


@bookgould_statistical_2010,
	title = Statistical and thermal physics: with computer applications,
	shorttitle = Statistical and thermal physics,
	publisher = Princeton University Press,
	author = Gould, H. and Tobochnik, J.,
	year = 2010,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/RYU7ASWC/books.html:text/html


@articlekramer_superinsulator_1998,
	title = Superinsulator Phase of two-dimensional Superconductors,
	volume = 81,
	doi = 10.1103/PhysRevLett.81.3523,
	number = 16,
	journal = Physical review letters,
	author = Krämer, A. and Doniach, S.,
	year = 1998,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/LMDSH8PQ/Krämer and Doniach - 1998 - Superinsulator Phase of two-dimensional Supercondu.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/KFBE29JY/PhysRevLett.81.html:text/html


@articlediamantini_gauge_1996,
	title = Gauge theories of Josephson junction arrays,
	volume = 474,
	doi = 10.1016/0550-3213(96)00309-4,
	number = 3,
	journal = Nuclear Physics B,
	author = Diamantini, M. C. and Sodano, P. and Trugenberger, C. A.,
	year = 1996


@articlesankar_disordered_2018,
	title = Disordered Berezinskii-Kosterlitz-Thouless transition and superinsulation,
	volume = 97,
	url = https://link.aps.org/doi/10.1103/PhysRevB.97.020507,
	doi = 10.1103/PhysRevB.97.020507,
	abstract = We investigate the critical Berezinskii-Kosterlitz-Thouless (BKT) behavior of disordered two-dimensional Josephson-junction arrays (JJA) on the insulating side of the superconductor-insulator transition (SIT) taking into account the effect of hitherto ignored residual random dipole moments of the superconducting grains. We show that for weak Josephson coupling the model is equivalent to a Coulomb gas subjected to a disorder potential with logarithmic correlations. We demonstrate that strong enough disorder transforms the BKT divergence of the correlation length, ξBKT∝exp(const/√T−TBKT), characterizing the average distance between the unbound topological excitations of the opposite signs, into a more singular Vogel-Fulcher-Tamman (VFT) behavior, ξVFT∝exp[const/(T−TVFT)], which is viewed as a hallmark of glass transitions in glass-forming materials. We further show that the VFT criticality is a precursor of the transition into a nonergodic superinsulating state, while the BKT critical behavior implies freezing into an ergodic confined BKT state. Our finding sheds light on the yet unresolved problem of the origin of the VFT criticality.,
	number = 2,
	urldate = 2018-03-22,
	journal = Physical Review B,
	author = Sankar, S. and Vinokur, V. M. and Tripathi, V.,
	year = 2018


@articlekhrapak_internal_2015,
	title = On the internal energy of the classical two-dimensional one-component-plasma,
	volume = 5,
	url = https://aip.scitation.org/doi/full/10.1063/1.4929778,
	doi = 10.1063/1.4929778,
	number = 8,
	urldate = 2018-04-22,
	journal = AIP Advances,
	author = Khrapak, A. G. and Khrapak, S. A.,
	year = 2015


@incollectionvinokur_superinsulatorsuperconductor_2013,
	title = Superinsulator–Superconductor Duality in Two Dimensions and Berezinskii–Kosterlitz–Thouless Transition,
	booktitle = 40 Years of Berezinskii–Kosterlitz–Thouless Theory,
	publisher = World Scientific,
	author = Vinokur, V. M. and Baturina, T. I.,
	year = 2013


@incollectionfazio_charges_2013-1,
	title = Charges and Vortices in Josephson Junction Arrays,
	booktitle = 40 Years of Berezinskii–Kosterlitz–Thouless Theory,
	publisher = World Scientific,
	author = Fazio, R. and Schön, G.,
	year = 2013,
	pages = 237–254


@articlegupta_phase_1988,
	title = Phase transition in the 2D XY model,
	volume = 61,
	doi = 10.1103/PhysRevLett.61.1996,
	number = 17,
	journal = Physical review letters,
	author = Gupta, R. and DeLapp, J. and Batrouni, G. G. and Fox, G. C. and Baillie, C. F. and Apostolakis, J.,
	year = 1988,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/H7T3786W/PhysRevLett.61.html:text/html


@articlecosta_berezinskiikosterlitzthouless_2013,
	title = Berezinskii–Kosterlitz–Thouless transition close to the percolation threshold,
	volume = 377,
	doi = 10.1016/j.physleta.2013.03.030,
	number = 18,
	journal = Physics Letters A,
	author = Costa, B. V. and Coura, P. Z. and Leonel, S. A.,
	year = 2013,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/Y5I2CE2Q/S0375960113003150.html:text/html;Snapshot:/Users/carolinegorham/Zotero/storage/N32SIF8F/S0375960113003150.html:text/html


@articlejose_renormalization_1977,
	title = Renormalization, vortices, and symmetry-breaking perturbations in the two-dimensional planar model,
	volume = 16,
	doi = 10.1103/PhysRevB.16.1217,
	number = 3,
	journal = Physical Review B,
	author = José, J. V. and Kadanoff, L. P. and Kirkpatrick, S. and Nelson, D. R.,
	year = 1977,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/L5KWDCHZ/PhysRevB.16.html:text/html


@articleparker_finite-temperature_2018,
	title = Finite-temperature behavior of a classical spin-orbit-coupled model for YbMgGaO4 with and without bond disorder,
	volume = 97,
	url = https://link.aps.org/doi/10.1103/PhysRevB.97.184413,
	doi = 10.1103/PhysRevB.97.184413,
	abstract = We present the results of finite-temperature classical Monte Carlo simulations of a strongly spin-orbit-coupled nearest-neighbor triangular-lattice model for the candidate U(1) quantum spin liquid YbMgGaO4 at large system sizes. We find a single continuous finite-temperature stripe-ordering transition with slowly diverging heat capacity that completely breaks the sixfold ground-state degeneracy, despite the absence of a known conformal field theory describing such a transition. We also simulate the effect of random-bond disorder in the model, and find that even weak bond disorder destroys the transition by fragmenting the system into very large domains—possibly explaining the lack of observed ordering in the real material. The Imry-Ma argument only partially explains this fragility to disorder, and we extend the argument with a physical explanation for the preservation of our system's time-reversal symmetry even under a disorder model that preserves the same symmetry.,
	number = 18,
	urldate = 2018-07-27,
	journal = Physical Review B,
	author = Parker, E. and Balents, L.,
	year = 2018,
	file = APS Snapshot:/Users/carolinegorham/Zotero/storage/NU3PCWTN/PhysRevB.97.html:text/html


@articleberker_superfluidity_1979,
	title = Superfluidity and phase separation in helium films,
	volume = 19,
	doi = 10.1103/PhysRevB.19.2488,
	number = 5,
	journal = Physical Review B,
	author = Berker, A. N. and Nelson, David R.,
	year = 1979,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/BPRBK3WI/PhysRevB.19.html:text/html


@articlejaeger_ehrenfest_1998,
	title = The Ehrenfest classification of phase transitions: introduction and evolution,
	volume = 53,
	shorttitle = The Ehrenfest classification of phase transitions,
	doi = 10.1007/s004070050,
	number = 1,
	journal = Archive for history of exact sciences,
	author = Jaeger, G.,
	year = 1998,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/4MQIF5NP/Jaeger - 1998 - The Ehrenfest classification of phase transitions.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/ANHN4RXJ/s004070050021.html:text/html


@articlebauer_phase_2005,
	title = Phase transition with the Berezinskii-Kosterlitz-Thouless singularity in the ising model on a growing network,
	volume = 94,
	doi = 10.1103/PhysRevLett.94.200602,
	number = 20,
	journal = Physical review letters,
	author = Bauer, M. and Coulomb, S. and Dorogovtsev, S. N.,
	year = 2005,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/UNVSL83C/Bauer et al. - 2005 - Phase transition with the Berezinskii-Kosterlitz-T.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/TCGM9PKD/PhysRevLett.94.html:text/html


@articlesun_berezinskiikosterlitzthouless_2010,
	title = Berezinskii–Kosterlitz–Thouless phase transition of 2D dilute generalized XY model,
	volume = 389,
	doi = 10.1016/j.physa.2009.12.023,
	number = 7,
	journal = Physica A: Statistical Mechanics and its Applications,
	author = Sun, Y-Z and Liang, J-C and Xu, S-L and Yi, L,
	year = 2010,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/RWNTTYKM/S037843710901019X.html:text/html


@articlecosta_monte_2001,
	title = Monte Carlo study of the critical behavior of the two-dimensional biquadratic planar rotator model,
	volume = 64,
	doi = 10.1103/PhysRevB.64.092407,
	number = 9,
	journal = Physical Review B,
	author = Costa, B. V. and Pires, A. S. T.,
	year = 2001


@articlelee_phase_1998,
	title = Phase transitions in the fully frustrated triangular XY model,
	volume = 57,
	doi = 10.1103/PhysRevB.57.8472,
	number = 14,
	journal = Physical Review B,
	author = Lee, S. and Lee, K.-C.,
	year = 1998


@articleolsson_monte_1995,
	title = Monte Carlo analysis of the two-dimensional XY model. II. Comparison with the Kosterlitz renormalization-group equations,
	volume = 52,
	doi = 10.1103/PhysRevB.52.4526,
	number = 6,
	journal = Physical Review B,
	author = Olsson, P.,
	year = 1995,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/PADGG6YH/PhysRevB.52.html:text/html


@articleolsson_monte_1995-1,
	title = Monte Carlo analysis of the two-dimensional XY model. I. Self-consistent boundary conditions,
	volume = 52,
	number = 6,
	journal = Physical Review B,
	author = Olsson, P.,
	year = 1995,
	pages = 4511,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/HB4ZX9VH/PhysRevB.52.html:text/html


@articletobochnik_monte_1979,
	title = Monte Carlo study of the planar spin model,
	volume = 20,
	doi = 10.1103/PhysRevB.20.3761,
	number = 9,
	journal = Physical Review B,
	author = Tobochnik, J. and Chester, G. V.,
	year = 1979,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/U4BKPDUR/PhysRevB.20.html:text/html


@articlehalperin_resistance_2010,
	title = Resistance in Superconductors,
	volume = 24,
	issn = 0217-9792,
	url = http://adsabs.harvard.edu/abs/2010IJMPB..24.4039H,
	doi = 10.1142/S021797921005644X,
	urldate = 2018-07-29,
	journal = International Journal of Modern Physics B,
	author = Halperin, B. I. and Refael, G. and Demler, E.,
	year = 2010


@inproceedingsbelkin_discrete_2008,
	title = Discrete laplace operator on meshed surfaces,
	doi = 10.1145/1377676.1377725,
	booktitle = Proceedings of the twenty-fourth annual symposium on Computational geometry,
	publisher = ACM,
	author = Belkin, M. and Sun, J. and Wang, Y.,
	year = 2008,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/EIRVIQ2S/citation.html:text/html


@articlemooij_unbinding_1990,
	title = Unbinding of charge-anticharge pairs in two-dimensional arrays of small tunnel junctions,
	volume = 65,
	url = https://link.aps.org/doi/10.1103/PhysRevLett.65.645,
	doi = 10.1103/PhysRevLett.65.645,
	abstract = We describe the behavior of charges in two-dimensional arrays of normal-metal tunnel junctions with very small capacitance. A Kosterlitz-Thouless-Berezinskii phase transition with unbinding of charge-anticharge pairs occurs at a transition temperature of about Tc=e2/8πCkB, with C the junction capacitance. We calculate the influence of tunneling conductance; Tc is reduced with increasing conductance and no transition occurs for junction conductance above (14 kΩ)−1. In the superconducting state a similar transition occurs at a 4 times higher Tc. We present the first experimental results on the conductive transition of an array in the normal and superconducting states.,
	number = 5,
	urldate = 2018-03-20,
	journal = Physical Review Letters,
	author = Mooij, J. E. and van Wees, B. J. and Geerligs, L. J. and Peters, M. and Fazio, R. and Schön, G.,
	year = 1990


@articleblanter_duality_1997-1,
	title = Duality in Josephson junction arrays,
	volume = 58,
	doi = 10.1016/S0920-5632(97)00414-3,
	journal = Nuclear Physics B-Proceedings Supplements,
	author = Blanter, Y. M. and Fazio, R. and Schön, G.,
	year = 1997,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/PUIA2S5Z/Blanter et al. - 1997 - Duality in Josephson junction arrays.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/262B4Z7J/S0920563297004143.html:text/html


@articleteitel_josephson-junction_1983,
	title = Josephson-junction arrays in transverse magnetic fields,
	volume = 51,
	doi = 10.1103/PhysRevLett.51.1999,
	number = 21,
	journal = Physical review letters,
	author = Teitel, S. and Jayaprakash, C.,
	year = 1983


@articleleemann_kosterlitz-thouless_1987,
	title = The Kosterlitz-Thouless transition in Josephson junction arrays.,
	volume = 60,
	number = 1,
	journal = HELVET. PHYS. ACTA.,
	author = Leemann, Ch and Lerch, Ph and Théron, R. and Martinoli, P.,
	year = 1987


@articlemooij_phase-slip_2005,
	title = Phase-slip flux qubits,
	volume = 7,
	issn = 1367-2630,
	url = http://stacks.iop.org/1367-2630/7/i=1/a=219,
	doi = 10.1088/1367-2630/7/1/219,
	abstract = In thin superconducting wires, phase-slip by thermal activation near the critical temperature is a well-known effect. It has recently become clear that phase-slip by quantum tunnelling through the energy barrier can also have a significant rate at low temperatures. In this paper, it is suggested that quantum phase-slip can be used to realize a superconducting quantum bit without Josephson junctions. A loop containing very thin nanofabricated wire is biased with an externally applied magnetic flux of half a flux quantum, resulting in two states with opposite circulating current and equal energy. Quantum phase-slip should provide coherent coupling between these two macroscopic states. Numbers are given for a wire of amorphous niobium-silicon that can be fabricated with advanced electron beam lithography.,
	language = en,
	number = 1,
	urldate = 2018-03-26,
	journal = New Journal of Physics,
	author = Mooij, J. E. and Harmans, C. J. P. M.,
	year = 2005


@articleguichard_phase-charge_2010-1,
	title = Phase-charge duality in Josephson junction circuits: Role of inertia and effect of microwave irradiation,
	volume = 81,
	shorttitle = Phase-charge duality in Josephson junction circuits,
	doi = 10.1103/PhysRevB.81.064508,
	number = 6,
	journal = Physical Review B,
	author = Guichard, W. and Hekking, F. W. J.,
	year = 2010


@articlejoshi_fabricating_2009,
	title = Fabricating nanoscale aperture arrays for superfluid helium-4 weak link experiments,
	volume = 150,
	issn = 1742-6596,
	url = http://stacks.iop.org/1742-6596/150/i=1/a=012018,
	doi = 10.1088/1742-6596/150/1/012018,
	abstract = Arrays of nanoscale apertures have been found to exhibit fascinating quantum phenomena such as the Josephson effect and collective quantized phase-slippage. To be in the Josephson regime, the aperture size must be comparable to the healing length of the 4He order parameter. For 50nm apertures this regime is attained mK below T λ . Collective phase slippage occurs at considerably lower temperatures. Fabricating aperture arrays with appropriate properties (strength, temporal stability and reproducibility) at these length scales has been a long-standing goal for our group. Here, we present the techniques used thus far, based on recent work performed at the Cornell Nanoscale Facility. We discuss some issues that arise and their possible solutions.,
	language = en,
	number = 1,
	urldate = 2018-04-05,
	journal = Journal of Physics: Conference Series,
	author = Joshi, A. and Sato, Y. and Packard, R.,
	year = 2009


@articlesukhatme_observation_2001,
	title = Observation of the ideal Josephson effect in superfluid ^4$He,
	volume = 411,
	copyright = 2001 Nature Publishing Group,
	issn = 1476-4687,
	url = https://www.nature.com/articles/35077024,
	doi = 10.1038/35077024,
	abstract = Superfluids and superconductors are the only states of condensed matter that can be described by a single wavefunction, with a coherent quantum phase Φ. The mass flow in a superfluid can be described by classical hydrodynamics for small flow velocity, but above a critical velocity, quantized vortices are created and the classical picture breaks down. This can be observed for a superfluid flowing through a microscopic aperture when the mass flow is measured as a function of the phase difference across the aperture; the curve resembles a hysteretic sawtooth where each jump corresponds to the creation of a vortex1,2,3. When the aperture is made small enough, the system can enter the so-called ‘ideal’ Josephson regime1,4, where the superfluid mass flow becomes a continuous function of the phase difference. This regime has been detected1,5,6 in superfluid 3He, but was hitherto believed to be unobservable, owing to fluctuations7, in 4He. Here we report the observation of the ideal Josephson effect in 4He. We study the flow of 4He through an array of micro-apertures and observe a transition to the ideal Josephson regime as the temperature is increased towards the superfluid transition temperature, Tλ.,
	language = en,
	number = 6835,
	urldate = 2018-03-29,
	journal = Nature,
	author = Sukhatme, Kalyani and Mukharsky, Yury and Chui, Talso and Pearson, David,
	year = 2001


@articlekhorana_ac_1969,
	title = ac Josephson Effect in Superfluid Helium,
	volume = 185,
	doi = 10.1103/PhysRev.185.299,
	abstract = Two superfluid He baths were linked to each other through a small orifice. A quartz transducer produced a sound wave in the vicinity of the orifice, which served to couple the rate of vortex formation to the sound frequency. When the transducer was on, arrest of the flow at certain head differences was observed. The spacing between most of these steps in the flow curves was found to be in integral multiples of the basic unit z0=hνmg, although in a few instances it was (n2n1)z0. A model for the phase slippage due to the motion of quantized vortex rings, which can account for the observed effect, is discussed. The stability of the liquid level at one of these "steps" appears to be indefinite: Once arrested, the liquid remains arrested until disturbed by fluctuations. These observations provide convincing confirmation of the ac Josephson Effect in liquid He II.,
	number = 1,
	journal = Physical Review,
	author = Khorana, B. M.,
	year = 1969


@articlerichards_observation_1965,
	title = Observation of the analog of the ac Josephson effect in superfluid helium,
	volume = 14,
	doi = 10.1103/PhysRevLett.14.540,
	number = 14,
	journal = Physical Review Letters,
	author = Richards, P. L. and Anderson, P. W.,
	year = 1965


@articleabrikosov_magnetic_1957,
	title = Magnetic properties of superconductors of the second group,
	volume = 5,
	number = 6,
	journal = Sov. Phys. JETP,
	author = Abrikosov, Alexei A.,
	year = 1957


@articlegraber_neutron_2017,
	title = Neutron stars in the laboratory,
	volume = 26,
	doi = 10.1142/S0218271817300154,
	number = 8,
	journal = International Journal of Modern Physics D,
	author = Graber, V. and Andersson, N. and Hogg, M.,
	year = 2017


@articleanderson_considerations_1966,
	title = Considerations on the Flow of Superfluid Helium,
	volume = 38,
	url = https://link.aps.org/doi/10.1103/RevModPhys.38.298,
	doi = 10.1103/RevModPhys.38.298,
	abstract = First, we show that the most important equations of the dynamics of the two types of superfluids, He ii and superconductors, follow quite directly from the simple assumption that the quantum field of the particles has a mean value which may be treated as a macroscopic variable. The background of this ansatz is also discussed. Second, we apply these equations to various physical situations in He ii, notably the orifice geometry and the superfluid film, and show how they, and particularly the idea of phase slippage accompanying all dissipative processes, can be applied and what kinds of macroscopic interference phenomena may be expected. The effect of synchronization in the ac interference experiment is discussed.,
	number = 2,
	urldate = 2018-07-29,
	journal = Reviews of Modern Physics,
	author = ANDERSON, P. W.,
	year = 1966,
	file = APS Snapshot:/Users/carolinegorham/Zotero/storage/DXB66533/RevModPhys.38.html:text/html


