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Continuous space-time symmetries in a lattice field theory
H. B. Thacker
For purposes of regularization as well as numerical simulation, the discretization of Lorentz invariant continuum field theories on a space-time lattice is often convenient. In general, this discretization destroys the rotational or Lorentz-frame independence of the theory, which is only recovered in the continuum limit. The Baxter 8-vertex model may be interpreted as a particular discretization of a self-interacting massive Dirac fermion theory in two dimensions (the massive Thirring model). Here it is shown that, in the 8-vertex/massive Thirring model, the Lorentz frame independence of the theory remains undisturbed on the lattice. The only effect of the discretization is to compactify the manifold of Lorentz frames. The relationship between this lattice Lorentz symmetry and the Yang-Baxter relations is discussed.
Optical Activities as Computing Resources for Space-time Symmetries
Y. S. Kim
It is known that optical activities can perform rotations. It is shown that the rotation, if modulated by attenuations, can perform symmetry operations of Wigner's little group which dictates the internal space-time symmetries of elementary particles.
From Discrete Space-Time to Minkowski Space: Basic Mechanisms, Methods and Perspectives
Felix Finster
This survey article reviews recent results on fermion system in discrete space-time and corresponding systems in Minkowski space. After a basic introduction to the discrete setting, we explain a mechanism of spontaneous symmetry breaking which leads to the emergence of a discrete causal structure. As methods to study the transition between discrete space-time and Minkowski space, we describe a lattice model for a static and isotropic space-time, outline the analysis of regularization tails of vacuum Dirac sea configurations, and introduce a Lorentz invariant action for the masses of the Dirac seas. We mention the method of the continuum limit, which allows to analyze interacting systems. Open problems are discussed.
Space-time symmetries of noncommutative spaces
Calmet, Xavier [Department of Physics and Astronomy, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599 (United States)
We define a noncommutative Lorentz symmetry for canonical noncommutative spaces. The noncommutative vector fields and the derivatives transform under a deformed Lorentz transformation. We show that the star product is invariant under noncommutative Lorentz transformations. We then apply our idea to the case of actions obtained by expanding the star product and the fields taken in the enveloping algebra via the Seiberg-Witten maps and verify that these actions are invariant under these new noncommutative Lorentz transformations. We finally consider general coordinate transformations and show that the metric is undeformed.
Internal Symmetry of Space-Time Connections with Torsion
David Robert Bergman
In this brief article an internal symmetry of a generic metric compatible space-time connection, metric and generalized volume element is introduced. The symmetry arises naturally by considering a space-time connection containing a generic torsion tensor, and would otherwise be missed in the absence of torsion. When the transformation is applied to the Hilbert-Einstein action it is shown that by a choice of gauge all possible field theories arising from the Hilbert-Einstein action are equivalent to the standard theory of gravity described by general relativity.
The Modification of the Oppenheimer and Snyder Collapsing Dust Ball to a Static Ball in Discrete Space-time
G. Chen
Besides the singularity problem, the famous Oppenheimer and Snyder solution is discovered to be of deficiency in two aspects: the internal Friedmann space-time does not have the inherent symmetry and cannot connect to the external Schwarzschild space-time. So the process of gravitational collapse described by this solution is doubtful. The deficiency, together with the singularity problem, result from the imperfection of the field theory in continuous space-time, which is expressed by the infinite precision function theory. The space-time structure of the Oppenheimer and Snyder dust ball is founded to be discrete rather than continuous, and to describe the field theory in discrete space-time it requires a function theory with finite precision. Based on the i order real number and its equivalence class, which is defined in the real number field, the infinite precision function theory is extended to the finite precision function theory. The Einstein field equations are expressed in the form of finite precision, and then the collapsing dust ball solution in continuous space-time is modified to a static ball solution in discrete space-time. It solves all the problems of Oppenheimer and Snyder solution and shows that, with Planck length and Planck time as space-time quantum, a mechanism to resist the gravitational collapse could be obtained by the discretization of space-time.
Internal Space-time Symmetries of Particles derivable from Periodic Systems in Optics
Y. S. Kim
While modern optics is largely a physics of harmonic oscillators and two-by-two matrices, it is possible to learn about some hidden properties of the two-by-two matrix from optical systems. Since two-by-two matrices can be divided into three conjugate classes depending on their traces, optical systems force us to establish continuity from one class to another. It is noted that those three classes are equivalent to three different branches of Wigner's little groups dictating the internal space-time symmetries massive, massless, and imaginary-mass particles. It is shown that the periodic systems in optics can also be described by have the same class-based matrix algebra. The optical system allow us to make continuous, but not analytic, transitions from massiv to massless, and massless to imaginary-mass cases.