@articledu_analysis_1992,
	title = Analysis and Approximation of the Ginzburg-Landau Model of Superconductivity,
	volume = 34,
	url = http://www.jstor.org/stable/2132785,
	doi = 10.1137/1034003,
	number = 1,
	urldate = 2018-06-19,
	journal = SIAM Review,
	author = Du, Q. and Gunzburger, M. D. and Peterson, J. S.,
	year = 1992,
	file = JSTOR Full Text PDF:/Users/carolinegorham/Zotero/storage/QGPSTND7/Du et al. - 1992 - Analysis and Approximation of the Ginzburg-Landau .pdf:application/pdf


@articlewagner_long-wavelength_1966,
	title = Long-wavelength excitations and the Goldstone theorem in many-particle systems with “broken symmetries”,
	volume = 195,
	url = https://link.springer.com/article/10.1007/BF01325630,
	doi = 10.1007/BF01325630,
	number = 3,
	urldate = 2018-06-19,
	journal = Zeitschrift für Physik,
	author = Wagner, H.,
	year = 1966,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/LLJ8RDV6/BF01325630.html:text/html


@articlelange_goldstone_1965,
	title = Goldstone theorem in nonrelativistic theories,
	volume = 14,
	doi = 10.1103/PhysRevLett.14.3,
	number = 1,
	journal = Physical Review Letters,
	author = Lange, R. V.,
	year = 1965,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/YJKSM6HJ/PhysRevLett.14.html:text/html


@articleanderson_random-phase_1958,
	title = Random-phase approximation in the theory of superconductivity,
	volume = 112,
	doi = 10.1103/PhysRev.112.1900,
	number = 6,
	journal = Physical Review,
	author = Anderson, P. W.,
	year = 1958,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/8NQIH5PM/PhysRev.112.html:text/html


@articlegreiter_hydrodynamic_1989,
	title = Hydrodynamic relations in superconductivity.,
	volume = 3,
	doi = 10.1142/S0217984989001400,
	number = 12,
	journal = MOD. PHYS. LETT. B.,
	author = Greiter, M. and Wilczek, F. and Witten, E.,
	year = 1989,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/WQFJNENH/Greiter et al. - 1989 - Hydrodynamic relations in superconductivity..pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/FSGETJDN/Greiter et al. - 1989 - Hydrodynamic relations in superconductivity..pdf:application/pdf


@articlehastings_phenomenolgical_1975,
	title = Phenomenolgical two-branch model for the long-wavelength excitation spectrum of superfluid He-4,
	volume = 12,
	url = https://link.aps.org/doi/10.1103/PhysRevB.12.267,
	doi = 10.1103/PhysRevB.12.267,
	number = 1,
	urldate = 2018-06-19,
	journal = Physical Review B,
	author = Hastings, R. and Halley, J. W.,
	year = 1975,
	pages = 267–275,
	file = APS Snapshot:/Users/carolinegorham/Zotero/storage/ES7C2AAI/PhysRevB.12.html:text/html


@articlegoldstone_broken_1962,
	title = Broken Symmetries,
	volume = 127,
	url = http://link.aps.org/doi/10.1103/PhysRev.127.965,
	doi = 10.1103/PhysRev.127.965,
	number = 3,
	urldate = 2016-02-25,
	journal = Physical Review,
	author = Goldstone, J. and Salam, A. and Weinberg, S.,
	year = 1962


@articleporan_quantum_2017,
	title = Quantum criticality at the superconductor-insulator transition revealed by specific heat measurements,
	volume = 8,
	doi = 10.1038/ncomms14464,
	journal = Nature Communications,
	author = Poran, S and Nguyen-Duc, T and Auerbach, A and Dupuis, N and Frydman, A and Bourgeois, O,
	year = 2017


@incollectionteitel_two-dimensional_2013,
	title = The two-dimensional fully frustrated XY model,
	booktitle = 40 Years of Berezinskii Kosterlitz Thouless Theory,
	publisher = World Scientific,
	author = Teitel, S.,
	year = 2013,
	pages = 201–235


@articleteitel_phase_1983,
	title = Phase transtions in frustrated two-dimensional XY models,
	volume = 27,
	doi = 10.1103/PhysRevB.27.598,
	number = 1,
	journal = Physical Review B,
	author = Teitel, S. and Jayaprakash, C.,
	year = 1983


@articlelee_symmetry_1986,
	title = Symmetry analysis and Monte Carlo study of a frustrated antiferromagnetic planar (XY) model in two dimensions,
	volume = 33,
	doi = 10.1103/PhysRevB.33.450,
	number = 1,
	journal = Physical Review B,
	author = Lee, D. H. and Joannopoulos, J. D. and Negele, J. W. and Landau, D. P.,
	year = 1986


@articlekosterlitz_critical_1974,
	title = The critical properties of the two-dimensional xy model,
	volume = 7,
	doi = 10.1088/0022-3719/7/6/005,
	number = 6,
	journal = Journal of Physics C: Solid State Physics,
	author = Kosterlitz, J. M.,
	year = 1974


@articlemosseri_hierarchical_1984,
	title = Hierarchical structure of defects in non-crystalline sphere packings,
	volume = 45,
	doi = 10.1051/jphyslet:019840045017082700,
	number = 17,
	journal = Journal de Physique Lettres,
	author = Mosseri, R. and Sadoc, J. F.,
	year = 1984


@articlesadoc_hierarchical_1985,
	title = Hierarchical interlaced networks of disclination lines in non-periodic structures,
	volume = 46,
	doi = 10.1051/jphys:0198500460110180900,
	number = 11,
	journal = Journal de Physique,
	author = Sadoc, J.-F. and Mosseri, R.,
	year = 1985


@articlesadoc_disclination_1984,
	title = Disclination density in atomic structures described in curved spaces,
	volume = 45,
	doi = 10.1051/jphys:019840045060102500,
	number = 6,
	journal = Journal de Physique,
	author = Sadoc, J. F. and Mosseri, R.,
	year = 1984


@articlesachdev_order_1985,
	title = Order in metallic glasses and icosahedral crystals,
	volume = 32,
	doi = 10.1103/PhysRevB.32.4592,
	number = 7,
	journal = Physical Review B,
	author = Sachdev, Subir and Nelson, David R.,
	year = 1985


@articlesachdev_theory_1984,
	title = Theory of the structure factor of metallic glasses,
	volume = 53,
	doi = 10.1103/PhysRevLett.53.1947,
	number = 20,
	journal = Physical Review Letters,
	author = Sachdev, Subir and Nelson, David R.,
	year = 1984


@articlemosseri_polytopes_1985,
	title = From polytopes to non-crystalline structures: the iterative flattening method,
	volume = 75,
	shorttitle = From polytopes to non-crystalline structures,
	doi = 10.1016/0022-3093(85)90211-X,
	number = 1-3,
	journal = Journal of Non-Crystalline Solids,
	author = Mosseri, R. and Sadoc, J. F.,
	year = 1985


@articlesadoc_order_1982,
	title = Order and disorder in amorphous, tetrahedrally coordinated semiconductors A curved-space description,
	volume = 45,
	doi = 10.1080/13642818208246413,
	number = 5,
	journal = Philosophical Magazine B,
	author = Sadoc, J. F. and Mosseri, R.,
	year = 1982


@articlekleman_tentative_1979,
	title = A tentative description of the crystallography of amorphous solids,
	volume = 40,
	doi = 10.1051/jphyslet:019790040021056900,
	number = 21,
	journal = Journal de Physique Lettres,
	author = Kleman, M. and Sadoc, J. F.,
	year = 1979


@articlesadoc_use_1981,
	title = Use of regular polytopes for the mathematical description of the order in amorphous structures,
	volume = 44,
	doi = 10.1016/0022-3093(81)90128-9,
	number = 1,
	journal = Journal of Non-Crystalline Solids,
	author = Sadoc, J. F.,
	year = 1981


@articlefrank_complex_1959,
	title = Complex alloy structures regarded as sphere packings. II. Analysis and classification of representative structures,
	volume = 12,
	doi = 10.1107/S0365110X59001499,
	number = 7,
	journal = Acta Crystallographica,
	author = Frank, F. C. and Kasper, J. S.,
	year = 1959


@articlefrank_complex_1958,
	title = Complex alloy structures regarded as sphere packings. I. Definitions and basic principles,
	volume = 11,
	doi = 10.1107/S0365110X58000487,
	number = 3,
	journal = Acta Crystallographica,
	author = Frank, F. C. and Kasper, J. S.,
	year = 1958


@articlefrank_supercooling_1952,
	title = Supercooling of Liquids,
	volume = 215,
	doi = 10.1098/rspa.1952.0194,
	journal = Proceedings of the Royal Society of London Series A,
	author = Frank, F. C.,
	year = 1952


@bookcoxeter_regular_1973,
	title = Regular Polytopes,
	publisher = Courier Corporation,
	author = Coxeter, H. S. M.,
	year = 1973,
	keywords = Mathematics / Algebra / General, Mathematics / Geometry / General


@bookde_graef_structure_2012,
	title = Structure of materials: an introduction to crystallography, diffraction and symmetry,
	publisher = Cambridge University Press,
	author = De Graef, M. and McHenry, M. E.,
	year = 2012,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/RHCLXEQ2/De Graef and McHenry - 2012 - Structure of materials an introduction to crystal.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/GVVG7V9M/books.html:text/html


@articlecremer_director_2012,
	title = Director field in plastic crystals,
	volume = 99,
	doi = 10.1209/0295-5075/99/38005,
	number = 3,
	journal = EPL (Europhysics Letters),
	author = Cremer, P. and Marechal, M. and Löwen, H.,
	year = 2012


@articlealexander_colloquium:_2012,
	title = Colloquium: Disclination loops, point defects, and all that in nematic liquid crystals,
	volume = 84,
	shorttitle = Colloquium,
	doi = 10.1103/RevModPhys.84.497,
	number = 2,
	urldate = 2017-05-15,
	journal = Reviews of Modern Physics,
	author = Alexander, G. P. and Chen, B. G.-G. and Matsumoto, E. A. and Kamien, R.D.,
	year = 2012


@articleromanov_disclinations_1983,
	title = Disclinations in solids,
	volume = 78,
	doi = 10.1002/pssa.2210780102,
	number = 1,
	journal = Physica status solidi (a),
	author = Romanov, A. E. and Vladimirov, V. I.,
	year = 1983


@bookhull_introduction_2001,
	title = Introduction to dislocations,
	publisher = Butterworth-Heinemann,
	author = Hull, D. and Bacon, D. J.,
	year = 2001


@articlekleman_defects_1989,
	title = Defects in liquid crystals,
	volume = 52,
	doi = 10.1088/0034-4885/52/5/002,
	abstract = Defects are local breakings of symmetry in an ordered medium. The physics of defects has long been reduced to the study of dislocations in solids, and to the main physical phenomena they are responsible for, like plastic deformation. Dislocations break translational symmetries. Disclinations break rotational symmetries and are the basic defects of media with continuous symmetries, like liquid crystals. In this review, it is stressed how their study has contributed to a renewal of the physics of defects. Static and dynamic properties in the nematic, cholesteric, blue, smectic and columnar phases of liquid crystals are described in detail, up to the most recent results, for small-molecule thermotropic liquid crystals as well as for lyotropic and polymeric liquid crystals. The authors also discuss the homotopy classification of defects, including point defects, and compare it with the Volterra classification; finally they present the curved-crystal description of frustration in the light of the relevant situation in liquid crystals. The usefulness of the concepts introduced for liquid crystals for the study of other systems (structural problems in biology, dissipative structures, magnetic domains, etc.) is also emphasised.,
	language = en,
	number = 5,
	urldate = 2018-04-25,
	journal = Reports on Progress in Physics,
	author = Kleman, M.,
	year = 1989


@articleatiyah_topological_1978-1,
	title = Topological aspects of Yang-Mills theory,
	volume = 61,
	doi = 10.1007/BF01609489,
	number = 2,
	journal = Communications in Mathematical Physics,
	author = Atiyah, M. F. and Jones, J. D. S.,
	year = 1978


@articlerivier_gauge_1990,
	title = Gauge theory and geometry of condensed matter,
	doi = 10.1142/9789814368315_0001,
	journal = Geometry in condensed matter physics,
	author = Rivier, Nicolas,
	year = 1990


@articlethouless_topological_1997,
	title = Topological quantum numbers in nonrelativistic physics,
	volume = 11,
	doi = 10.1142/S0217979297001623,
	number = 28,
	journal = International Journal of Modern Physics B,
	author = Thouless, D. J.,
	year = 1997,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/GVQDDV6Z/S0217979297001623.html:text/html


@articlekosterlitz_early_2016,
	title = Early work on defect driven phase transitions,
	volume = 30,
	doi = 10.1142/S0217979216300188,
	number = 30,
	journal = International Journal of Modern Physics B,
	author = Kosterlitz, J. M. and Thouless, D. J.,
	year = 2016


@articlepeierls_quelques_1935,
	title = Quelques proprietes typiques des corpses solides,
	volume = 5,
	journal = Ann. IH Poincare,
	author = Peierls, R. E.,
	year = 1935


@articleteo_topological_2017,
	title = Topological Defects in Symmetry-Protected Topological Phases,
	volume = 8,
	doi = 10.1146/annurev-conmatphys-031016-025154,
	urldate = 2017-02-23,
	journal = Annual Review of Condensed Matter Physics,
	author = Teo, J. C. T. and Hughes, T. L.,
	year = 2017


@articletoulouse_principles_1976,
	title = Principles of a classification of defects in ordered media,
	volume = 37,
	doi = 10.1051/jphyslet:01976003706014900,
	number = 6,
	journal = Journal de Physique Lettres,
	author = Toulouse, G. and Kléman, M.,
	year = 1976


@articlegorham_su2_2018,
	title = SU(2) orientational ordering in restricted dimensions: evidence for a Berezinskii-Kosterlitz-Thouless transition of topological point defects in four dimensions,
	volume = 2,
	url = http://iopscience.iop.org/10.1088/2399-6528/aace2a,
	doi = 10.1088/2399-6528/aace2a,
	number = 7,
	urldate = 2018-06-24,
	journal = Journal of Physics Communications,
	author = Gorham, C. S. and Laughlin, D. E.,
	year = 2018,
	file = IOP Full Text PDF:/Users/carolinegorham/Zotero/storage/DKXZZ3WU/Gorham and Laughlin - 2018 - iSU(2)i orientational ordering in restricted .pdf:application/pdf


@articlegantmakher_superconductor-insulator_2010,
	title = Superconductor-insulator quantum phase transition,
	volume = 53,
	url = http://www.turpion.org/php/paper.phtml?journal_id=pu   paper_id=7085,
	doi = 10.3367/UFNe.0180.201001a.0003,
	number = 1,
	journal = Physics-Uspekhi,
	author = Gantmakher, V. F. and Dolgopolov, V. T.,
	year = 2010


@articlejose_duality_2017,
	title = Duality, gauge symmetries, renormalization groups and the BKT Transition,
	volume = 31,
	doi = 10.1142/S0217979217300018,
	number = 6,
	journal = International Journal of Modern Physics B,
	author = José, J. V.,
	year = 2017


@articlefisher_helicity_1973,
	title = Helicity modulus, superfluidity, and scaling in isotropic systems,
	volume = 8,
	doi = 10.1103/PhysRevA.8.1111,
	number = 2,
	journal = Physical Review A,
	author = Fisher, M. E. and Barber, M. N. and Jasnow, D.,
	year = 1973


@articleberezinskii_destruction_1971,
	title = Destruction of long-range order in one-dimensional and two-dimensional systems having a continuous symmetry group I. classical systems,
	volume = 32,
	number = 3,
	journal = Sov. Phys. JETP,
	author = Berezinskii, V. L.,
	year = 1971


@articlekadanoff_scaling_1990,
	title = Scaling and universality in statistical physics,
	volume = 163,
	doi = 10.1016/0378-4371(90)90309-G,
	number = 1,
	journal = Physica A: Statistical Mechanics and its Applications,
	author = Kadanoff, Leo P.,
	year = 1990


@articlekosterlitz_ordering_1973,
	title = Ordering, metastability and phase transitions in two-dimensional systems,
	volume = 6,
	doi = 10.1088/0022-3719/6/7/010,
	number = 7,
	journal = Journal of Physics C: Solid State Physics,
	author = Kosterlitz, J. M. and Thouless, D. J.,
	year = 1973


@articlemermin_topological_1979,
	title = The topological theory of defects in ordered media,
	volume = 51,
	doi = 10.1103/RevModPhys.51.591,
	number = 3,
	journal = Reviews of Modern Physics,
	author = Mermin, N. David,
	year = 1979


@articlebaturina_superinsulatorsuperconductor_2013,
	title = Superinsulator–superconductor duality in two dimensions,
	volume = 331,
	doi = 10.1016/j.aop.2012.12.007,
	journal = Annals of Physics,
	author = Baturina, Tatyana I. and Vinokur, Valerii M.,
	year = 2013


@articlemermin_homotopy_1978,
	title = The homotopy groups of condensed matter physics,
	volume = 19,
	doi = 10.1063/1.523811,
	number = 6,
	journal = Journal of Mathematical Physics,
	author = Mermin, N. D.,
	year = 1978


@articlesethna_relieving_1983,
	title = Relieving cholesteric frustration: the blue phase in a curved space,
	volume = 51,
	url = https://doi.org/10.1103/PhysRevLett.51.467,
	doi = 10.1103/PhysRevLett.51.467,
	number = 6,
	journal = Physical review letters,
	author = Sethna, J. P. and Wright, D. C. and Mermin, N. D.,
	year = 1983


@incollectionslack_thermal_1979,
	series = Solid State Physics,
	title = The Thermal Conductivity of Nonmetallic Crystals,
	volume = 34,
	url = https://doi.org/10.1016/S0081-1947(08)60359-8,
	publisher = Academic Press,
	author = Slack, G. A.,
	editor = Henry Ehrenreich, F. S. and Turnbull, D.,
	year = 1979,
	keywords = polycrystalline


@articlevinokur_superinsulator_2008,
	title = Superinsulator and quantum synchronization,
	volume = 452,
	url = http://dx.doi.org/10.1038/nature06837,
	doi = 10.1038/nature06837,
	number = 7187,
	journal = Nature,
	author = Vinokur, V. M. and Baturina, Tatyana I. and Fistul, Mikhail V. and Mironov, Aleksey Yu and Baklanov, Mikhail R. and Strunk, Christoph,
	year = 2008


@articledemchik_monte_2009,
	title = Monte Carlo simulations on graphics processing units,
	journal = arXiv preprint arXiv:0903.3053,
	author = Demchik, V. and Strelchenko, A.,
	year = 2009,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/N6363WWS/Demchik and Strelchenko - 2009 - Monte Carlo simulations on graphics processing uni.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/Q2ZCSPL2/0903.html:text/html


@articlespeedy_kauzmanns_2003,
	series = Walter Kauzmann`s 85th Birthday,
	title = Kauzmann's paradox and the glass transition,
	volume = 105,
	issn = 0301-4622,
	url = http://www.sciencedirect.com/science/article/pii/S0301462203001054,
	doi = 10.1016/S0301-4622(03)00105-4,
	abstract = Kauzmann showed that the entropy of a liquid decreases rapidly on cooling towards the kinetic glass transition temperature and extrapolates to unreasonable values at lower temperature. The temperature where the extrapolated liquid entropy meets the crystal entropy is now called the Kauzmann temperature. Thermodynamics, with Planck's statement of the third law, shows that the entropy of a liquid cannot be less than the entropy of a glass with the same enthalpy. This is the thermodynamic condition violated by the Kauzmann extrapolation and it suggests a thermodynamic glass transition. Simulations show that, for the simple models studied and regardless of how the liquid entropy is extrapolated, the Kauzmann temperature cannot be reached because the entropy of glasses with the same enthalpy as the liquid is greater than that of the crystal.,
	number = 2,
	urldate = 2018-07-07,
	journal = Biophysical Chemistry,
	author = Speedy, R. J.,
	year = 2003,
	keywords = Glass transition, Kauzmann paradox,
	file = ScienceDirect Snapshot:/Users/carolinegorham/Zotero/storage/8HY2HL2F/S0301462203001054.html:text/html


@bookconway_sphere_1999,
	address = New York,
	edition = 3,
	series = Grundlehren der mathematischen Wissenschaften,
	title = Sphere Packings, Lattices and Groups,
	isbn = 978-0-387-98585-5,
	url = //www.springer.com/us/book/9780387985855,
	urldate = 2018-06-26,
	publisher = Springer-Verlag,
	author = Conway, J. and Sloane, N. J. A.,
	year = 1999,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/5ZIUJDXM/9780387985855.html:text/html


@bookziman_electrons_2001,
	title = Electrons and phonons: the theory of transport phenomena in solids,
	publisher = OUP Oxford,
	author = Ziman, J. M,
	year = 2001,
	keywords = (polycrystalline), born von karman, sine-type


@bookdulong_recherches_1819,
	title = Recherches sur quelques points importans de la theorie de la Chaleur,
	author = Dulong, P. L. and Petit, A.-T.,
	year = 1819


@articleeinstein_plancks_1907,
	title = Planck’s theory of radiation and the theory of specific heat,
	volume = 22,
	journal = Ann. Phys,
	author = Einstein, A.,
	year = 1907,
	pages = 180–190


@bookashcroft_solid_1976,
	title = Solid state physics,
	volume = 403,
	isbn = 978-0-03-083993-1,
	publisher = Holt, Rinehart and Winston,
	author = Ashcroft, N. W. and Mermin, N. D.,
	year = 1976


@articledebye_zur_1912,
	title = Zur theorie der spezifischen wärmen,
	volume = 344,
	number = 14,
	journal = Annalen der Physik,
	author = Debye, P.,
	year = 1912,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/QAEGSF4T/andp.html:text/html


@bookvincenti_introduction_1965,
	title = Introduction to physical gas dynamics,
	volume = 246,
	publisher = Wiley New York,
	author = Vincenti, W. G. and Kruger, C. H.,
	year = 1965,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/XN8EVGM3/Vincenti and Kruger - 1965 - Introduction to physical gas dynamics.pdf:application/pdf


@articletaraskin_ioffe-regel_2000,
	title = Ioffe-Regel crossover for plane-wave vibrational excitations in vitreous silica,
	volume = 61,
	doi = 10.1103/PhysRevB.61.12031,
	number = 18,
	journal = Physical Review B,
	author = Taraskin, S. N. and Elliott, S. R.,
	year = 2000,
	keywords = (polycrystalline)


@articlegorham_formation_2018-1,
	title = On the formation of crystalline and non-crystalline structures from undercooled atomic liquids: Comments on the thermal transport properties of solid states,
	journal = In progress,
	author = Gorham, C. S. and Laughlin, D. E.,
	year = 2018


@articlefazio_charge-vortex_1992,
	title = Charge-Vortex Duality in Josephson Junction Arrays,
	volume = 65,
	url = http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.68.3686   rep=rep1   type=pdf,
	number = 228,
	journal = Helv. Phys. Acta,
	author = Fazio, R. and Van Otterlo, A. and Schön, Gerd and Van Der Zant, H. S. J. and Mooij, J. E.,
	year = 1992


@articlevojta_quantum_2006,
	title = Quantum phase transitions of the diluted O(3) rotor model,
	volume = 74,
	url = https://link.aps.org/doi/10.1103/PhysRevB.74.094415,
	doi = 10.1103/PhysRevB.74.094415,
	number = 9,
	journal = Physical Review B,
	author = Vojta, T. and Sknepnek, R.,
	month = sep,
	year = 2006,
	pages = 094415


@inproceedingshamilton_proof_1847,
	title = On a Proof of Pascal's Theorem by Means of Quaternions; and on some other connected subjects,
	volume = 3,
	booktitle = Proceedings of the Royal Irish Academy,
	author = Hamilton, W. R.,
	year = 1847,
	pages = 273–292,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/RBMUJLZE/Hamilton - 1847 - ON A PROOF OF PASCAL’S THEOREM BY MEANS OF QUATERN.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/TLG6CTC9/Hamilton - 1847 - ON A PROOF OF PASCAL’S THEOREM BY MEANS OF QUATERN.pdf:application/pdf


@bookchaikin_principles_2000,
	title = Principles of condensed matter physics,
	volume = 1,
	publisher = Cambridge Univ Press,
	author = Chaikin, P. M. and Lubensky, T. C.,
	year = 2000


@articlenelson_symmetry_1984,
	title = Symmetry, Landau theory and polytope models of glass,
	volume = 240,
	doi = 10.1016/0550-3213(84)90281-5,
	number = 1,
	journal = Nuclear Physics B,
	author = Nelson, D. R. and Widom, M.,
	month = aug,
	year = 1984,
	pages = 113–139


@articlecahill_lower_1992,
	title = Lower limit to the thermal conductivity of disordered crystals,
	volume = 46,
	doi = 10.1103/PhysRevB.46.6131,
	number = 10,
	journal = Phys. Rev. B,
	author = Cahill, D. G. and Watson, S. K. and Pohl, R. O.,
	month = sep,
	year = 1992,
	keywords = fractal, fracton, thermal conductivity, disordered,
	pages = 6131–6140


@booknelson_defects_2002,
	title = Defects and geometry in condensed matter physics,
	publisher = Cambridge University Press,
	author = Nelson, D. R.,
	year = 2002


@articlechern_modeling_2008,
	title = Modeling the Berezinskii-Kosterlitz-Thouless transition in NiGa 2 S 4,
	volume = 78,
	number = 2,
	journal = Physical Review B,
	author = Chern, Chyh-Hong,
	year = 2008,
	pages = 020403,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/HMJCWRCN/Chern - 2008 - Modeling the Berezinskii-Kosterlitz-Thouless trans.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/U46EL6T4/PhysRevB.78.html:text/html


@articlesilsbee_simulations_1997,
	title = Simulations for Solid State Physics,
	language = en,
	urldate = 2018-06-29,
	journal = Cambridge, UK: Cambridge University Press,
	author = Silsbee, Robert H. and Draeger, Joerg,
	year = 1997,
	pages = 366,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/M9ZIVTTT/1997sssp.book.....html:text/html


@bookhooft_recent_2013,
	title = Recent Developments in Gauge Theories,
	abstract = Almost all theories of fundamental interactions are nowadays based on the gauge concept. Starting with the historical example of quantum electrodynamics, we have been led to the successful unified gauge theory of weak and electromagnetic interactions, and finally to a non abelian gauge theory of strong interactions with the notion of permanently confined quarks. The. early theoretical work on gauge theories was devoted to proofs of renormalizability, investigation of short distance behaviour, the discovery of asymptotic freedom, etc . . , aspects which were accessible to tools extrapolated from renormalised perturbation theory. The second phase of the subject is concerned with the problem of quark confinement which necessitates a non-perturbative understanding of gauge theories. This phase has so far been marked by the introduc tion of ideas from geometry, topology and statistical mechanics in particular the theory of phase transitions. The 1979 Cargese Institute on "Recent Developments on Gauge Theories" was devoted to a thorough discussion of these non-perturbative, global aspects of non-abelian gauge theories. In the lectures and seminars reproduced in this volume the reader wilf find detailed reports on most of the important developments of recent times on non perturbative gauge fields by some of the leading experts and innovators in this field. Aside from lectures on gauge fields proper, there were lectures on gauge field concepts in condensed matter physics and lectures by mathematicians on global aspects of the calculus of variations, its relation to geometry and topology, and related topics.,
	publisher = Springer Science & Business Media,
	author = Hooft, G. 't,
	year = 2013,
	keywords = Science / Physics / Electricity, Science / Physics / Nuclear, Science / Physics / Optics & Light, Science / Physics / Atomic & Molecular, Science / Physics / Quantum Theory


@articlenelson_liquids_1983,
	title = Liquids and Glasses in Spaces of Incommensurate Curvature,
	volume = 50,
	doi = 10.1103/PhysRevLett.50.982,
	abstract = Supercooled liquids and metallic glasses can be viewed as defected states of bond orientational order. Surfaces of constant negative curvature contain an irreducible density of point disclinations in a hexatic order parameter. Analogous defect lines in an icosahedral order parameter appear in three-dimensional flat space. The Frank-Kasper phases are ordered networks of these lines, which, when disordered, provide an appealing model for structure in metallic glasses.,
	number = 13,
	journal = Physical Review Letters,
	author = Nelson, David R.,
	year = 1983,
	pages = 982–985


@articleolson_specific_1993,
	title = Specific heat and thermal conductivity of solid fullerenes,
	volume = 259,
	doi = 10.1126/science.259.5098.1145,
	journal = Phonon Scattering in Condensed Matter VII,
	author = Olson, J. R. and Topp, K. A. and Pohl, R. O.,
	year = 1993,
	keywords = polycrystalline, einstein oscillators, FULLERENES, DEBYE approximation, LATTICE VIBRATIONS, SOLID STATE, specific heat,
	pages = 1145–1148


@articleanderson_through_1995,
	title = Through the glass lightly,
	volume = 267,
	issn = 0036-8075,
	doi = 10.1126/science.267.5204.1615-e,
	language = eng,
	number = 5204,
	journal = Science (New York, N.Y.),
	author = Anderson, P. W.,
	year = 1995,
	pmid = 17808155,
	pages = 1615–1616


@articlecahill_thermal_1987,
	title = Thermal conductivity of amorphous solids above the plateau,
	volume = 35,
	url = http://link.aps.org/doi/10.1103/PhysRevB.35.4067,
	doi = 10.1103/PhysRevB.35.4067,
	number = 8,
	author = Cahill, D. G. and Pohl, R. O.,
	year = 1987,
	keywords = amorphous, fractal, fracton,
	pages = 4067–4073


@booksadoc_geometrical_2006,
	title = Geometrical frustration,
	publisher = Cambridge University Press,
	author = Sadoc, J.-F. and Mosseri, R.,
	year = 2006


@articlemermin_absence_1966,
	title = Absence of Ferromagnetism or Antiferromagnetism in One- or Two-Dimensional Isotropic Heisenberg Models,
	volume = 17,
	doi = 10.1103/PhysRevLett.17.1133,
	number = 22,
	journal = Physical Review Letters,
	author = Mermin, N. D. and Wagner, H.,
	year = 1966,
	pages = 1133–1136


@bookcoleman_aspects_1988,
	title = Aspects of symmetry: selected Erice lectures,
	shorttitle = Aspects of symmetry,
	publisher = Cambridge University Press,
	author = Coleman, S.,
	year = 1988


@bookcoleman_aspects_1988-1,
	title = Aspects of symmetry: selected Erice lectures,
	shorttitle = Aspects of symmetry,
	publisher = Cambridge University Press,
	author = Coleman, S.,
	year = 1988


@booksadoc_foams_2013,
	title = Foams and emulsions,
	volume = 354,
	publisher = Springer Science & Business Media,
	author = Sadoc, J.-F. and Rivier, N.,
	year = 2013


@articlemosseri_geometrical_2008,
	title = Geometrical frustration and defects in condensed matter systems,
	volume = 11,
	issn = 1631-0748,
	url = http://www.sciencedirect.com/science/article/pii/S1631074807002020,
	doi = 10.1016/j.crci.2007.03.019,
	abstract = The concept of geometrical frustration is recalled, in particular in the case of frustrated icosahedral order. The curved space approach allows one to relax the frustration at the price of curving the underlying space. Topological defects are then introduced to produce a realistic structure in R3. In this paper we focus on the description of two types of large cell crystalline structures with frustrated order, the metallic Frank–Kasper alloys and the cholesteric blue phases. Both structures can be described as a periodic array of disclination line defects threading a medium with (slightly deformed) local and medium range order.,
	number = 3,
	urldate = 2018-01-16,
	journal = Comptes Rendus Chimie,
	author = Mosseri, Rémy,
	year = 2008,
	keywords = Topological defects, Curved space model, Geometrical frustration,
	pages = 192–197


@bookvenkataraman_beyond_1989,
	title = Beyond the crystalline state: an emerging perspective,
	volume = 84,
	publisher = Springer Science & Business Media,
	author = Venkataraman, G. and Sahoo, D. and Balakrishnan, V.,
	year = 1989


@articlerivier_disclination_1979,
	title = Disclination lines in glasses,
	volume = 40,
	issn = 0141-8610,
	url = https://doi.org/10.1080/01418617908234879,
	doi = 10.1080/01418617908234879,
	abstract = It is shown that line defects are topologically stable in disordered condensed matter, and that they are disclinations, associated with rotation distortions. These disclinations are constructed explicitly in continuous random networks, where they are shown to be uninterrupted lines threading through the odd-numbered rings of bonds. Their topological stability is associated with the fact that the rotation group is not simply connected. The disclinations are of one type only and are characterized by oddness rather than by intensity as in crystals; they are described by the two-element group Zr2.,
	number = 6,
	urldate = 2018-03-19,
	journal = Philosophical Magazine A,
	author = Rivier, N.,
	year = 1979,
	pages = 859–868


@articlesethna_meissner_1992-1,
	title = Meissner Effect and Constraints,
	url = http://arxiv.org/abs/cond-mat/9204010,
	abstract = We notice some beautiful geometrical defects found in liquid crystals, and explain them by imposing a constraint. We study the way constraints can occur, and introduce the concept of massive fields. We develop the theory of magnetic field expulsion in superconductors as an example. We notice strong analogies with the formation of grain boundaries in crystals, and realize that we do not understand crystals very deeply,
	urldate = 2018-06-19,
	journal = arXiv:cond-mat/9204010,
	author = Sethna, J. P. and Huang, M.,
	year = 1992,
	keywords = Condensed Matter,
	annote = arXiv: cond-mat/9204010,
	annote = Comment: Lectures Given at the Santa Fe Complexity Institute Summer School, 1991. Figures added,
	file = arXiv cond-mat/9204010 PDF:/Users/carolinegorham/Zotero/storage/8D28KTQP/Sethna and Huang - 1992 - Meissner Effect and Constraints.pdf:application/pdf;arXiv.org Snapshot:/Users/carolinegorham/Zotero/storage/MTGZM5C2/9204010.html:text/html


@bookbognar_indefinite_2012,
	title = Indefinite Inner Product Spaces,
	isbn = 978-3-642-65567-8,
	language = en,
	publisher = Springer Science & Business Media,
	author = Bognar, J.,
	year = 2012,
	keywords = Mathematics / Algebra / General,
	annote = Google-Books-ID: uQrpCAAAQBAJ


@bookjackson_classical_1975,
	title = Classical Electrodynamics,
	publisher = Wiley Online Library,
	author = Jackson, J. D.,
	year = 1975


@articlehalperin_resistive_1979,
	title = Resistive transition in superconducting films,
	volume = 36,
	issn = 0022-2291, 1573-7357,
	url = https://link.springer.com/article/10.1007/BF00116988,
	doi = 10.1007/BF00116988,
	abstract = The consequences of a vortex unbinding picture of two-dimensional superconductivity are worked out. Although there is no true finite-temperature phase transition, dirty superconducting films should display anomalous behavior below the BCS transition temperature and above an effective Kosterlitz-Thouless vortex unbinding temperature. In particular, both the conductivity and fluctuation diamagnetism behave like ξ+2in this regime, where ξ+ is the correlation length calculated by Kosterlitz, ξ+-ξc exp (B/T − Tc)1/2. We estimate ξc, B, and the vortex unbinding temperature, and determine the nonlinear resistivity below Tc. A recent theory of vortex dynamics, together with a time-dependent Ginzburg-Landau theory, lead to a determination of the frequency-dependent conductivity.,
	language = en,
	number = 5-6,
	urldate = 2017-08-03,
	journal = Journal of Low Temperature Physics,
	author = Halperin, B. I. and Nelson, D. R.,
	year = 1979,
	pages = 599–616


@bookblundell_concepts_2009,
	title = Concepts in thermal physics,
	publisher = OUP Oxford,
	author = Blundell, S. J. and Blundell, K. M.,
	year = 2009,
	file = Fulltext:/Users/carolinegorham/Zotero/storage/N5YHXJ4U/Blundell and Blundell - 2009 - Concepts in thermal physics.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/2JUBMTVF/books.html:text/html


@bookhatcher_algebraic_2002,
	address = Cambridge,
	title = Algebraic topology,
	publisher = Cambridge UP,
	author = Hatcher, Allen,
	year = 2002


@articledevoret_superconducting_2004,
	title = Superconducting qubits: A short review,
	shorttitle = Superconducting qubits,
	journal = arXiv preprint cond-mat/0411174,
	author = Devoret, Michel H. and Wallraff, Andreas and Martinis, John M.,
	year = 2004,
	file = Full Text:/Users/carolinegorham/Zotero/storage/UQIMKLNC/Devoret et al. - 2004 - Superconducting qubits A short review.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/D95AX45D/0411174.html:text/html


@articleefetov_phase_1980,
	title = Phase transitions in granulated superconductors,
	volume = 78,
	journal = Zhurnal Eksperimental'noi i Teoreticheskoi Fiziki,
	author = Efetov, K. B.,
	year = 1980,
	pages = 2017–2032,
	file = Full Text:/Users/carolinegorham/Zotero/storage/96D82KRS/Efetov - 1980 - Phase transitions in granulated superconductors.pdf:application/pdf


@articlehohenberg_existence_1967-1,
	title = Existence of long-range order in one and two dimensions,
	volume = 158,
	number = 2,
	journal = Physical Review,
	author = Hohenberg, Pierre C.,
	year = 1967,
	pages = 383,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/FWHQANU5/PhysRev.158.html:text/html


@articlenieto_duality_2018-1,
	title = Duality, matroids, qubits, twistors and surreal numbers,
	journal = arXiv preprint arXiv:1810.04521,
	author = Nieto, Juan Antonio,
	year = 2018,
	file = Full Text:/Users/carolinegorham/Zotero/storage/EME7NKZZ/Nieto - 2018 - Duality, matroids, qubits, twistors and surreal nu.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/HKKCKZ98/1810.html:text/html


@articlekarasawa_conservation-law-induced_2007,
	title = Conservation-law-induced quantum limits for physical realizations of the quantum NOT gate,
	volume = 75,
	number = 3,
	journal = Physical Review A,
	author = Karasawa, Tokishiro and Ozawa, Masanao,
	year = 2007,
	pages = 032324,
	file = Full Text:/Users/carolinegorham/Zotero/storage/MWWK9C57/Karasawa and Ozawa - 2007 - Conservation-law-induced quantum limits for physic.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/XVZJZG36/PhysRevA.75.html:text/html


@phdthesissteiger_quantum_2010,
	type = PhD Thesis,
	title = Quantum Uncertainty and Conservation Law Restrictions on Gate Fidelity,
	school = Brigham Young University. Department of Physics and Astronomy,
	author = Steiger, Nathan John,
	year = 2010,
	file = Full Text:/Users/carolinegorham/Zotero/storage/6KNCQ3W2/Steiger - 2010 - Quantum Uncertainty and Conservation Law Restricti.pdf:application/pdf


@articlesvetogorov_theory_2018,
	title = Theory of coherent quantum phase slips in Josephson junction chains with periodic spatial modulations,
	volume = 97,
	number = 10,
	journal = Physical Review B,
	author = Svetogorov, Aleksandr E. and Taguchi, Masahiko and Tokura, Yasuhiro and Basko, Denis M. and Hekking, Frank WJ,
	year = 2018,
	pages = 104514,
	file = Full Text:/Users/carolinegorham/Zotero/storage/J5I6V2KP/Svetogorov et al. - 2018 - Theory of coherent quantum phase slips in Josephso.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/SHNLK6J9/PhysRevB.97.html:text/html


@articlekitaev_quantum_1997,
	title = Quantum computations: algorithms and error correction,
	volume = 52,
	shorttitle = Quantum computations,
	number = 6,
	journal = Russian Mathematical Surveys,
	author = Kitaev, A. Yu,
	year = 1997,
	pages = 1191–1249,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/WCXVYM4I/authorize.html:text/html