Error bounds for space-time discretizations of a 3D model for shape-memory materials
Stefanelli, Ulisse
Error bounds for space-time discretizations of a 3D model for shape-memory materials Alexander in shape- memory materials. After recalling existence and uniqueness results, a fully evolution of shape-memory alloys (SMAs). The latter are metallic alloys showing some surprising thermo
Neutrino Mixing and Discrete Symmetries
Hu, Bo
A model independent study of neutrino mixing based on a new method to derive mixing patterns is presented. An interesting result we find is that, in the case where unbroken residual symmetries of the Majorana neutrino and left-handed charged-lepton mass matrices obey some general assumptions, the complete set of possible mixing patterns can be determined by the solutions to the constraint equation with the help of algebraic number theory. This method can also be applied to more general cases beyond the minimal scenario. Several applications and phenomenological implications are discussed.
Quantization of Point Particles in 2+1 Dimensional Gravity and Space-Time Discreteness
G. 't Hooft
By investigating the canonical commutation rules for gravitating quantized particles in a 2+1 dimensional world it is found that these particles live on a space-time lattice. The space-time lattice points can be characterized by three integers. Various representations are possible, the details depending on the topology chosen for energy-momentum space. We find that an $S_2\\times S_1$ topology yields a physically most interesting lattice within which first quantization of Dirac particles is possible. An $S_3$ topology also gives a lattice, but does not allow first quantized particles.
Discrete Symmetry and Stability in Hamiltonian Dynamics
Tassos Bountis; George Chechin; Vladimir Sakhnenko
In this tutorial we address the existence and stability of periodic and quasiperiodic orbits in N degree of freedom Hamiltonian systems and their connection with discrete symmetries. Of primary importance in our study are the nonlinear normal modes (NNMs), i.e periodic solutions which represent continuations of the system's linear normal modes in the nonlinear regime. We examine the existence of such solutions and discuss different methods for constructing them and studying their stability under fixed and periodic boundary conditions. In the periodic case, we employ group theoretical concepts to identify a special type of NNMs called one-dimensional "bushes". We describe how to use linear combinations such NNMs to construct s(>1)-dimensional bushes of quasiperiodic orbits, for a wide variety of Hamiltonian systems and exploit the symmetries of the linearized equations to simplify the study of their destabilization. Applying this theory to the Fermi Pasta Ulam (FPU) chain, we review a number of interesting results, which have appeared in the recent literature. We then turn to an analytical and numerical construction of quasiperiodic orbits, which does not depend on the symmetries or boundary conditions. We demonstrate that the well-known "paradox" of FPU recurrences may be explained in terms of the exponential localization of the energies Eq of NNM's excited at the low part of the frequency spectrum, i.e. q=1,2,3,.... Thus, we show that the stability of these low-dimensional manifolds called q-tori is related to the persistence or FPU recurrences at low energies. Finally, we discuss a novel approach to the stability of orbits of conservative systems, the GALIk, k=2,...,2N, by means of which one can determine accurately and efficiently the destabilization of q-tori, leading to the breakdown of recurrences and the equipartition of energy, at high values of the total energy E.
On Discrete Symmetries and Torsion Homology in F-Theory
Christoph Mayrhofer; Eran Palti; Oskar Till; Timo Weigand
We study the relation between discrete gauge symmetries in F-theory compactifications and torsion homology on the associated Calabi-Yau manifold. Focusing on the simplest example of a $\\mathbb Z_2$ symmetry, we show that there are two physically distinct ways that such a discrete gauge symmetry can arise. First, compactifications of M-Theory on Calabi-Yau threefolds which support a genus-one fibration with a bi-section are known to be dual to six-dimensional F-theory vacua with a $\\mathbb Z_2$ gauge symmetry. We show that the resulting five-dimensional theories do not have a $\\mathbb Z_2$ symmetry but that the latter emerges only in the F-theory decompactification limit. Accordingly the genus-one fibred Calabi-Yau manifolds do not exhibit discrete torsion. Associated to the bi-section fibration is a Jacobian fibration which does support a section. Compactifying on these related but distinct varieties does lead to a $\\mathbb Z_2$ symmetry in five dimensions and, accordingly, we find explicitly an associated discrete torsion. We identify the expected particle and membrane system of the discrete symmetry in terms of wrapped M2 and M5 branes and present a field-theory description of the physics for both cases in terms of circle reductions of six-dimensional theories. Our results and methods generalise straightforwardly to larger discrete symmetries and to four-dimensional compactifications.