@articledeutsch_quantum_1989,
	title = Quantum computational networks,
	volume = 425,
	number = 1868,
	journal = Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences,
	author = Deutsch, David Elieser,
	year = 1989,
	pages = 73–90,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/PRMKETKM/rspa.1989.html:text/html


@articleurbantke_two-level_1991,
	title = Two-level quantum systems: States, phases, and holonomy,
	volume = 59,
	shorttitle = Two-level quantum systems,
	number = 6,
	journal = American Journal of Physics,
	author = Urbantke, H.,
	year = 1991,
	pages = 503–509,
	file = Full Text:/Users/carolinegorham/Zotero/storage/NMVBVQ7T/Urbantke - 1991 - Two-level quantum systems States, phases, and hol.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/2SXHVSR4/1.html:text/html


@articlemosseri_geometry_2001-1,
	title = Geometry of entangled states, Bloch spheres and Hopf fibrations,
	volume = 34,
	issn = 0305-4470,
	url = https://doi.org/10.1088
	doi = 10.1088/0305-4470/34/47/324,
	abstract = We discuss a generalization of the standard Bloch sphere representation for a single qubit to two qubits, in the framework of Hopf fibrations of high-dimensional spheres by lower dimensional spheres. The single-qubit Hilbert space is the three-dimensional sphere S 3. The S 2 base space of a suitably oriented S 3 Hopf fibration is nothing but the Bloch sphere, while the circular fibres represent the overall qubit phase degree of freedom. For the two-qubits case, the Hilbert space is a seven-dimensional sphere S 7, which also allows for a Hopf fibration, with S 3 fibres and a S 4 base. The most striking result is that suitably oriented S 7 Hopf fibrations are entanglement sensitive. The relation with the standard Schmidt decomposition is also discussed.,
	language = en,
	number = 47,
	urldate = 2019-03-19,
	journal = Journal of Physics A: Mathematical and General,
	author = Mosseri, Rémy and Dandoloff, Rossen,
	month = nov,
	year = 2001,
	pages = 10243–10252,
	file = IOP Full Text PDF:/Users/carolinegorham/Zotero/storage/4VJMAURY/Mosseri and Dandoloff - 2001 - Geometry of entangled states, Bloch spheres and Ho.pdf:application/pdf


@articlekitaev_fault-tolerant_2003-1,
	title = Fault-tolerant quantum computation by anyons,
	volume = 303,
	issn = 0003-4916,
	url = http://www.sciencedirect.com/science/article/pii/S0003491602000180,
	doi = 10.1016/S0003-4916(02)00018-0,
	abstract = A two-dimensional quantum system with anyonic excitations can be considered as a quantum computer. Unitary transformations can be performed by moving the excitations around each other. Measurements can be performed by joining excitations in pairs and observing the result of fusion. Such computation is fault-tolerant by its physical nature.,
	number = 1,
	urldate = 2019-03-19,
	journal = Annals of Physics,
	author = Kitaev, A. Yu.,
	month = jan,
	year = 2003,
	pages = 2–30,
	file = ScienceDirect Full Text PDF:/Users/carolinegorham/Zotero/storage/GB2NLP3L/Kitaev - 2003 - Fault-tolerant quantum computation by anyons.pdf:application/pdf;ScienceDirect Snapshot:/Users/carolinegorham/Zotero/storage/CCVRK9SX/S0003491602000180.html:text/html


@articlebarbashov_quantum_2006,
	title = Quantum Gravity as Theory of “Superfluidity”,
	volume = 841,
	issn = 0094-243X,
	url = https://aip.scitation.org/doi/abs/10.1063/1.2218193,
	doi = 10.1063/1.2218193,
	number = 1,
	urldate = 2019-03-27,
	journal = AIP Conference Proceedings,
	author = Barbashov, B. M. and Pervushin, V. N. and Zakharov, A. F. and Zinchuk, V. A.,
	month = jun,
	year = 2006,
	pages = 362–369,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/3MS6KGQP/1.html:text/html;Submitted Version:/Users/carolinegorham/Zotero/storage/MXDLF78Z/Barbashov et al. - 2006 - Quantum Gravity as Theory of “Superfluidity”.pdf:application/pdf


@bookconway_sphere_1999-1,
	address = New York,
	edition = 3,
	series = Grundlehren der mathematischen Wissenschaften,
	title = Sphere Packings, Lattices and Groups,
	isbn = 978-0-387-98585-5,
	url = https://www.springer.com/us/book/9780387985855,
	language = en,
	urldate = 2019-04-01,
	publisher = Springer-Verlag,
	author = Conway, John and Sloane, Neil J. A.,
	year = 1999,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/G438FQHZ/9780387985855.html:text/html


@articleelser_highly_1987,
	title = A highly symmetric four-dimensional quasicrystal,
	volume = 20,
	issn = 0305-4470,
	url = https://doi.org/10.1088
	doi = 10.1088/0305-4470/20/18/016,
	abstract = A quasiperiodic pattern (or quasicrystal) is constructed in real four-dimensional Euclidean space, having the non-crystallographic reflection group (3, 3, 5) of order 14 400 as its point group. It is obtained as a projection of the eight-dimensional lattice E8, and has as a cross section a three-dimensional quasicrystal with icosahedral symmetry.,
	language = en,
	number = 18,
	urldate = 2019-04-01,
	journal = Journal of Physics A: Mathematical and General,
	author = Elser, V. and Sloane, N. J. A.,
	month = dec,
	year = 1987,
	pages = 6161–6167,
	file = Submitted Version:/Users/carolinegorham/Zotero/storage/HHQ4KSAL/Elser and Sloane - 1987 - A highly symmetric four-dimensional quasicrystal.pdf:application/pdf


@articlegorham_quantized_2019,
	title = Quantized Hall Effect Phenomena and Topological-Order in 4D Josephson Junction Arrays in the Vicinity of a Quantum Phase Transition,
	url = http://arxiv.org/abs/1903.11945,
	abstract = Recently, generalizations of quantum Hall effects (QHE) have been made from 2D to 4D and 8D by considering their mathematical frameworks within complex (C), quaternion (H) and octonion (O) compact (gauge) Lie algebra domains. Just as QHE in two-dimensional electron gases can be understood in terms of Chern number topological invariants that belong to the first Chern class, QHE in 4D and 8D can be understood in terms of Chern number topological invariants that belong to the 2nd and 4th Chern classes. It has been shown that 2D QHE phenomena are related to topologically-ordered ground states of Josephson junction arrays (JJAs), which map onto an Abelian gauge theory with a periodic topological term that describes charge-vortex coupling. In these 2D JJAs, magnetic point defects and Cooper pair electric charges are dual to one another via electric-magnetic duality (Montonen-Olive). This leads to a quantum phase transition between phase-coherent superconductor and dual phase-incoherent superinsulator ground states, at a "self-dual" critical point. In this article, a framework for topological-ordering of Bose-Einstein condensates is extended to consider four-dimensional quaternion ordered systems that are related to 4D QHE. This is accomplished with the incorporation of a non-Abelian topological term that describes coupling between third homotopy group point defects (as generalized magnetic vortices) and Cooper pair-like charges. Point defects belonging to the third homotopy group are dual to charge excitations, and this leads to the manifestation of a quantum phase transition between orientationally-ordered and orientationally-disordered ground states at a "self-dual" critical point. The frustrated ground state in the vicinity of this "self-dual" critical point, are characterized by global topological invariants belonging to the 2nd Chern class.,
	urldate = 2019-04-03,
	journal = arXiv:1903.11945 [hep-th, physics:math-ph],
	author = Gorham, Caroline S. and Laughlin, David E.,
	month = mar,
	year = 2019,
	note = arXiv: 1903.11945,
	keywords = High Energy Physics - Theory, Mathematical Physics,
	file = arXiv 1903.11945 PDF:/Users/carolinegorham/Zotero/storage/KFF8ELA4/Gorham and Laughlin - 2019 - Quantized Hall Effect Phenomena and Topological-Or.pdf:application/pdf;arXiv.org Snapshot:/Users/carolinegorham/Zotero/storage/2WZX3DUQ/1903.html:text/html


@articlemoriwake_electric_2016,
	title = The electric field induced ferroelectric phase transition of AgNbO3,
	volume = 119,
	issn = 0021-8979,
	url = https://aip.scitation.org/doi/abs/10.1063/1.4941319,
	doi = 10.1063/1.4941319,
	number = 6,
	urldate = 2019-04-03,
	journal = Journal of Applied Physics,
	author = Moriwake, Hiroki and Konishi, Ayako and Ogawa, Takafumi and Fisher, Craig A. J. and Kuwabara, Akihide and Fu, Desheng,
	month = feb,
	year = 2016,
	pages = 064102,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/GFVHGNTH/1.html:text/html


@articleharris_phonon_1997,
	title = Phonon Softening and Lattice Melting at the Ferroelastic Phase Transition in ${\mathrm{Na}}_{2}{\mathrm{CO}}_{3}$,
	volume = 79,
	url = https://link.aps.org/doi/10.1103/PhysRevLett.79.4846,
	doi = 10.1103/PhysRevLett.79.4846,
	abstract = We present the results of a detailed inelastic neutron scattering study of the dynamics of the ferroelastic phase transition in Na2CO3. The driving instability is a transverse acoustic mode that softens over a plane of wave vectors, resulting in a continuous loss of long-range order, in accord with theoretical predictions. At Tc a wide distribution of excitations is observed in the plane of critical wave vectors, similar to the dynamics of a liquid. Perpendicular to this plane the system possesses one-dimensional order.,
	number = 24,
	urldate = 2019-04-03,
	journal = Physical Review Letters,
	author = Harris, M. J. and McMorrow, D. F. and Godfrey, K. W.,
	month = dec,
	year = 1997,
	pages = 4846–4849,
	file = APS Snapshot:/Users/carolinegorham/Zotero/storage/LYQABQXP/PhysRevLett.79.html:text/html;Full Text:/Users/carolinegorham/Zotero/storage/JQYCM3G9/Harris et al. - 1997 - Phonon Softening and Lattice Melting at the Ferroe.pdf:application/pdf


@articlerivier_nicolas_curvature_1996,
	title = Curvature and frustration in cellular systems,
	volume = 354,
	url = https://royalsocietypublishing.org/doi/abs/10.1098/rsta.1996.0091,
	doi = 10.1098/rsta.1996.0091,
	abstract = A cellular structure is a compromise between best local packing and filling space without gaps or overlap. The fact that soap bubble froths or the human epidermis are and remain steadily disordered, demonstrates that this compromise is essential. Two alternative methods are presented: decurving progressively and at random a cellular structure initially ordered in curved space, or building up the structure layer by layer from an arbitrary seed cell, like a puzzle without boundary. There is a narrow range of structures sandwiched between the froth with lowest interfacial energy and that with highest orientational entropy. Diese scheinbare Regellosigkeit sehr wohl geregelt ist. Strasburger 1866,
	number = 1715,
	urldate = 2019-04-05,
	journal = Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences,
	author = Rivier Nicolas and Aste Tomaso and Klinowski Jacek and Mackay Alan Lindsay,
	month = sep,
	year = 1996,
	pages = 2055–2069,
	file = Full Text PDF:/Users/carolinegorham/Zotero/storage/GSL6ZYY6/Rivier Nicolas et al. - 1996 - Curvature and frustration in cellular systems.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/ZCGW2TI8/rsta.1996.html:text/html


@articledunleavy_mutual_2015,
	title = Mutual information reveals multiple structural relaxation mechanisms in a model glass former,
	volume = 6,
	journal = Nature communications,
	author = Dunleavy, Andrew J. and Wiesner, Karoline and Yamamoto, Ryoichi and Royall, C. Patrick,
	year = 2015,
	pages = 6089,
	file = Full Text:/Users/carolinegorham/Zotero/storage/TMAQXWIW/ncomms7089.html:text/html


@articleleocmach_roles_2012,
	title = Roles of icosahedral and crystal-like order in the hard spheres glass transition,
	volume = 3,
	journal = Nature communications,
	author = Leocmach, Mathieu and Tanaka, Hajime,
	year = 2012,
	pages = 974,
	file = Full Text:/Users/carolinegorham/Zotero/storage/LD2T9WQ6/ncomms1974.html:text/html


@articletarjus_frustration-based_2005,
	title = The frustration-based approach of supercooled liquids and the glass transition: a review and critical assessment,
	volume = 17,
	shorttitle = The frustration-based approach of supercooled liquids and the glass transition,
	number = 50,
	journal = Journal of Physics: Condensed Matter,
	author = Tarjus, Gilles and Kivelson, Steven A. and Nussinov, Z. and Viot, Pascal,
	year = 2005,
	pages = R1143,
	file = Full Text:/Users/carolinegorham/Zotero/storage/8IJTCP5C/Tarjus et al. - 2005 - The frustration-based approach of supercooled liqu.pdf:application/pdf


@articleelser_diffraction_1986,
	title = The diffraction pattern of projected structures,
	volume = 42,
	number = 1,
	journal = Acta Crystallographica Section A: Foundations of Crystallography,
	author = Elser, Veit,
	year = 1986,
	pages = 36–43,
	file = Full Text:/Users/carolinegorham/Zotero/storage/9PZYX42S/Elser - 1986 - The diffraction pattern of projected structures.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/DED72IK6/paper.html:text/html


@articlekatz_quasiperiodic_1986,
	title = Quasiperiodic patterns and icosahedral symmetry,
	volume = 47,
	number = 2,
	journal = Journal de Physique,
	author = Katz, A. and Duneau, M.,
	year = 1986,
	pages = 181–196,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/PHVRR547/jphys_1986__47_2_181_0.html:text/html


@articlegorham_crystallization_2019,
	title = Crystallization in three dimensions: Defect-driven topological ordering and the role of geometrical frustration,
	volume = 99,
	shorttitle = Crystallization in three dimensions,
	url = https://link.aps.org/doi/10.1103/PhysRevB.99.144106,
	doi = 10.1103/PhysRevB.99.144106,
	abstract = Herein, fundamentals of topology and symmetry breaking are used to understand crystallization and geometrical frustration in topologically close-packed structures. This frames solidification from a new perspective that is unique from thermodynamic discussions. Crystallization is considered as developing from undercooled liquids, in which orientational order is characterized by a surface of a sphere in four-dimensions (quaternion) with the binary polyhedral representation of the preferred orientational order of atomic clustering inscribed on its surface. As a consequence of the dimensionality of the quaternion orientational order parameter, crystallization is seen as occurring in “restricted dimensions.” Homotopy theory is used to classify all topologically stable defects, and third homotopy group defect elements are considered to be generalized vortices that are available in superfluid ordered systems. This topological perspective approaches the liquid-to-crystalline solid transition in three-dimensions from fundamental concepts of: Bose-Einstein condensation, the Mermin-Wagner theorem and Berezinskii-Kosterlitz-Thouless (BKT) topological-ordering transitions. In doing so, in this article, concepts that apply to superfluidity in “restricted dimensions” are generalized to consider the solidification of crystalline solid states.,
	number = 14,
	urldate = 2019-05-06,
	journal = Physical Review B,
	author = Gorham, Caroline S. and Laughlin, David E.,
	month = apr,
	year = 2019,
	pages = 144106,
	file = APS Snapshot:/Users/carolinegorham/Zotero/storage/6C4ELCLW/PhysRevB.99.html:text/html;Submitted Version:/Users/carolinegorham/Zotero/storage/G24A7XW2/Gorham and Laughlin - 2019 - Crystallization in three dimensions Defect-driven.pdf:application/pdf


@articlehalperin_hohenbergmerminwagner_2018,
	title = On the Hohenberg–Mermin–Wagner Theorem and Its Limitations,
	issn = 1572-9613,
	url = https://doi.org/10.1007/s10955-018-2202-y,
	doi = 10.1007/s10955-018-2202-y,
	abstract = Just over 50 years ago, Pierre Hohenberg developed a rigorous proof of the non-existence of long-range order in a two-dimensional superfluid or superconductor at finite temperatures. The proof was immediately extended by Mermin and Wagner to the Heisenberg ferromagnet and antiferromagnet, and shortly thereafter, by Mermin to prove the absence of translational long-range order in a two-dimensional crystal, whether in quantum or classical mechanics. In this paper, we present an extension of the Hohenberg–Mermin–Wagner theorem to give a rigorous proof of the impossibility of long-range ferromagnetic order in an itinerant electron system without spin-orbit coupling or magnetic dipole interactions. We also comment on some situations where there are compelling arguments that long-range order is impossible but no rigorous proof has been given, as well as situations, such as a magnet with long range interactions, or orientational order in a two-dimensional crystal, where long-range order can occur that breaks a continuous symmetry.,
	language = en,
	urldate = 2019-05-06,
	journal = Journal of Statistical Physics,
	author = Halperin, Bertrand I.,
	month = dec,
	year = 2018,
	keywords = Fluctuations, Long-range order, Superfluid, Two dimensions,
	file = Submitted Version:/Users/carolinegorham/Zotero/storage/RXGYZAFX/Halperin - 2018 - On the Hohenberg–Mermin–Wagner Theorem and Its Lim.pdf:application/pdf


@articleshechtman_metallic_1984,
	title = Metallic phase with long-range orientational order and no translational symmetry,
	volume = 53,
	number = 20,
	journal = Physical review letters,
	author = Shechtman, Dan and Blech, Ilan and Gratias, Denis and Cahn, John W.,
	year = 1984,
	pages = 1951,
	file = Full Text:/Users/carolinegorham/Zotero/storage/88V2WTAY/Shechtman et al. - 1984 - Metallic phase with long-range orientational order.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/XAAU3QVA/PhysRevLett.53.html:text/html


@articlesadoc_new_1990,
	title = A new method to generate quasicrystalline structures: examples in 2D tilings,
	volume = 51,
	shorttitle = A new method to generate quasicrystalline structures,
	number = 3,
	journal = Journal de Physique,
	author = Sadoc, Jean-François and Mosseri, R.,
	year = 1990,
	pages = 205–221,
	file = Full Text:/Users/carolinegorham/Zotero/storage/DIBWKQST/Sadoc and Mosseri - 1990 - A new method to generate quasicrystalline structur.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/5KHMVWCB/jphys_1990__51_3_205_0.html:text/html


@articlesadoc_e8_1993-2,
	title = The E8 lattice and quasicrystals: geometry, number theory and quasicrystals,
	volume = 26,
	issn = 0305-4470,
	shorttitle = The E8 lattice and quasicrystals,
	url = https://doi.org/10.1088
	doi = 10.1088/0305-4470/26/8/009,
	abstract = The authors study the quasiperiodic structures which can be derived from E8. This lattice, suitably oriented, leads to a 4D quasicrystal which has (3,3,5) symmetry. They develop a modified version of the out and projection method. The high-dimensional lattice is first foliated into successive shells surrounding a vertex. The shells are embedded into 7D S7 spheres. They then use the so-called Hopf fibration of S7 to gather families of E8 shell sites into S3 fibres which contain 24 sites (or a multiple of 24) which are symmetrically disposed in S3. This has two advantages: first, in the selection process, a whole fibre is either selected or rejected, which reduces the computation; more importantly, the selection process for a fiber amounts to simple arithmetical criteria. The whole process leads to a shell-by-shell analysis of the 4D quasicrystal, which can be brought onto a 2D-1D algorithm similar to the Fibonacci chain construction. They propose an arithmetic formula which gives the number of points on the shells. This 4D quasicrystal has the interesting feature that it can be sliced into lower-dimensional quasicrystals, for example with icosahedral and tetrahedral symmetry in three dimensions.,
	language = en,
	number = 8,
	urldate = 2019-05-14,
	journal = Journal of Physics A: Mathematical and General,
	author = Sadoc, J. F. and Mosseri, R.,
	month = apr,
	year = 1993,
	pages = 1789–1809,
	file = IOP Full Text PDF:/Users/carolinegorham/Zotero/storage/NVJ4WX99/Sadoc and Mosseri - 1993 - The E8 lattice and quasicrystals geometry, number.pdf:application/pdf


@articlelichtenstein_atomic_2012,
	title = Atomic Arrangement in Two-Dimensional Silica: From Crystalline to Vitreous Structures,
	volume = 116,
	issn = 1932-7447,
	shorttitle = Atomic Arrangement in Two-Dimensional Silica,
	url = https://doi.org/10.1021/jp3062866,
	doi = 10.1021/jp3062866,
	abstract = The atomic structure of vitreous and crystalline regions of a thin silica film on Ru(0001) was investigated using noncontact atomic force microscopy (nc-AFM) and scanning tunneling microscopy (STM). We were able to resolve the atomic arrangement of the Si and the O atoms in the crystalline and the vitreous structures. We discuss characteristic structural properties of the films, such as distances, orientations, and angles, and we compare our results to experiments and simulations of bulk vitreous silica networks. It was found that order in two-dimensional vitreous networks can extend up to 2 nm.,
	number = 38,
	urldate = 2019-05-21,
	journal = The Journal of Physical Chemistry C,
	author = Lichtenstein, Leonid and Heyde, Markus and Freund, Hans-Joachim,
	month = sep,
	year = 2012,
	pages = 20426–20432,
	file = ACS Full Text Snapshot:/Users/carolinegorham/Zotero/storage/BF6IA3MA/jp3062866.html:text/html


@bookabbot_flatland_1884-1,
	title = Flatland,
	publisher = Domaine public,
	author = Abbot, Edwin,
	year = 1884,
	file = Full Text:/Users/carolinegorham/Zotero/storage/HTTHQB93/Abbot - 1884 - Flatland.pdf:application/pdf


@bookplato_republic_2007,
	edition = 2,
	title = The Republic,
	publisher = Penguin Classics,
	author = Plato,
	year = 2007


@incollectionrivier_gauge_1990-1,
	title = Gauge theory and geometry of condensed matter,
	booktitle = Geometry in condensed matter physics,
	publisher = World Scientific,
	author = Rivier, Nicolas,
	year = 1990,
	pages = 1–88,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/R57A6GY4/9789814368315_0001.html:text/html


@articlemaciejko_yangmills_1978,
	title = Yang–Mills equations in Maxwell form,
	volume = 19,
	issn = 0022-2488,
	url = https://aip.scitation.org/doi/abs/10.1063/1.523629,
	doi = 10.1063/1.523629,
	number = 12,
	urldate = 2019-05-23,
	journal = Journal of Mathematical Physics,
	author = Maciejko, R.,
	month = dec,
	year = 1978,
	pages = 2491–2493,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/GAYCERRP/1.html:text/html


@articlebuoncristiani_algebra_1973,
	title = An algebra of the Yang‐Mills field,
	volume = 14,
	issn = 0022-2488,
	url = https://aip.scitation.org/doi/abs/10.1063/1.1666407,
	doi = 10.1063/1.1666407,
	number = 7,
	urldate = 2019-05-23,
	journal = Journal of Mathematical Physics,
	author = Buoncristiani, A. M.,
	month = jul,
	year = 1973,
	pages = 849–854,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/XLZIK2AS/1.html:text/html


@articlebloch_many-body_2008,
	title = Many-body physics with ultracold gases,
	volume = 80,
	number = 3,
	journal = Reviews of modern physics,
	author = Bloch, Immanuel and Dalibard, Jean and Zwerger, Wilhelm,
	year = 2008,
	pages = 885,
	file = Full Text:/Users/carolinegorham/Zotero/storage/AICJLM29/Bloch et al. - 2008 - Many-body physics with ultracold gases.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/U5SPGRWD/RevModPhys.80.html:text/html


@articlejaksch_cold_1998,
	title = Cold bosonic atoms in optical lattices,
	volume = 81,
	number = 15,
	journal = Physical Review Letters,
	author = Jaksch, Dieter and Bruder, Christoph and Cirac, Juan Ignacio and Gardiner, Crispin W. and Zoller, Peter,
	year = 1998,
	pages = 3108,
	file = Full Text:/Users/carolinegorham/Zotero/storage/HWSMNM2R/Jaksch et al. - 1998 - Cold bosonic atoms in optical lattices.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/HCNZ9KAP/PhysRevLett.81.html:text/html


@articlecoropceanu_systematic_2019,
	title = Systematic Mapping of Binary Nanocrystal Superlattices: The Role of Topology in Phase Selection,
	volume = 141,
	issn = 0002-7863,
	shorttitle = Systematic Mapping of Binary Nanocrystal Superlattices,
	url = https://doi.org/10.1021/jacs.8b12539,
	doi = 10.1021/jacs.8b12539,
	abstract = The self-assembly of two sizes of spherical nanocrystals has revealed a surprisingly diverse library of structures. To date, at least 15 distinct binary nanocrystal superlattice (BNSL) structures have been identified. The stability of these binary phases cannot be fully explained using the traditional conceptual framework treating the assembly process as entropy-driven crystallization of rigid spherical particles. Such deviation from hard sphere behavior may be explained by the soft and deformable layer of ligands that envelops the nanocrystals, which contributes significantly to the overall size and shape of assembling particles. In this work, we describe a set of experiments designed to elucidate the role of the ligand corona in shaping the thermodynamics and kinetics of BNSL assembly. Using hydrocarbon-capped Au and PbS nanocrystals as a model binary system, we systematically tuned the core radius (R) and ligand chain length (L) of particles and subsequently assembled them into binary superlattices. The resulting database of binary structures enabled a detailed analysis of the role of effective nanocrystal size ratio, as well as softness expressed as L/R, in directing the assembly of binary structures. This catalog of superlattices allowed us to not only study the frequency of different phases but to also systematically measure the geometric parameters of the BNSLs. This analysis allowed us to evaluate new theoretical models treating the cocrystallization of deformable spheres and to formulate new hypotheses about the factors affecting the nucleation and growth of the binary superlattices. Among other insights, our results suggest that the relative abundance of the binary phases observed may be explained not only by considerations of thermodynamic stability, but also by a postulated preordering of the binary fluid into local structures with icosahedral or polytetrahedral symmetry prior to nucleation.,
	number = 14,
	urldate = 2019-05-29,
	journal = Journal of the American Chemical Society,
	author = Coropceanu, Igor and Boles, Michael A. and Talapin, Dmitri V.,
	month = apr,
	year = 2019,
	pages = 5728–5740


@articlemuller_towards_2017,
	title = Towards understanding two-level-systems in amorphous solids-Insights from quantum devices,
	journal = arXiv preprint arXiv:1705.01108,
	author = Müller, Clemens and Cole, Jared H. and Lisenfeld, Jürgen,
	year = 2017,
	file = Full Text:/Users/carolinegorham/Zotero/storage/H5TVX8T7/Müller et al. - 2017 - Towards understanding two-level-systems in amorpho.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/GNYLPGLY/1705.html:text/html


@articledirac_application_1944,
	title = Application of Quaternions to Lorentz Transformations,
	volume = 50,
	issn = 0035-8975,
	url = https://www.jstor.org/stable/20520646,
	urldate = 2019-06-05,
	journal = Proceedings of the Royal Irish Academy. Section A: Mathematical and Physical Sciences,
	author = Dirac, P. A. M.,
	year = 1944,
	pages = 261–270


@articleni_observation_2019,
	title = Observation of Hofstadter butterfly and topological edge states in reconfigurable quasi-periodic acoustic crystals,
	volume = 2,
	copyright = 2019 The Author(s),
	issn = 2399-3650,
	url = https://www.nature.com/articles/s42005-019-0151-7,
	doi = 10.1038/s42005-019-0151-7,
	abstract = Hofstadter’s butterfly is a fractal pattern which pictorially represents the behavior of electrons under an applied magnetic field in a 2D lattice as a pair of butterfly wings. Here, the authors recreate this pattern by measuring the acoustic density of states in a&nbsp;fine-tuned one-dimensional acoustic array.,
	language = En,
	number = 1,
	urldate = 2019-06-11,
	journal = Communications Physics,
	author = Ni, Xiang and Chen, Kai and Weiner, Matthew and Apigo, David J. and Prodan, Camelia and Alù, Andrea and Prodan, Emil and Khanikaev, Alexander B.,
	month = jun,
	year = 2019,
	pages = 55,
	file = Full Text PDF:/Users/carolinegorham/Zotero/storage/UIR2FFKG/Ni et al. - 2019 - Observation of Hofstadter butterfly and topologica.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/YEJI8VDN/s42005-019-0151-7.html:text/html


@articlediamantini_bose_2019,
	title = The Bose topological insulator nature of the anomalous metal,
	journal = arXiv preprint arXiv:1906.07969,
	author = Diamantini, M. C. and Trugenberger, C. A. and Kopelevich, Ya and Postolova, S. V. and Mironov, A. Yu and Silevitch, D. M. and Vinokur, V. M.,
	year = 2019,
	file = Full Text:/Users/carolinegorham/Zotero/storage/MIHS8EUK/Diamantini et al. - 2019 - The Bose topological insulator nature of the anoma.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/CUMS6SWB/1906.html:text/html


@articlelantagne-hurtubise_topology_2019,
	title = Topology in abundance,
	volume = 1,
	copyright = 2019 The Publisher,
	issn = 2522-5820,
	url = https://www.nature.com/articles/s42254-019-0041-7,
	doi = 10.1038/s42254-019-0041-7,
	abstract = Three Nature papers report the complete topological classification of all known non-magnetic crystalline compounds, revealing thousands of new candidate topological materials waiting to be explored in the lab.,
	language = En,
	number = 3,
	urldate = 2019-06-27,
	journal = Nature Reviews Physics,
	author = Lantagne-Hurtubise, Étienne and Franz, Marcel,
	month = mar,
	year = 2019,
	pages = 183,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/WMARZR7E/s42254-019-0041-7.html:text/html


@articlediamantini_confinement_2018,
	title = Confinement and asymptotic freedom with Cooper pairs,
	volume = 1,
	copyright = 2018 The Author(s),
	issn = 2399-3650,
	url = https://www.nature.com/articles/s42005-018-0073-9,
	doi = 10.1038/s42005-018-0073-9,
	abstract = The standard model describes many aspects of particle physics but mechanisms such as the binding of quarks into hadrons, still remain a mystery. The authors theoretically outline an analogy with the Cooper pairs of a superinsulator to demonstrate that the mechanisms behind the infinite resistance of a superinsulator are analogous to that which confine quarks into hadrons.,
	language = En,
	number = 1,
	urldate = 2019-06-28,
	journal = Communications Physics,
	author = Diamantini, M. C. and Trugenberger, C. A. and Vinokur, V. M.,
	month = nov,
	year = 2018,
	pages = 77,
	file = Full Text PDF:/Users/carolinegorham/Zotero/storage/F99CL4WN/Diamantini et al. - 2018 - Confinement and asymptotic freedom with Cooper pai.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/EEXC8EV7/s42005-018-0073-9.html:text/html


@incollectionnussinov_?glass_2018,
	title = The ?glass transition? as a topological defect driven transition in a distribution of crystals and a prediction of a universal viscosity collapse,
	isbn = 978-981-327-133-3,
	shorttitle = The ?,
	url = https://www.worldscientific.com/doi/abs/10.1142/9789813271340_0006,
	urldate = 2019-06-28,
	booktitle = Topological Phase Transitions and New Developments,
	publisher = WORLD SCIENTIFIC,
	author = Nussinov, Z. and Weingartner, N. B. and Nogueira, F. S.,
	month = apr,
	year = 2018,
	doi = 10.1142/9789813271340_0006,
	pages = 61–79,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/AMC32E7D/9789813271340_0006.html:text/html


@articlemizuno_continuum_2017,
	title = Continuum limit of the vibrational properties of amorphous solids,
	volume = 114,
	number = 46,
	journal = Proceedings of the National Academy of Sciences,
	author = Mizuno, Hideyuki and Shiba, Hayato and Ikeda, Atsushi,
	year = 2017,
	pages = E9767–E9774,
	file = Full Text:/Users/carolinegorham/Zotero/storage/KS33ZCU7/E9767.html:text/html;Snapshot:/Users/carolinegorham/Zotero/storage/4RQD9AEV/E9767.html:text/html


@articlegorham_solidification_2019,
	title = Solidification of Icosahedral Quasicrystals: Viewpoint Based on a Quaternion Orientational Order Parameter and the Formation of the E8 Lattice,
	shorttitle = Solidification of Icosahedral Quasicrystals,
	url = http://arxiv.org/abs/1905.12165,
	abstract = In this article, the solidification phase transition between isotropic liquids and icosahedral quasicrystalline structures is classified by the application of a quaternion orientational order parameter. We suggest that the formation of the E8 lattice in 8-dimensions, from which three-dimensional icosahedral quasicrystals derive by projection, occurs without dimensionally restricting the degrees of freedom of the quaternion orientational order parameter to the quaternion plane. This is different from the development of regular crystalline solids in three-dimensions, which occurs in "restricted dimensions" and requires topological-ordering, as previously discussed by the authors. In other words, herein, the formation of lattices in eight-dimensions is considered as a higher-dimensional analogy to the formation of "bulk" superfluidity. It follows that, the solidification of lattices in 8-dimensions (and derivative icosahedral quasicrystalline solids) should occur without the necessity of topological defects.,
	urldate = 2019-07-01,
	journal = arXiv:1905.12165 [cond-mat, physics:gr-qc, physics:hep-lat, physics:math-ph, physics:physics],
	author = Gorham, Caroline S. and Laughlin, David E.,
	month = may,
	year = 2019,
	note = arXiv: 1905.12165,
	keywords = Condensed Matter - Materials Science, General Relativity and Quantum Cosmology, Mathematical Physics, High Energy Physics - Lattice, Physics - Atomic and Molecular Clusters,
	file = arXiv 1905.12165 PDF:/Users/carolinegorham/Zotero/storage/5NWRTBS7/Gorham and Laughlin - 2019 - Solidification of Icosahedral Quasicrystals Viewp.pdf:application/pdf;arXiv.org Snapshot:/Users/carolinegorham/Zotero/storage/4JP28MZD/1905.html:text/html


@articlepolyakov_confining_1997,
	title = Confining strings,
	volume = 486,
	number = 1-2,
	journal = Nuclear Physics B,
	author = Polyakov, Alexander M.,
	year = 1997,
	pages = 23–33,
	file = Full Text:/Users/carolinegorham/Zotero/storage/JF4RTMVZ/Polyakov - 1997 - Confining strings.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/YAXT8GLB/S0550321396006013.html:text/html


@articlehooft_phase_1978,
	title = On the phase transition towards permanent quark confinement,
	volume = 138,
	number = 1,
	journal = Nuclear Physics: B,
	author = Hooft, Gerard’t,
	year = 1978,
	pages = 1–25,
	file = Full Text:/Users/carolinegorham/Zotero/storage/KEAMBT36/Hooft - 1978 - On the phase transition towards permanent quark co.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/49C8MUZG/4701.html:text/html


@articlediamantini_bose_2019-1,
	title = The Bose topological insulator nature of the anomalous metal,
	journal = arXiv preprint arXiv:1906.07969,
	author = Diamantini, M. C. and Trugenberger, C. A. and Kopelevich, Ya and Postolova, S. V. and Mironov, A. Yu and Silevitch, D. M. and Vinokur, V. M.,
	year = 2019,
	file = Full Text:/Users/carolinegorham/Zotero/storage/CZBKD9QT/Diamantini et al. - 2019 - The Bose topological insulator nature of the anoma.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/HAL6VTTU/1906.html:text/html


@articlegopalakrishnan_disclination_2013,
	title = Disclination classes, fractional excitations, and the melting of quantum liquid crystals,
	volume = 111,
	number = 2,
	journal = Physical review letters,
	author = Gopalakrishnan, Sarang and Teo, Jeffrey CY and Hughes, Taylor L.,
	year = 2013,
	pages = 025304,
	file = Full Text:/Users/carolinegorham/Zotero/storage/KG498TEB/Gopalakrishnan et al. - 2013 - Disclination classes, fractional excitations, and .pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/9N4DWF8K/PhysRevLett.111.html:text/html


@phdthesishuang_meissner_1991,
	type = PhD Thesis,
	title = Meissner Effects, Vortex Core States and the Vortex Glass Phase Transition,
	school = Cornell University,
	author = Huang, Ming,
	year = 1991,
	file = Full Text:/Users/carolinegorham/Zotero/storage/M65NT9SJ/Huang - 1991 - Meissner Effects, Vortex Core States and the Vorte.pdf:application/pdf


@articlechang_topological_2018,
	title = Topological quantum properties of chiral crystals,
	volume = 17,
	number = 11,
	journal = Nature materials,
	author = Chang, Guoqing and Wieder, Benjamin J. and Schindler, Frank and Sanchez, Daniel S. and Belopolski, Ilya and Huang, Shin-Ming and Singh, Bahadur and Wu, Di and Chang, Tay-Rong and Neupert, Titus,
	year = 2018,
	pages = 978,
	file = Full Text:/Users/carolinegorham/Zotero/storage/WD2DMVWH/Chang et al. - 2018 - Topological quantum properties of chiral crystals.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/6MEEZDB6/s41563-018-0169-3.html:text/html


@articlesuzuki_energymomentum_2016,
	title = Energy–momentum tensor on the lattice: recent developments,
	shorttitle = Energy–momentum tensor on the lattice,
	journal = arXiv preprint arXiv:1612.00210,
	author = Suzuki, Hiroshi,
	year = 2016,
	file = Full Text:/Users/carolinegorham/Zotero/storage/JJFFRFLC/Suzuki - 2016 - Energy–momentum tensor on the lattice recent deve.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/3RXJY6L9/1612.html:text/html


@articlepretko_fracton_2018,
	title = The fracton gauge principle,
	volume = 98,
	number = 11,
	journal = Physical Review B,
	author = Pretko, Michael,
	year = 2018,
	pages = 115134,
	file = Full Text:/Users/carolinegorham/Zotero/storage/PUH4EEX7/Pretko - 2018 - The fracton gauge principle.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/C5MR8JGC/PhysRevB.98.html:text/html


@articlepretko_generalized_2017,
	title = Generalized Electromagnetism of Subdimensional Particles: A Spin Liquid Story,
	volume = 96,
	issn = 2469-9950, 2469-9969,
	shorttitle = Generalized Electromagnetism of Subdimensional Particles,
	url = http://arxiv.org/abs/1606.08857,
	doi = 10.1103/PhysRevB.96.035119,
	abstract = It has recently been shown that there exists a class of stable gapless spin liquids in 3+1 dimensions described by higher rank tensor U(1) gauge fields, giving rise to an emergent tensor electromagnetism. The tensor gauge field of these theories couples naturally to subdimensional particles (such as fractons), which are restricted by gauge invariance to move only along lower-dimensional subspaces of the system. We here work out some of the basic generalized electromagnetic properties of subdimensional particles coupled to tensor electromagnetism, such as generalized electrostatic fields, potential formulations, Lorentz forces, Maxwell equations, and Biot-Savart laws. Some concepts from conventional electromagnetism will carry over directly, while others require significant modification.,
	number = 3,
	urldate = 2019-07-02,
	journal = Physical Review B,
	author = Pretko, Michael,
	month = jul,
	year = 2017,
	note = arXiv: 1606.08857,
	keywords = Condensed Matter - Strongly Correlated Electrons, High Energy Physics - Theory,
	pages = 035119,
	annote = Comment: 14+4 pages,
	file = arXiv 1606.08857 PDF:/Users/carolinegorham/Zotero/storage/X58M8ALS/Pretko - 2017 - Generalized Electromagnetism of Subdimensional Par.pdf:application/pdf;arXiv.org Snapshot:/Users/carolinegorham/Zotero/storage/RWDX2DHT/1606.html:text/html


@articleslagle_symmetric_2018,
	title = Symmetric Tensor Gauge Theories on Curved Spaces,
	journal = arXiv preprint arXiv:1807.00827,
	author = Slagle, Kevin and Prem, Abhinav and Pretko, Michael,
	year = 2018,
	file = Full Text:/Users/carolinegorham/Zotero/storage/EMTJ2QJI/Slagle et al. - 2018 - Symmetric Tensor Gauge Theories on Curved Spaces.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/N5TI8LCZ/1807.html:text/html