Weakly bound molecules trapped with discrete scaling symmetries
Yusuke Nishida; Dean Lee
When the scattering length is proportional to the distance from the center of the system, two particles are shown to be trapped about the center. Furthermore, their spectrum exhibits discrete scale invariance, whose scale factor is controlled by the slope of the scattering length. While this resembles the Efimov effect, our system has a number of advantages when realized with ultracold atoms. We also elucidate how the emergent discrete scaling symmetry is violated for more than two bosons, which may shed new light on Efimov physics. Our system thus serves as a tunable model system to investigate universal physics involving scale invariance, quantum anomaly, and renormalization group limit cycle, which are important in a broad range of quantum physics.
Breaking discrete symmetries in the effective field theory of inflation
Dario Cannone; Jinn-Ouk Gong; Gianmassimo Tasinato
We study the phenomenon of discrete symmetry breaking during the inflationary epoch, using a model-independent approach based on the effective field theory of inflation. We work in a context where both time reparameterization symmetry and spatial diffeomorphism invariance can be broken during inflation. We determine the leading derivative operators in the quadratic action for fluctuations that break parity and time-reversal. Within suitable approximations, we study their consequences for the dynamics of linearized fluctuations. Both in the scalar and tensor sectors, we show that such operators can lead to new direction-dependent phases for the modes involved. They do not affect the power spectra, but can have consequences for higher correlation functions. Moreover, a small quadrupole contribution to the sound speed can be generated.
Maia, M.D.
The concept of contact between manifolds is applied to space--times of general relativity. For a given background space--time a contact approximation of second order is defined and interpreted both from the point of view of a metric pertubation and of a higher order tangent manifold. In the first case, an application to the high frequency gravitational wave hypothesis is suggested. In the second case, a constant curvature tangent bundle is constructed and suggested as a means to define a ten parameter local space--time symmetry.
Non-Abelian discrete gauge symmetries in F-theory
Thomas W. Grimm; Tom G. Pugh; Diego Regalado
The presence of non-Abelian discrete gauge symmetries in four-dimensional F-theory compactifications is investigated. Such symmetries are shown to arise from seven-brane configurations in genuine F-theory settings without a weak string coupling description. Gauge fields on mutually non-local seven-branes are argued to gauge both R-R and NS-NS two-form bulk axions. The gauging is completed into a generalisation of the Heisenberg group with either additional seven-brane gauge fields or R-R bulk gauge fields. The former case relies on having seven-brane fluxes, while the latter case requires torsion cohomology and is analysed in detail through the M-theory dual. Remarkably, the M-theory reduction yields an Abelian theory that becomes non-Abelian when translated into the correct duality frame to perform the F-theory limit. The reduction shows that the gauge coupling function depends on the gauged scalars and transforms non-trivially as required for the groups encountered. This field dependence agrees with the expectations for the kinetic mixing of seven-branes and is unchanged if the gaugings are absent.
Non-Abelian discrete gauge symmetries in F-theory
Grimm, Thomas W; Regalado, Diego
The presence of non-Abelian discrete gauge symmetries in four-dimensional F-theory compactifications is investigated. Such symmetries are shown to arise from seven-brane configurations in genuine F-theory settings without a weak string coupling description. Gauge fields on mutually non-local seven-branes are argued to gauge both R-R and NS-NS two-form bulk axions. The gauging is completed into a generalisation of the Heisenberg group with either additional seven-brane gauge fields or R-R bulk gauge fields. The former case relies on having seven-brane fluxes, while the latter case requires torsion cohomology and is analysed in detail through the M-theory dual. Remarkably, the M-theory reduction yields an Abelian theory that becomes non-Abelian when translated into the correct duality frame to perform the F-theory limit. The reduction shows that the gauge coupling function depends on the gauged scalars and transforms non-trivially as required for the groups encountered. This field dependence agrees with the exp...
Discrete Symmetries (C,P,T) in Noncommutative Field Theories
M. M. Sheikh-Jabbari
In this paper we study the invariance of the noncmmutative gauge theories under C, P and T transformations. For the noncommutative space (when only the spatial part of $\\theta$ is non-zero) we show that NCQED is Parity invariant. In addition, we show that under charge conjugation the theory on noncommutative $R^4_{\\theta}$ is transformed to the theory on $R^4_{-\\theta}$, so NCQED is a CP violating theory. The theory remains invariant under time reversal if, together with proper changes in fields, we also change $\\theta$ by $-\\theta$. Hence altogether NCQED is CPT invariant. Moreover we show that the CPT invariance holds for general noncommutative space-time.