@articlemaxwell_physical_2010,
	title = On physical lines of force,
	volume = 90,
	number = S1,
	journal = Philosophical Magazine,
	author = Maxwell, James Clerk,
	year = 2010,
	pages = 11–23,
	file = Full Text:/Users/carolinegorham/Zotero/storage/QDHPH2WS/Maxwell - 2010 - On physical lines of force.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/RGCLBK4Z/14786431003659180.html:text/html


@articlehall_new_1880,
	title = On a new action of the magnet on electric currents,
	number = 111,
	journal = American Journal of Science,
	author = Hall, E. H.,
	year = 1880,
	pages = 200–205,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/4UTVAAT9/200.html:text/html


@articlepolyakov_gauge_1987,
	title = Gauge Fields and Strings,
	volume = 3,
	journal = Contemp. Concepts Phys.,
	author = Polyakov, Alexander M.,
	year = 1987,
	pages = 1–301,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/WV9PCNNG/255378.html:text/html


@articlebirch_thermal_1940,
	title = The thermal conductivity of rocks and its dependence upon temperature and composition,
	volume = 238,
	number = 8,
	journal = American Journal of Science,
	author = Birch, Albert Francis and Clark, Harry,
	year = 1940,
	pages = 529–558,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/B6QVJAMY/529.html:text/html


@articleeinstein_elementary_1911,
	title = Elementary observations on thermal molecular motion in solids,
	volume = 35,
	journal = Annalen der Physik,
	author = Einstein, A.,
	year = 1911,
	pages = 679–694


@articleleggett_amorphous_1991,
	title = Amorphous materials at low temperatures: why are they so similar?,
	volume = 169,
	shorttitle = Amorphous materials at low temperatures,
	number = 1-4,
	journal = Physica B: Condensed Matter,
	author = Leggett, Anthony J.,
	year = 1991,
	pages = 322–327,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/XCAAKB5X/092145269190246B.html:text/html


@articlecohn_packing_2016,
	title = Packing, coding, and ground states,
	url = http://arxiv.org/abs/1603.05202,
	abstract = These are the lecture notes from my 2014 PCMI graduate summer school lectures. In these lectures, we'll study simple models of materials from several different perspectives: geometry (packing problems), information theory (error-correcting codes), and physics (ground states of interacting particle systems). These perspectives each shed light on some of the same problems and phenomena, while highlighting different techniques and connections. One noteworthy phenomenon is the exceptional symmetry that is found in certain special cases, and we'll examine when and why it occurs. The overall theme of the lectures is thus order vs. disorder. How much symmetry can we expect to see in optimal geometric structures?,
	urldate = 2019-07-04,
	journal = arXiv:1603.05202 [math],
	author = Cohn, Henry,
	month = mar,
	year = 2016,
	note = arXiv: 1603.05202,
	keywords = Mathematics - Metric Geometry,
	annote = Comment: 61 pages, 7 figures,
	file = arXiv 1603.05202 PDF:/Users/carolinegorham/Zotero/storage/46LXCN8C/Cohn - 2016 - Packing, coding, and ground states.pdf:application/pdf;arXiv.org Snapshot:/Users/carolinegorham/Zotero/storage/ZPH8VRU4/1603.html:text/html


@articlecohn_conceptual_2017,
	title = A conceptual breakthrough in sphere packing,
	volume = 64,
	issn = 0002-9920, 1088-9477,
	url = http://arxiv.org/abs/1611.01685,
	doi = 10.1090/noti1474,
	abstract = This expository paper describes Viazovska's breakthrough solution of the sphere packing problem in eight dimensions, as well as its extension to twenty-four dimensions by Cohn, Kumar, Miller, Radchenko, and Viazovska.,
	number = 02,
	urldate = 2019-07-04,
	journal = Notices of the American Mathematical Society,
	author = Cohn, Henry,
	month = feb,
	year = 2017,
	note = arXiv: 1611.01685,
	keywords = Mathematics - Metric Geometry, Mathematics - Number Theory,
	pages = 102–115,
	annote = Comment: 24 pages, 9 figures,
	file = arXiv 1611.01685 PDF:/Users/carolinegorham/Zotero/storage/BNRCZLKI/Cohn - 2017 - A conceptual breakthrough in sphere packing.pdf:application/pdf;arXiv.org Snapshot:/Users/carolinegorham/Zotero/storage/F3ZNKPB7/1611.html:text/html


@articlehales_proof_2005,
	title = A proof of the Kepler conjecture,
	journal = Annals of mathematics,
	author = Hales, Thomas C.,
	year = 2005,
	pages = 1065–1185,
	file = Full Text:/Users/carolinegorham/Zotero/storage/6DMQH45T/Hales - 2005 - A proof of the Kepler conjecture.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/9FXUWQN7/20159940.html:text/html


@bookkepler_six-cornered_2010,
	title = The six-cornered snowflake,
	publisher = Paul Dry Books,
	author = Kepler, Johannes,
	year = 2010,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/ZVRUJTHF/books.html:text/html


@articleviazovska_sphere_2017,
	title = The sphere packing problem in dimension 8,
	journal = Annals of Mathematics,
	author = Viazovska, Maryna S.,
	year = 2017,
	pages = 991–1015,
	file = Full Text:/Users/carolinegorham/Zotero/storage/LR592CU7/Viazovska - 2017 - The sphere packing problem in dimension 8.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/DPSJ46IC/26395747.html:text/html


@miscknudson_stacking_2019,
	title = Stacking Cannonballs In 8 Dimensions,
	url = https://www.forbes.com/sites/kevinknudson/2016/03/29/stacking-cannonballs-in-8-dimensions/,
	abstract = The densest sphere packing in 8 dimensions has been discovered.,
	language = en,
	urldate = 2019-07-18,
	journal = Forbes,
	author = Knudson, Kevin,
	year = 2019,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/I3S7ACMT/stacking-cannonballs-in-8-dimensions.html:text/html


@articlehales_kepler_1998,
	title = The Kepler conjecture,
	journal = arXiv preprint math.MG/9811078,
	author = Hales, Thomas C.,
	year = 1998,
	file = Full Text:/Users/carolinegorham/Zotero/storage/DFJVFCQ4/Hales - 1998 - The kepler conjecture.pdf:application/pdf


@articlekepler_strena_1611,
	title = Strena Seu de Nive Sexangul,
	journal = Frankfurt, Gottfied Tampach,
	author = Kepler, Johannes,
	year = 1611


@articlegauss_untersuchungen_1831,
	title = Untersuchungen über die Eigenschaften der positiven ternären quadratischen Formen von Ludwig August Seber,
	journal = Göttingische Gelehrte Anzeigen,
	author = Gauss, Carl F.,
	year = 1831


@articlesloane_keplers_1998,
	title = Kepler's conjecture confirmed,
	volume = 395,
	number = 6701,
	journal = Nature,
	author = Sloane, Neil JA,
	year = 1998,
	pages = 435,
	file = Full Text:/Users/carolinegorham/Zotero/storage/GGZKPTT7/Sloane - 1998 - Kepler's conjecture confirmed.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/DRHYVJRX/26609.html:text/html


@articlebernal_bakerian_1964,
	title = The Bakerian lecture, 1962. The structure of liquids,
	volume = 280,
	number = 1382,
	journal = Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences,
	author = Bernal, John Desmond,
	year = 1964,
	pages = 299–322,
	file = Full Text:/Users/carolinegorham/Zotero/storage/D7MSFZX2/Bernal - 1964 - The Bakerian lecture, 1962. The structure of liqui.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/HZAH2Q3E/2415872.html:text/html


@articlebernal_random_1967,
	title = Random packing of spheres in non-rigid containers,
	volume = 214,
	number = 5085,
	journal = Nature,
	author = Bernal, J. D. and Finney, J. L.,
	year = 1967,
	pages = 265,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/LGY8HGW2/214265a0.html:text/html


@articlediamantini_electrostatics_2019,
	title = Electrostatics of a superinsulator,
	url = http://arxiv.org/abs/1906.12265,
	abstract = In 1978, to explain quark confinement in hadrons, 't Hooft coined the notion of "superinsulator", a hypothetical ground state endowed with infinite electric resistance and representing thus an extreme opposite to a superconductor. In condensed matter, the superinsulating ground state was first predicted for Josephson junction arrays (JJA) and was rediscovered as a phase emerging at the insulating side of the superconductor-insulator transition (SIT) in superconducting films due to the duality of the phase-amplitude uncertainty principle. Superinsulators, dissipationless Bose condensates of vortices retain an infinite resistance at finite temperatures and, as such, have been gaining an intense research attention. Here we investigate the response of a superinsulator to a dc electric field and show that small fields, EEc1 are completely suppressed inside the material, a dual, electric version of the Meissner effect. Intermediate fields, Ec1EEc2, penetrate the superinsulator as electric filaments, realizing Polyakov's electric strings in compact QED, a dual, electric version of the mixed state of superconductors, and, finally, large fields, EEc2, break down superinsulation completely. We report transport measurements in NbTiN films revealing both thresholds and their linear scaling with the system size. We demonstrate that the asymptotically free behaviour of quarks within mesons maps onto the metal-like behaviour of small films. Our findings open the route to measurements of Polyakov's string tension as a function of the system's parameters, enabling the exploration of strong coupling gauge theory concepts via desktop experiments.,
	urldate = 2019-07-20,
	journal = arXiv:1906.12265 [cond-mat],
	author = Diamantini, M. C. and Gammaitoni, L. and Strunk, C. and Postolova, S. V. and Mironov, A. Yu and Trugenberger, C. A. and Vinokur, V. M.,
	month = jun,
	year = 2019,
	note = arXiv: 1906.12265,
	keywords = Condensed Matter - Superconductivity,
	file = arXiv 1906.12265 PDF:/Users/carolinegorham/Zotero/storage/CD6FT96E/Diamantini et al. - 2019 - Electrostatics of a superinsulator.pdf:application/pdf;arXiv.org Snapshot:/Users/carolinegorham/Zotero/storage/MHA3THNL/1906.html:text/html


@articlezhang_supersolidity_2019,
	title = Supersolidity around a Critical Point in Dipolar Bose-Einstein Condensates,
	volume = 123,
	url = https://link.aps.org/doi/10.1103/PhysRevLett.123.015301,
	doi = 10.1103/PhysRevLett.123.015301,
	abstract = We explore spatial symmetry breaking of a dipolar Bose-Einstein condensate in the thermodynamic limit and reveal a critical point in the phase diagram at which crystallization occurs via a second-order phase transition. This behavior is traced back to the significant effects of quantum fluctuations in dipolar condensates, which moreover stabilize a new supersolid phase, namely a regular honeycomb pattern with high modulational contrast and near-perfect superfluidity.,
	number = 1,
	urldate = 2019-07-21,
	journal = Physical Review Letters,
	author = Zhang, Yong-Chang and Maucher, Fabian and Pohl, Thomas,
	month = jul,
	year = 2019,
	pages = 015301,
	file = APS Snapshot:/Users/carolinegorham/Zotero/storage/DVQ9LFHQ/PhysRevLett.123.html:text/html


@articleluminet_dodecahedral_2003,
	title = Dodecahedral space topology as an explanation for weak wide-angle temperature correlations in the cosmic microwave background,
	volume = 425,
	number = 6958,
	journal = Nature,
	author = Luminet, Jean-Pierre and Weeks, Jeffrey R. and Riazuelo, Alain and Lehoucq, Roland and Uzan, Jean-Philippe,
	year = 2003,
	pages = 593,
	file = Full Text:/Users/carolinegorham/Zotero/storage/6KI9TNJI/Luminet et al. - 2003 - Dodecahedral space topology as an explanation for .pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/4ARD8KZ7/nature01944.html:text/html


@articlelew_test_2008,
	title = A test of the Poincaré dodecahedral space topology hypothesis with the WMAP CMB data,
	volume = 482,
	number = 3,
	journal = Astronomy & Astrophysics,
	author = Lew, Bartosz and Roukema, Boudewijn,
	year = 2008,
	pages = 747–753,
	file = Full Text:/Users/carolinegorham/Zotero/storage/X9KMTHUF/Lew and Roukema - 2008 - A test of the Poincaré dodecahedral space topology.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/XXMINLMF/aa8777-07.html:text/html


@articleiii_map_2005,
	title = A Map of the Universe,
	volume = 624,
	issn = 0004-637X,
	url = https://iopscience.iop.org/article/10.1086/428890/meta,
	doi = 10.1086/428890,
	language = en,
	number = 2,
	urldate = 2019-07-21,
	journal = The Astrophysical Journal,
	author = Iii, J. Richard Gott and Jurić, Mario and Schlegel, David and Hoyle, Fiona and Vogeley, Michael and Tegmark, Max and Bahcall, Neta and Brinkmann, Jon,
	month = may,
	year = 2005,
	pages = 463,
	file = Full Text PDF:/Users/carolinegorham/Zotero/storage/PDZYRSVK/Iii et al. - 2005 - A Map of the Universe.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/63V43BRF/428890.html:text/html


@articlecornish_constraining_2004,
	title = Constraining the Topology of the Universe,
	volume = 92,
	url = https://link.aps.org/doi/10.1103/PhysRevLett.92.201302,
	doi = 10.1103/PhysRevLett.92.201302,
	abstract = The first year data from the Wilkinson Microwave Anisotropy Probe are used to place stringent constraints on the topology of the Universe. We search for pairs of circles on the sky with similar temperature patterns along each circle. We restrict the search to back-to-back circle pairs, and to nearly back-to-back circle pairs, as this covers the majority of the topologies that one might hope to detect in a nearly flat universe. We do not find any matched circles with radius greater than 25°. For a wide class of models, the nondetection rules out the possibility that we live in a universe with topology scale smaller than 24 Gpc.,
	number = 20,
	urldate = 2019-07-21,
	journal = Physical Review Letters,
	author = Cornish, Neil J. and Spergel, David N. and Starkman, Glenn D. and Komatsu, Eiichiro,
	month = may,
	year = 2004,
	pages = 201302,
	file = APS Snapshot:/Users/carolinegorham/Zotero/storage/W6JUFHZ5/PhysRevLett.92.html:text/html;Submitted Version:/Users/carolinegorham/Zotero/storage/Q8DTM8JF/Cornish et al. - 2004 - Constraining the Topology of the Universe.pdf:application/pdf


@articleweeks_poincare_2004,
	title = The Poincaré dodecahedral space and the mystery of the missing fluctuations,
	volume = 51,
	number = 6,
	journal = Notices of the AMS,
	author = Weeks, Jeffrey,
	year = 2004,
	pages = 610–619,
	file = Full Text:/Users/carolinegorham/Zotero/storage/HHCJWMJB/Weeks - 2004 - The Poincaré dodecahedral space and the mystery of.pdf:application/pdf


@inproceedingsreboucas_brief_2005,
	title = A brief introduction to cosmic topology,
	volume = 782,
	booktitle = AIP Conference Proceedings,
	publisher = AIP,
	author = Rebouças, Marcelo J.,
	year = 2005,
	pages = 188–201,
	file = Full Text:/Users/carolinegorham/Zotero/storage/HWG459YK/Rebouças - 2005 - A brief introduction to cosmic topology.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/E7S48T8L/1.html:text/html


@articleaurich_circles—sky_2006,
	title = The circles-in-the-sky signature for three spherical universes,
	volume = 369,
	issn = 0035-8711,
	url = https://academic.oup.com/mnras/article/369/1/240/1053527,
	doi = 10.1111/j.1365-2966.2006.10296.x,
	abstract = Abstract.  The mysteriously low cosmic microwave background (CMB) power on the largest scales might point to a Universe which consists of a multi-connected spac,
	language = en,
	number = 1,
	urldate = 2019-07-21,
	journal = Monthly Notices of the Royal Astronomical Society,
	author = Aurich, R. and Lustig, S. and Steiner, F.,
	month = jun,
	year = 2006,
	pages = 240–248,
	file = Full Text PDF:/Users/carolinegorham/Zotero/storage/FXKT2VAZ/Aurich et al. - 2006 - The circles-in-the-sky signature for three spheric.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/VQDM7MGE/1053527.html:text/html


@articleluminet_science_2009,
	title = Science, art and geometrical imagination,
	volume = 5,
	issn = 1743-9221, 1743-9213,
	url = https://www.cambridge.org/core/journals/proceedings-of-the-international-astronomical-union/article/science-art-and-geometrical-imagination/2BB41394FCE04925F665C38462241319,
	doi = 10.1017/S1743921311002377,
	abstract = From the geocentric, closed world model of Antiquity to the wraparound universe models of relativistic cosmology, the parallel history of space representations in science and art illustrates the fundamental rôle of geometric imagination in innovative findings. Through the analysis of works of various artists and scientists like Plato, Dürer, Kepler, Escher, Grisey or the author, it is shown how the process of creation in science and in the arts rests on aesthetical principles such as symmetry, regular polyhedra, laws of harmonic proportion, tessellations, group theory, etc., as well as on beauty, conciseness and an emotional approach of the world.,
	language = en,
	number = S260,
	urldate = 2019-07-21,
	journal = Proceedings of the International Astronomical Union,
	author = Luminet, Jean-Pierre,
	month = jan,
	year = 2009,
	keywords = art, geometry, history,
	pages = 248–273,
	file = Full Text PDF:/Users/carolinegorham/Zotero/storage/ZXPYBIZT/Luminet - 2009 - Science, art and geometrical imagination.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/D34QK3WC/2BB41394FCE04925F665C38462241319.html:text/html


@articlesugawa_observation_2016,
	title = Observation of a non-Abelian Yang monopole: From new Chern numbers to a topological transition,
	shorttitle = Observation of a non-Abelian Yang monopole,
	journal = arXiv preprint arXiv:1610.06228,
	author = Sugawa, Seiji and Salces-Carcoba, Francisco and Perry, Abigail R. and Yue, Yuchen and Spielman, Ian B.,
	year = 2016,
	file = Full Text:/Users/carolinegorham/Zotero/storage/NPDMVLY5/Sugawa et al. - 2016 - Observation of a non-Abelian Yang monopole From n.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/AULHAZAH/1610.html:text/html


@articleqi_topological_2008,
	title = Topological field theory of time-reversal invariant insulators,
	volume = 78,
	number = 19,
	journal = Physical Review B,
	author = Qi, Xiao-Liang and Hughes, Taylor L. and Zhang, Shou-Cheng,
	year = 2008,
	pages = 195424,
	file = Full Text:/Users/carolinegorham/Zotero/storage/Z9IQMQFN/Qi et al. - 2008 - Topological field theory of time-reversal invarian.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/6IW9ZNHB/PhysRevB.78.html:text/html


@articleonnes_resistance_1911,
	title = The resistance of pure mercury at helium temperatures,
	volume = 120,
	journal = Commun. Phys. Lab. Univ. Leiden, b,
	author = Onnes, H. Kamerlingh,
	year = 1911,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/ZYP3GUFM/10029970951.html:text/html


@articlekapitza_viscosity_1938,
	title = Viscosity of Liquid Helium below the $\lambda$-Point,
	volume = 141,
	copyright = 1938 Nature Publishing Group,
	issn = 1476-4687,
	url = https://www.nature.com/articles/141074a0,
	doi = 10.1038/141074a0,
	abstract = THE abnormally high heat conductivity of helium II below the λ-point, as first observed by Keesom, suggested to me the possibility of an explanation in terms of convection currents. This explanation would require helium II to have an abnormally low viscosity; at present, the only viscosity measurements on liquid helium have been made in Toronto1, and showed that there is a drop in viscosity below the λ-point by a factor of 3 compared with liquid helium at normal pressure, and by a factor of 8 compared with the value just above the λ-point. In these experiments, however, no check was made to ensure that the motion was laminar, and not turbulent.,
	language = en,
	number = 3558,
	urldate = 2019-08-18,
	journal = Nature,
	author = Kapitza, P.,
	month = jan,
	year = 1938,
	pages = 74–74,
	file = Full Text PDF:/Users/carolinegorham/Zotero/storage/K2PC5WSR/Kapitza - 1938 - Viscosity of Liquid Helium below the λ-Point.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/IW495V2G/141074a0.html:text/html


@articleginzburg_alexandru_1950,
	title = Alexandru Proca (1897-1955) and his equation of the massive vector boson field,
	volume = 20,
	journal = Zh. Eksp. Teor. Fiz,
	author = Ginzburg, V. L. and Landau, L. D.,
	year = 1950,
	pages = 1064


@articleginzburg_theory_1950,
	title = On the Theory of superconductivity,
	volume = 20,
	journal = Zh.Eksp.Teor.Fiz.,
	author = Ginzburg, V. L. and Landau, L. D.,
	year = 1950,
	pages = 1064–1082,
	file = INSPIRE Snapshot:/Users/carolinegorham/Zotero/storage/ZHG5DPA5/9135.html:text/html


@articlemakhlin_quantum-state_2001-1,
	title = Quantum-state engineering with Josephson-junction devices,
	volume = 73,
	number = 2,
	journal = Reviews of modern physics,
	author = Makhlin, Yuriy and Schön, Gerd and Shnirman, Alexander,
	year = 2001,
	pages = 357,
	file = Full Text:/Users/carolinegorham/Zotero/storage/M4F5BEX9/Makhlin et al. - 2001 - Quantum-state engineering with Josephson-junction .pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/HK377BFG/RevModPhys.73.html:text/html


@articletang_three-dimensional_2019,
	title = Three-dimensional quantum Hall effect and metal–insulator transition in ZrTe 5,
	volume = 569,
	copyright = 2019 The Author(s), under exclusive licence to Springer Nature Limited,
	issn = 1476-4687,
	url = https://www.nature.com/articles/s41586-019-1180-9,
	doi = 10.1038/s41586-019-1180-9,
	abstract = Evidence of the three-dimensional quantum Hall effect and a magnetic-field-driven quantum phase transition are observed in zirconium pentatelluride crystals.,
	language = en,
	number = 7757,
	urldate = 2019-08-19,
	journal = Nature,
	author = Tang, Fangdong and Ren, Yafei and Wang, Peipei and Zhong, Ruidan and Schneeloch, John and Yang, Shengyuan A. and Yang, Kun and Lee, Patrick A. and Gu, Genda and Qiao, Zhenhua and Zhang, Liyuan,
	month = may,
	year = 2019,
	pages = 537–541,
	file = Full Text PDF:/Users/carolinegorham/Zotero/storage/Y3DFNZLS/Tang et al. - 2019 - Three-dimensional quantum Hall effect and metal–in.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/G8JANPRR/s41586-019-1180-9.html:text/html


@articleliu_2d_2019,
	title = 2D materials for quantum information science,
	copyright = 2019 Springer Nature Limited,
	issn = 2058-8437,
	url = https://www.nature.com/articles/s41578-019-0136-x,
	doi = 10.1038/s41578-019-0136-x,
	abstract = 2D materials exhibit diverse properties and can be integrated in heterostructures: this makes them ideal platforms for quantum information science. This Review surveys recent progress and identifies future opportunities for 2D materials as quantum-dot qubits, single-photon emitters, superconducting qubits and topological quantum computing elements.,
	language = en,
	urldate = 2019-08-20,
	journal = Nature Reviews Materials,
	author = Liu, Xiaolong and Hersam, Mark C.,
	month = aug,
	year = 2019,
	pages = 1–16,
	file = Full Text PDF:/Users/carolinegorham/Zotero/storage/EUFHVH68/Liu and Hersam - 2019 - 2D materials for quantum information science.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/29YNJ9NY/s41578-019-0136-x.html:text/html


@articleqinyan_gu_superconducting_2019,
	title = Superconducting Single-Layer T-Graphene and Novel Synthesis Routes,
	volume = 36,
	issn = 0256-307X,
	url = http://cpl.iphy.ac.cn/EN/10.1088/0256-307X/36/9/097401,
	doi = 10.1088/0256-307X/36/9/097401,
	language = en,
	number = 9,
	urldate = 2019-08-20,
	journal = Chinese Physics Letters,
	author = Qinyan Gu, Dingyu Xing and Qinyan Gu, Dingyu Xing,
	month = aug,
	year = 2019,
	pages = 97401–097401,
	file = Full Text PDF:/Users/carolinegorham/Zotero/storage/DUPP9G8A/Qinyan Gu and Qinyan Gu - 2019 - Superconducting Single-Layer T-Graphene and Novel .pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/5FKFRUHV/097401.html:text/html


@articlefeynman_simulating_1982,
	title = Simulating physics with computers,
	volume = 21,
	issn = 1572-9575,
	url = https://doi.org/10.1007/BF02650179,
	doi = 10.1007/BF02650179,
	language = en,
	number = 6,
	urldate = 2019-08-20,
	journal = International Journal of Theoretical Physics,
	author = Feynman, Richard P.,
	year = 1982,
	keywords = Calcite, Cellular Automaton, Quantum Mechanic, Quantum System, Wigner Function,
	pages = 467–488,
	file = Springer Full Text PDF:/Users/carolinegorham/Zotero/storage/XUY7F6IW/Feynman - 1982 - Simulating physics with computers.pdf:application/pdf


@articlekallosh_strings_2006,
	title = Strings, Black Holes, and Quantum Information,
	volume = 73,
	issn = 1550-7998, 1550-2368,
	url = http://arxiv.org/abs/hep-th/0602061,
	doi = 10.1103/PhysRevD.73.104033,
	abstract = We find multiple relations between extremal black holes in string theory and 2- and 3-qubit systems in quantum information theory. We show that the entropy of the axion-dilaton extremal black hole is related to the concurrence of a 2-qubit state, whereas the entropy of the STU black holes, BPS as well as non-BPS, is related to the 3-tangle of a 3-qubit state. We relate the 3-qubit states with the string theory states with some number of D-branes. We identify a set of "large" black holes with the maximally entangled GHZ-class of states and "small" black holes with separable, bipartite and W states. We sort out the relation between 3-qubit states, twistors, octonions, and black holes. We give a simple expression for the entropy and the area of stretched horizon of "small” black holes in terms of a norm and 2-tangles of a 3-qubit system. Finally, we show that the most general expression for the black hole and black ring entropy in N=8 supergravity/M-theory, which is given by the famous quartic Cartan E_{7(7)} invariant, can be reduced to Cayley's hyperdeterminant describing the 3-tangle of a 3-qubit state.,
	number = 10,
	urldate = 2019-08-20,
	journal = Physical Review D,
	author = Kallosh, Renata and Linde, Andrei,
	month = may,
	year = 2006,
	note = arXiv: hep-th/0602061,
	keywords = High Energy Physics - Theory, Astrophysics, General Relativity and Quantum Cosmology, High Energy Physics - Phenomenology, Quantum Physics,
	pages = 104033,
	annote = Comment: 31 pages, 10 figures. A version to appear in Physical Review,
	file = arXiv hep-th/0602061 PDF:/Users/carolinegorham/Zotero/storage/4BIKCT97/Kallosh and Linde - 2006 - Strings, Black Holes, and Quantum Information.pdf:application/pdf;arXiv.org Snapshot:/Users/carolinegorham/Zotero/storage/LLQXJEL9/0602061.html:text/html


@articleduff_string_2007,
	title = String triality, black hole entropy and Cayley's hyperdeterminant,
	volume = 76,
	issn = 1550-7998, 1550-2368,
	url = http://arxiv.org/abs/hep-th/0601134,
	doi = 10.1103/PhysRevD.76.025017,
	abstract = The four-dimensional N=2 STU model of string compactification is invariant under an SL(2,Z)_S x SL(2,Z)_T x SL(2,Z)_U duality acting on the dilaton/axion S, complex Kahler form T and the complex structure fields U, and also under a string/string/string triality S-T-U. The model admits an extremal black hole solution with four electric and four magnetic charges whose entropy must respect these symmetries. It is given by the square root of the hyperdeterminant introduced by Cayley in 1845. This also features in three-qubit quantum entanglement.,
	number = 2,
	urldate = 2019-08-20,
	journal = Physical Review D,
	author = Duff, M. J.,
	month = jul,
	year = 2007,
	note = arXiv: hep-th/0601134,
	keywords = High Energy Physics - Theory, General Relativity and Quantum Cosmology, Quantum Physics, Mathematical Physics,
	pages = 025017,
	annote = Comment: Minor improvements. 9 pages latex,
	file = arXiv hep-th/0601134 PDF:/Users/carolinegorham/Zotero/storage/45S34NH3/Duff - 2007 - String triality, black hole entropy and Cayley's h.pdf:application/pdf;arXiv.org Snapshot:/Users/carolinegorham/Zotero/storage/L75FW8TC/0601134.html:text/html


@articlesmith_separating_2017,
	title = Separating the configurational and vibrational entropy contributions in metallic glasses,
	volume = 13,
	copyright = 2017 Nature Publishing Group,
	issn = 1745-2481,
	url = https://www.nature.com/articles/nphys4142,
	doi = 10.1038/nphys4142,
	abstract = Glassy materials exist in nature and play a critical role in technology, but key differences between the glass, liquid and crystalline phases are not well understood. Over several decades there has been controversy about the specific heat absorbed as a glass transforms to a liquid—does this originate from vibrational entropy or configurational entropy? Here we report direct in situ measurements of the vibrational spectra of strong and fragile metallic glasses in the glass, liquid and crystalline phases. For both types of material, the measured vibrational entropies of the glass and liquid show a tiny excess over the crystal, representing less than 5% of the total excess entropy measured with step calorimetry. These results reveal that the excess entropy of metallic glasses is almost entirely configurational in origin, consistent with the early theories of Gibbs and co-workers describing the glass transition as a purely configurational transition.,
	language = en,
	number = 9,
	urldate = 2019-08-27,
	journal = Nature Physics,
	author = Smith, Hillary L. and Li, Chen W. and Hoff, Andrew and Garrett, Glenn R. and Kim, Dennis S. and Yang, Fred C. and Lucas, Matthew S. and Swan-Wood, Tabitha and Lin, J. Y. Y. and Stone, M. B. and Abernathy, D. L. and Demetriou, Marios D. and Fultz, B.,
	month = sep,
	year = 2017,
	pages = 900–905,
	file = Full Text PDF:/Users/carolinegorham/Zotero/storage/H6WC7XGE/Smith et al. - 2017 - Separating the configurational and vibrational ent.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/4XVIRT7P/nphys4142.html:text/html


@articlereznik_gravitational_1995,
	title = Gravitational Analog of the Aharonov-Casher Effect,
	volume = 51,
	issn = 0556-2821,
	url = http://arxiv.org/abs/gr-qc/9409027,
	doi = 10.1103/PhysRevD.51.3108,
	abstract = The gravitational interaction between a massive particle and a spinning particle in the weak-field limit is studied. We show that a system of a spinning point-like particle and a massive rod exhibit a topological effect analogous to the electromagnetic Aharonov-Casher effect. We discuss the effect also for systems with a cosmic string instead of a massive rod and in the context of 2+1-dimensional gravity.,
	number = 6,
	urldate = 2019-08-28,
	journal = Physical Review D,
	author = Reznik, Benni,
	month = mar,
	year = 1995,
	note = arXiv: gr-qc/9409027,
	keywords = General Relativity and Quantum Cosmology,
	pages = 3108–3112,
	annote = Comment: 15 pages, Latex, TP-94-009,
	file = arXiv gr-qc/9409027 PDF:/Users/carolinegorham/Zotero/storage/3JCT3UCR/Reznik - 1995 - Gravitational Analog of the Aharonov-Casher Effect.pdf:application/pdf;arXiv.org Snapshot:/Users/carolinegorham/Zotero/storage/JNMWSX7J/9409027.html:text/html


@articlecaputa_quantum_2019,
	title = Quantum Computation as Gravity,
	volume = 122,
	url = https://link.aps.org/doi/10.1103/PhysRevLett.122.231302,
	doi = 10.1103/PhysRevLett.122.231302,
	abstract = We formulate Nielsen’s geometric approach to circuit complexity in the context of two-dimensional conformal field theories, where series of conformal transformations are interpreted as “unitary circuits” built from energy-momentum tensor gates. We show that the complexity functional in this setup can be written as the Polyakov action of two-dimensional gravity or, equivalently, as the geometric action on the coadjoint orbits of the Virasoro group. This way, we argue that gravity sets the rules for optimal quantum computation in conformal field theories.,
	number = 23,
	urldate = 2019-08-28,
	journal = Physical Review Letters,
	author = Caputa, Paweł and Magan, Javier M.,
	month = jun,
	year = 2019,
	pages = 231302,
	file = APS Snapshot:/Users/carolinegorham/Zotero/storage/LZMM5BRL/PhysRevLett.122.html:text/html;Full Text PDF:/Users/carolinegorham/Zotero/storage/TDUKZGWG/Caputa and Magan - 2019 - Quantum Computation as Gravity.pdf:application/pdf


@articlecaputa_quantum_2019-1,
	title = Quantum Computation as Gravity,
	volume = 122,
	url = https://link.aps.org/doi/10.1103/PhysRevLett.122.231302,
	doi = 10.1103/PhysRevLett.122.231302,
	abstract = We formulate Nielsen’s geometric approach to circuit complexity in the context of two-dimensional conformal field theories, where series of conformal transformations are interpreted as “unitary circuits” built from energy-momentum tensor gates. We show that the complexity functional in this setup can be written as the Polyakov action of two-dimensional gravity or, equivalently, as the geometric action on the coadjoint orbits of the Virasoro group. This way, we argue that gravity sets the rules for optimal quantum computation in conformal field theories.,
	number = 23,
	urldate = 2019-08-28,
	journal = Physical Review Letters,
	author = Caputa, Paweł and Magan, Javier M.,
	month = jun,
	year = 2019,
	pages = 231302,
	file = APS Snapshot:/Users/carolinegorham/Zotero/storage/H4RCUKYB/PhysRevLett.122.html:text/html;Full Text PDF:/Users/carolinegorham/Zotero/storage/TDF7HQD6/Caputa and Magan - 2019 - Quantum Computation as Gravity.pdf:application/pdf


@articlesimoncelli_unified_2019,
	title = Unified theory of thermal transport in crystals and glasses,
	volume = 15,
	copyright = 2019 The Author(s), under exclusive licence to Springer Nature Limited,
	issn = 1745-2481,
	url = https://www.nature.com/articles/s41567-019-0520-x,
	doi = 10.1038/s41567-019-0520-x,
	abstract = A unified theory for the conduction of heat in materials is derived and shown to account for both the limiting regimes of periodic crystals and aperiodic glasses.,
	language = en,
	number = 8,
	urldate = 2019-09-05,
	journal = Nature Physics,
	author = Simoncelli, Michele and Marzari, Nicola and Mauri, Francesco,
	month = aug,
	year = 2019,
	pages = 809–813,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/TY3SQ5YP/s41567-019-0520-x.html:text/html


@bookjorio_carbon_2007,
	title = Carbon nanotubes: advanced topics in the synthesis, structure, properties and applications,
	volume = 111,
	shorttitle = Carbon nanotubes,
	publisher = Springer Science & Business Media,
	author = Jorio, Ado and Dresselhaus, Gene and Dresselhaus, Mildred S.,
	year = 2007,
	file = Full Text:/Users/carolinegorham/Zotero/storage/9VCQKDMN/Jorio et al. - 2007 - Carbon nanotubes advanced topics in the synthesis.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/2P3LI2HF/books.html:text/html


@articlehopf_uber_1931,
	title = Uber die Abbildungen der 3-Sphs auf die Kugelfl∼ che,
	volume = 104,
	journal = Math. Ann,
	author = Hopf, Heinz,
	year = 1931,
	pages = 637–665


@articlemoore_topological_2009,
	title = Topological insulators: The next generation,
	volume = 5,
	copyright = 2009 Nature Publishing Group,
	issn = 1745-2481,
	shorttitle = Topological insulators,
	url = https://www.nature.com/articles/nphys1294,
	doi = 10.1038/nphys1294,
	abstract = Spin–orbit coupling in some materials leads to the formation of surface states that are topologically protected from scattering. Theory and experiments have found an important new family of such materials.,
	language = en,
	number = 6,
	urldate = 2019-09-09,
	journal = Nature Physics,
	author = Moore, Joel,
	month = jun,
	year = 2009,
	pages = 378–380,
	file = Snapshot:/Users/carolinegorham/Zotero/storage/EJK2YU3C/nphys1294.html:text/html


@articlebernevig_quantum_2006,
	title = Quantum Spin Hall Effect,
	volume = 96,
	url = https://link.aps.org/doi/10.1103/PhysRevLett.96.106802,
	doi = 10.1103/PhysRevLett.96.106802,
	abstract = The quantum Hall liquid is a novel state of matter with profound emergent properties such as fractional charge and statistics. The existence of the quantum Hall effect requires breaking of the time reversal symmetry caused by an external magnetic field. In this work, we predict a quantized spin Hall effect in the absence of any magnetic field, where the intrinsic spin Hall conductance is quantized in units of 2e4π. The degenerate quantum Landau levels are created by the spin-orbit coupling in conventional semiconductors in the presence of a strain gradient. This new state of matter has many profound correlated properties described by a topological field theory.,
	number = 10,
	urldate = 2019-09-09,
	journal = Physical Review Letters,
	author = Bernevig, B. Andrei and Zhang, Shou-Cheng,
	month = mar,
	year = 2006,
	pages = 106802,
	file = APS Snapshot:/Users/carolinegorham/Zotero/storage/K7PJKPWU/PhysRevLett.96.html:text/html;Submitted Version:/Users/carolinegorham/Zotero/storage/H2MKJ9XA/Bernevig and Zhang - 2006 - Quantum Spin Hall Effect.pdf:application/pdf


@articlefreedman_topological_2003,
	title = Topological quantum computation,
	volume = 40,
	number = 1,
	journal = Bulletin of the American Mathematical Society,
	author = Freedman, Michael and Kitaev, Alexei and Larsen, Michael and Wang, Zhenghan,
	year = 2003,
	pages = 31–38,
	file = Full Text:/Users/carolinegorham/Zotero/storage/9YLRDWHP/Freedman et al. - 2003 - Topological quantum computation.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/UCY4NCJR/S0273-0979-02-00964-3.html:text/html


@incollectionbouwmeester_physics_2000,
	title = The physics of quantum information: basic concepts,
	shorttitle = The physics of quantum information,
	booktitle = The physics of quantum information,
	publisher = Springer,
	author = Bouwmeester, Dirk and Zeilinger, Anton,
	year = 2000,
	pages = 1–14,
	file = Full Text:/Users/carolinegorham/Zotero/storage/4LCGHEB4/Bouwmeester and Zeilinger - 2000 - The physics of quantum information basic concepts.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/9578C8GY/978-3-662-04209-0_1.html:text/html


@articlemayer_phase_2019,
	title = Phase signature of topological transition in Josephson Junctions,
	journal = arXiv preprint arXiv:1906.01179,
	author = Mayer, William and Dartiailh, Matthieu C. and Yuan, Joseph and Wickramasinghe, Kaushini S. and Matos-Abiague, Alex and Žutić, Igor and Shabani, Javad,
	year = 2019,
	file = Full Text:/Users/carolinegorham/Zotero/storage/QSF9ZIPQ/Mayer et al. - 2019 - Phase signature of topological transition in Josep.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/QATAJSYQ/1906.html:text/html


@articlenajarbashi_two-and_2016,
	title = Two-and three-qubit geometry, quaternionic and octonionic conformal maps, and intertwining stereographic projection,
	volume = 15,
	number = 1,
	journal = Quantum Information Processing,
	author = Najarbashi, Ghader and Seifi, Bahman and Mirzaei, S.,
	year = 2016,
	pages = 509–528,
	file = Full Text:/Users/carolinegorham/Zotero/storage/569U4LQQ/Najarbashi et al. - 2016 - Two-and three-qubit geometry, quaternionic and oct.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/YSHANBW2/s11128-015-1172-0.html:text/html


@articleartin_theory_1947,
	title = Theory of braids,
	volume = 48,
	number = 2,
	journal = Ann. of Math,
	author = Artin, Emil,
	year = 1947,
	pages = 101–126,
	file = Full Text:/Users/carolinegorham/Zotero/storage/G7JEQHDK/Artin - 1947 - Theory of braids.pdf:application/pdf


@articlehe_nonlinear_2019,
	title = Nonlinear planar Hall effect,
	volume = 123,
	issn = 0031-9007, 1079-7114,
	url = http://arxiv.org/abs/1906.06462,
	doi = 10.1103/PhysRevLett.123.016801,
	abstract = An intriguing property of three-dimensional (3D) topological insulator (TI) is the existence of surface states with spin-momentum locking, which offers a new frontier of exploration in spintronics. Here, we report the observation of a new type of Hall effect in a 3D TI Bi2Se3 film. The Hall resistance scales linearly with both the applied electric and magnetic fields and exhibits a {\pi}/2 angle offset with respect to its longitudinal counterpart, in contrast to the usual angle offset of {\pi}/4 between the linear planar Hall effect and the anisotropic magnetoresistance. This novel nonlinear planar Hall effect originates from the conversion of a nonlinear transverse spin current to a charge current due to the concerted actions of spin-momentum locking and time reversal symmetry breaking, which also exists in a wide class of non-centrosymmetric materials with a large span of magnitude. It provides a new way to characterize and utilize the nonlinear spin-to-charge conversion in a variety of topological quantum materials.,
	number = 1,
	urldate = 2019-09-12,
	journal = Physical Review Letters,
	author = He, Pan and Zhang, Steven S.-L. and Zhu, Dapeng and Shi, Shuyuan and Heinonen, Olle G. and Vignale, Giovanni and Yang, Hyunsoo,
	month = jul,
	year = 2019,
	note = arXiv: 1906.06462,
	keywords = Condensed Matter - Materials Science, Condensed Matter - Mesoscale and Nanoscale Physics,
	pages = 016801,
	file = arXiv 1906.06462 PDF:/Users/carolinegorham/Zotero/storage/EJBPDUCD/He et al. - 2019 - Nonlinear planar Hall effect.pdf:application/pdf;arXiv.org Snapshot:/Users/carolinegorham/Zotero/storage/TZNIHW4N/1906.html:text/html


@articlecai_observation_2019,
	title = Observation of Topological Magnon Insulator States in a Superconducting Circuit,
	volume = 123,
	url = https://link.aps.org/doi/10.1103/PhysRevLett.123.080501,
	doi = 10.1103/PhysRevLett.123.080501,
	abstract = Searching topological states in artificial systems has recently become a rapidly growing field of research. Meanwhile, significant experimental progress on observing topological phenomena has been made in superconducting circuits. However, topological insulator states have not yet been reported in this system. Here, for the first time, we experimentally realize a tunable dimerized spin chain model and observe the topological magnon insulator states in a superconducting qubit chain. Via parametric modulations of the qubit frequencies, we show that the qubit chain can be flexibly tuned into topologically trivial or nontrivial magnon insulator states. Based on monitoring the quantum dynamics of a single-qubit excitation in the chain, we not only measure the topological winding numbers, but also observe the topological magnon edge and defect states. Our experiment exhibits the great potential of tunable superconducting qubit chain as a versatile platform for exploring noninteracting and interacting symmetry-protected topological states.,
	number = 8,
	urldate = 2019-09-12,
	journal = Physical Review Letters,
	author = Cai, W. and Han, J. and Mei, Feng and Xu, Y. and Ma, Y. and Li, X. and Wang, H. and Song, Y. P. and Xue, Zheng-Yuan and Yin, Zhang-qi and Jia, Suotang and Sun, Luyan,
	month = aug,
	year = 2019,
	pages = 080501,
	file = APS Snapshot:/Users/carolinegorham/Zotero/storage/XKXFEHEU/PhysRevLett.123.html:text/html;Full Text PDF:/Users/carolinegorham/Zotero/storage/LLYB7PCS/Cai et al. - 2019 - Observation of Topological Magnon Insulator States.pdf:application/pdf


@articlepfleiderer_why_2005,
	title = Why first order quantum phase transitions are interesting,
	volume = 17,
	issn = 0953-8984,
	url = https://doi.org/10.1088
	doi = 10.1088/0953-8984/17/11/031,
	abstract = It is frequently argued that only second order phase transitions at T = 0 deserve to be called quantum phase transitions, while first order quantum phase transitions are a contradiction in terms. However, quantum phase transitions differ from classical phase transitions in two fundamental ways. First, the free energy landscape need not be that of a classical second order phase transition for quantum fluctuations to drive the transition. Second, at T = 0 a rich variety of quantum correlation effects, such as magnetic rotons, instantons or skyrmion textures, are possible. The recent discovery of partial magnetic order, an extended non-Fermi liquid phase and superconductivity at the first order quantum phase transitions of itinerant-electron magnets underscore the need for detailed experimental studies of hitherto unexplored weak rigidities that are well known to generate first order behaviour. These include changes of the electronic valence, spin–orbit coupling, crystal electric field levels, and crystallographic structure driven by instabilities of the Fermi surface.,
	language = en,
	number = 11,
	urldate = 2019-09-17,
	journal = Journal of Physics: Condensed Matter,
	author = Pfleiderer, C.,
	month = mar,
	year = 2005,
	pages = S987–S997


@articlecharbonneau_glass_2017,
	title = Glass and jamming transitions: From exact results to finite-dimensional descriptions,
	volume = 8,
	shorttitle = Glass and jamming transitions,
	journal = Annual Review of Condensed Matter Physics,
	author = Charbonneau, Patrick and Kurchan, Jorge and Parisi, Giorgio and Urbani, Pierfrancesco and Zamponi, Francesco,
	year = 2017,
	pages = 265–288,
	file = Full Text:/Users/carolinegorham/Zotero/storage/YMSHB2AI/annurev-conmatphys-031016-025334.html:text/html;Snapshot:/Users/carolinegorham/Zotero/storage/7LLJ4XCH/annurev-conmatphys-031016-025334.html:text/html


@articlemauro_statistical_2014,
	title = Statistical mechanics of glass,
	volume = 396,
	journal = Journal of Non-Crystalline Solids,
	author = Mauro, John C. and Smedskjaer, Morten M.,
	year = 2014,
	pages = 41–53,
	file = Full Text:/Users/carolinegorham/Zotero/storage/V5Z8C25R/S0022309314001665.html:text/html


@articleangell_insights_2008,
	title = Insights into phases of liquid water from study of its unusual glass-forming properties,
	volume = 319,
	number = 5863,
	journal = Science,
	author = Angell, C. Austen,
	year = 2008,
	pages = 582–587,
	file = Full Text:/Users/carolinegorham/Zotero/storage/GM9UIQUQ/Angell - 2008 - Insights into phases of liquid water from study of.pdf:application/pdf;Snapshot:/Users/carolinegorham/Zotero/storage/NJDNB3JZ/582.html:text/html











caroling@cmu.edu
Department of Materials Science and Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA


laughlin@cmu.edu
Department of Materials Science and Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA




In this article, a theoretical description of the “ideal glass transition” is approached upon the adoption of a quaternion orientational order parameter. Unlike first-order phase transitions of liquids into crystalline solid states, glass transitions are entirely different phenomena that are non-equilibrium and that are highly dependent on the applied cooling rate. Herein, the “ideal glass transition" that occurs at the finite Kauzmann temperature at which point the configurational entropy of an undercooled liquid matches that of its crystalline counterpart is identified as a first-order quantum critical point. We suggest that this quantum critical point belongs to quaternion ordered systems that exist in four- and three-dimensions. The Kauzmann quantum critical point is considered to be a higher-dimensional analogue to the superfluid-to-Mott insulator quantum phase transition, in two- and one-dimensional complex ordered systems. Such quantum critical points are driven by tuning a non-thermal frustration parameter, and result due to characteristic softening of the `Higgs' type mode that corresponds to amplitude fluctuations of the order parameter. The first-order nature of the finite temperature Kauzmann quantum critical point is seen as a consequence of the discrete change of the topology of the ground state manifold that applies to crystalline and non-crystalline solid states.

Importance of the `Higgs' Amplitude Mode in Understanding the “Ideal Glass Transition” and the Kauzmann Entropy Paradox at the Four-Dimensional Crystal/Glass Quantum Critical Point
    David E. Laughlin
    December 30, 2023
====================================================================================================================================================================================








§ INTRODUCTION




The nature of the glass transition is widely thought to be one of the most challenging problems in condensed matter physics <cit.>. Despite their ubiquity, a fundamental understanding of amorphous solids and the glass transition has yet to be obtained. This is in stark contrast to our knowledge of crystalline solids, which result by first-order phase transitions and in which phonons (collective Nambu-Goldstone modes) develop to transport thermal energy. Unlike crystallization, glass formation is non-equilibrium and the glass transition results as an undercooled liquid breaks ergodicity to become a rigid solid. 

The glass transition is highly dependent on the cooling rate; with a slower cooling rate, an undercooled liquid may remain ergodic to lower temperatures. As the temperature of an undercooled liquid is decreased, the difference in entropy between the liquid and crystalline solid phase decreases. Because the entropy of undercooled fluids declines faster with temperature than does crystal entropy, this results in an entropy paradox at a certain finite temperature that may be achieved in the limit of an infinitely slow cooling rate <cit.>. At this finite temperature, known as the Kauzmann temperature T_K, the liquid adopts a unique state of lowest energy.

An “ideal glass," that forms at the Kauzmann temperature, has a configurational entropy that matches its crystalline counterpart. This is known in the literature  as the Kauzmann entropy paradox <cit.>. “Ideal glass transitions" have never been obtained in the laboratory, as any real glass transition occurs at a temperature higher than T_K and is caused by kinetic constraints that are responsible for a loss of ergodicity <cit.>. Yet, the physics underlying the Kauzmann entropy paradox presents an interesting problem in condensed matter physics.

The objective of this article is to describe the nature of formation of both crystalline and glassy solids from the liquid state, and the origin of the Kauzmann point, by the application of a quaternion orientational order parameter. This approach makes use of the principles of spontaneous symmetry breaking and of topological-ordering, that are known to play key roles in our understanding of condensed matter. Analogies between solidification and the formation of complex ordered states of matter, in two- and one-dimensions, are developed in order to frame the Kauzmann point as a quantum critical point (QCP) that exists to separate crystalline and glassy solid states. The topological properties of the free energy functions that apply to crystalline and glassy solids are compared, and the roles of the two types of fundamental exciations: massless phase modes (Nambu-Goldstone) and a massive amplitude mode (`Higgs') are discussed. These considerations enable the characterization of the “ideal glass transition," at the finite Kauzmann temperature, as a first-order QCP similar to the second-order superfluid/Mott-insulator quantum phase transition (QPT) that occurs in two- and one-dimensions <cit.>.



§ CRYSTALLINE-TO-GLASS FIRST-ORDER QUANTUM CRITICAL POINT AND THE KAUZMANN ENTROPY PARADOX



Quantum phase transitions <cit.> exist for O(N) quantum rotor models of N-vector ordered systems, which are constructed by taking into account both potential and kinetic energy terms. Such QPTs <cit.> are driven by tuning a dimensionless frustration parameter (g), that is a measure of the ratio of kinetic energy to potential energy. Such quantum rotor models have been applied extensively to understand the nature of the superfluid/Mott-insulator QPT in two- and one-dimensions <cit.>. 

In two- and one-dimensional complex ordered systems, an order parameter with N=2 components develops and O(2) quantum rotor models describe the dynamics of the complex order parameter (Ψ=|Ψ|e^îθ) near a QPT between a phase-coherent superfluid (|Ψ|>0) and a phase-incoherent Mott-insulator (|Ψ|=0). In the superfluid ordered state of matter, the free energy function has the form of a conventional `Mexican hat' (Figure <ref>A) where the order parameter has a non-zero value at the basin of the `Mexican hat.' In two- and one-dimensional complex ordered systems, as opposed to bulk three-dimensional complex ordered systems, phase-coherent superfluid ground states are achieved via a Kosterlitz-Thouless topological-ordering transition in which vortex defects and anti-defects form bound states (Figure <ref>). In the absence of kinetic energy effects, i.e., in the absence of frustration, the scalar phase angle θ acquires a definite value below the Kosterlitz-Thouless transition through breaking of rotational symmetry – and the superfluid ground state is perfectly phase-coherent. 

Around the symmetry-broken ground state, there are two mode types: a massless Nambu-Goldstone mode related to fluctuations in the scalar phase angle θ and a massive `Higgs' mode related to amplitude variations in Ψ. As the amount of frustration reaches a critical value, in the vicinity of the QPT to the phase-incoherent Mott-insulator, there is a characteristic softening of the excitation gap or mass of the Higgs amplitude mode <cit.>. This softening transforms the free energy into a function with a minimum at |Ψ|=0 in the phase-incoherent Mott-insulating state <cit.> (Figure <ref>B).



 

The order of the quantum phase transition, that belongs to an O(N) quantum rotor model, can be discerned by noting changes in the topological properties of the free energy function in its vicinity. In the case of the superfluid/Mott-insulator QPT, the topology of the `Mexican hat' that applies to the superfluid is circular and the free energy of the Mott-insulator retains U(1)≅ S^1 symmetry at the origin. Thus, the superfluid/Mott-insulator QPT is continuous and is therefore of second-order. Such a second-order QPT occurs at zero Kelvin (Figure <ref>A), and describes a change in the ground state as a result of quantum fluctuations arising from the Heisenberg uncertainty principle <cit.>.




In the same way that the degree of order in superfluids (phase-coherent) is described by a complex order parameter, it has recently been proposed by the authors that orientational-order in crystalline solids may be described by a quaternion order parameter <cit.>. Quaternion order parameters Ψ=|Ψ|e^τ̂ϕ, where τ̂^2=-1 and τ̂=u_1î+u_2ĵ+u_3k̂ is a unit imaginary quaternion vector, are four-dimensional and are described by a set of three scalar phase angle parameters. In four- and three-dimensions, O(4) quantum rotor models apply to mathematically model quaternion ordered systems – as these are “restricted dimensions” for quaternions in the Hohenberg-Mermin-Wagner sense <cit.>. When applied to the solidification problem, a first-order quantum critical point is anticipated to exist between crystalline (i.e., orientationally-ordered) and non-crystalline (i.e., orientationally-disordered) solids. 


Crystalline solids are anticipated to develop as a result of a defect-driven topological-ordering transition <cit.>, just as the Kosterlitz-Thouless mechanism <cit.> allows for the realization of superfluids in 2D/1D. Just as first homotopy group defects are available to complex ordered systems (i.e., π_1(S^1) vortices), third homotopy group defects are available to quaternion ordered systems (π_3(S^3)). Vortices are points in two-dimensions (complex plane) and, third homotopy group defects are points in four-dimensions (quaternion plane). In these “restricted dimensions" (Hohenberg-Mermin-Wagner theorem <cit.>), defect binding via a Kosterlitz-Thouless mechanism is necessary to prevent the mobility of misorientational fluctuations such that phase-coherency or long-range orientational-order may be obtained.

In addition to third homotopy group defects, closed-loop (fundamental group) defects <cit.> exist below the melting temperature as a consequence of the discrete orientational-order in clustered undercooled fluids. Such defects are known as disclinations. Just as complementary third homotopy group point defects form bound pairs on crystallization, disclinations of equal and opposite sign come together to form dislocations <cit.>. In perfect crystals, at absolute zero temperature, definite values for the set of three scalar phase angle parameters that define the quaternion order parameter are obtained as components of bound pair excitations come together and annihilate.





In the presence of finite frustration effects, on approaching the quantum critical point from the limit of a perfect crystal, crystalline solid states may form in which local orientational-order is incompatible with long-range crystallographic packing. Examples of such structures are topologically close-packed Frank-Kasper crystalline solids <cit.>, in which geometric frustration <cit.> prevents the development of long-range icosahedral orientational-order. Such geometrically frustrated crystalline structures (e.g., Frank-Kasper) are stabilized in the ground state by a periodic arrangement of signed topological defects. In particular, the frustration-induced signed disclination lines that are present carry negative curvature and form what is known as a “major skeleton network" (Figure <ref>). An entangled array of negative disclination lines is an attractive model for the structure of glasses <cit.>, that form above a critical amount of geometrical frustration. Just as topologically close-packed crystalline solids may be viewed as analogous to 2D/1D superfluids with a finite amount of frustration, orientationally-disordered glasses are similar to the phase-incoherent Mott-insulator state <cit.>.


     

In crystalline solids, the order parameter manifold has the topology of a three-dimensional torus (T^3≅ S^1× S^1× S^1) that accommodates periodic boundary conditions. This can be viewed as a higher-dimensional, quaternionic, version of the `Mexican hat' of superfluids (Figure <ref>A). Around the symmetry-broken crystalline ground state: three massless phonon modes (Nambu-Goldstone) and a massive mode (`Higgs'), related to the amplitude variations in Ψ, exist. 


Like the 2D/1D superfluid/Mott-insulator QPT <cit.>, softening of the excitation gap of the amplitude mode is anticipated as frustration is increased to approach the QCP that belongs to O(4) quantum rotor models. This softening transforms the order parameter manifold into a function with a minimum at |Ψ|=0, at the QCP, which retains SO(3)/H≅ SU(2)/H' symmetry at the origin (where H' is the binary polyhedral group of preferred local orientational order H∈ SO(3), e.g., H'=ℤ_2 in the case of the trivial group that applies to continuous random network glasses <cit.>). 

Owing to the discontinuous change in the genus topological invariant of the ground state manifold that applies to crystalline and glassy solids that the frustration-induced QCP is first-order, and thereby occurs at a finite temperature (Figure <ref>B). When considering solidification processes, the first-order QCP that belongs to O(4) quantum rotor models may be identified as the Kauzmann point <cit.> that occurs at the finite Kauzmann temperature ( “ideal glass transition”). At the Kauzmann temperature, a Kauzmann entropy paradox <cit.> occurs. This entropy paradox, where the configurational entropy of an undercooled liquid and its crystalline counterpart are equal, is physically acceptable at finite temperatures but would not be so at the absolute zero of temperature. Although the finite temperature nature of the “ideal glass transition” is well-understood based upon thermodynamic principles, this topological interpretation of the first-order nature of this QCP is novel.




§ CONCLUSIONS AND OUTLOOK


The abundance of literature that exists on the nature of both the real and the “ideal glass transition" clearly reflects the importance of the free energy landscape in providing a qualitative explanation of the phenomenon. In this article, we have suggested that crystallization and glass formation can be understood within a unified framework by the application of a four-dimensional quaternion orientational order parameter. As a generalization of the superfluid/Mott-insulator quantum phase transition (QPT) in two- or one-dimensions, a quantum critical point (QCP) is anticipated for quaternion ordered systems that  exist in four- or three-dimensions. This QCP has been identified with the “ideal glass transition,” that occurs at the finite Kauzmann temperature.
 
The first-order nature of the Kauzmann QCP has been determined by accounting for the discrete change in the topology of the ground state manifold that applies to crystalline (orientationally-ordered) and non-crystalline (orientationally-disordered) solid states. Just as in the case of the superfluid/Mott-insulator QPT, the ground state manifold is anticipated to become modified due to characteristic softening of the amplitude mode ('Higgs') on approaching the Kauzmann QCP from the limit of a perfect crystal. The first-principles approach presented in this article suggests that the Kauzmann temperature, at which the Kauzmann entropy paradox may be realized, is finite and thereby corresponds with experiments.




§ ACKNOWLEDGMENT


The authors acknowledge support from the ALCOA Chair in Physical Metallurgy. Additionally, CSG is grateful for insightful discussions with Prof. Mingda Li (MIT) and Prof. Di Xiao (CMU).