Lepton Mixing Predictions from (Generalised) CP and Discrete Flavour Symmetry
Thomas Neder
An important class of flavour groups, that are subgroups of $U(3)$ and that predict experimentally viable lepton mixing parameters including Majorana phases, is the $\\Delta(6n^2)$ series. The most well-known member is $\\Delta(24)=S_4$. I present results of several extensive studies of lepton mixing predictions obtained in models with a $\\Delta(6n^2)$ flavour group that preserve either the full residual $Z_2\\times Z_2$ or a $Z_2$ subgroup for neutrinos and can include a generalised CP symmetry. Predictions include mixing angles and Dirac CP phase generally; and if invariance under a generalised CP symmetry is included, also Majorana phases. For this, the interplay of flavour group and generalised CP symmetry has to be studied carefully.
Fermions in odd space-time dimensions: back to basics
Bashir, A; Galicia, Ma. de Jesus Anguiano
It is a well known feature of odd space-time dimensions $d$ that there exist two inequivalent fundamental representations $A$ and $B$ of the Dirac gamma matrices. Moreover, the parity transformation swaps the fermion fields living in $A$ and $B$. As a consequence, a parity invariant Lagrangian can only be constructed by incorporating both the representations. Based upon these ideas and contrary to long held belief, we show that in addition to a discrete exchange symmetry for the massless case, we can also define chiral symmetry provided the Lagrangian contains fields corresponding to both the inequivalent representations. We also study the transformation properties of the corresponding chiral currents under parity and charge conjugation operations. We work explicitly in 2+1 dimensions and later show how some of these ideas generalize to an arbitrary number of odd dimensions.
Fermions in odd space-time dimensions: back to basics
A. Bashir; Ma. de Jesus Anguiano Galicia
It is a well known feature of odd space-time dimensions $d$ that there exist two inequivalent fundamental representations $A$ and $B$ of the Dirac gamma matrices. Moreover, the parity transformation swaps the fermion fields living in $A$ and $B$. As a consequence, a parity invariant Lagrangian can only be constructed by incorporating both the representations. Based upon these ideas and contrary to long held belief, we show that in addition to a discrete exchange symmetry for the massless case, we can also define chiral symmetry provided the Lagrangian contains fields corresponding to both the inequivalent representations. We also study the transformation properties of the corresponding chiral currents under parity and charge conjugation operations. We work explicitly in 2+1 dimensions and later show how some of these ideas generalize to an arbitrary number of odd dimensions.
Metastring Theory and Modular Space-time
Laurent Freidel; Robert G. Leigh; Djordje Minic
String theory is canonically accompanied with a space-time interpretation which determines S-matrix-like observables, and connects to the standard physics at low energies in the guise of local effective field theory. Recently, we have introduced a reformulation of string theory which does not rely on an {\\it a priori} space-time interpretation or a pre-assumption of locality. This \\hlt{metastring theory} is formulated in such a way that stringy symmetries (such as T-duality) are realized linearly. In this paper, we study metastring theory on a flat background and develop a variety of technical and interpretational ideas. These include a formulation of the moduli space of Lorentzian worldsheets, a careful study of the symplectic structure and consequently consistent closed and open boundary conditions, and the string spectrum and operator algebra. What emerges from these studies is a new quantum notion of space-time that we refer to as a quantum Lagrangian or equivalently a \\hlt{modular space-time}. This concept embodies the standard tenets of quantum theory and implements in a precise way a notion of {relative locality}. The usual string backgrounds (non-compact space-time along with some toroidally compactified spatial directions) are obtained from modular space-time by a limiting procedure that can be thought of as a correspondence limit.
Space-time attributes of physical objects and the laws of space-time physics
J. H. Field
Physical time intervals are attributes of single physical object whereas physical space intervals are a relational attribute of two physical objects. Some consequences of the breaking of the space-time exchange symmetry inherent in the Lorentz transformation following from the above distinction are investigated. In particular, it is shown that the relativity of simultaneity and length contraction effects which naively follow from space-time symmetry of the Lorentz transformation do not occur. Seven laws describing the relation between observations of space intervals, time intervals and velocities in different reference frames are given. Only two of these laws are respected by conventional special relativity theory.
On the vacuum Einstein equations along curves with a discrete local rotational and reflection symmetry
Korzy?ski, Miko?aj; Bentivegna, Eloisa
We discuss the possibility of a dimensional reduction of the Einstein equations in S3 black-hole lattices. It was reported in previous literature that the evolution of spaces containing curves of local, discrete rotational and reflection Symmetry (LDRRS) can be carried out via a system of ODEs along these curves. However, 3+1 Numerical Relativity computations demonstrate that this is not the case, and we show analytically that this is due to the presence of a tensorial quantity which is not suppressed by the symmetry. We calculate the term analytically, and verify numerically for an 8-black-hole lattice that it fully accounts for the anomalous results, and thus quantify its magnitude in this specific case. The presence of this term prevents the exact evolution of these spaces via previously-reported methods which do not involve a full 3+1 integration of Einstein's equation.
A Vector-Like Fourth Generation with A Discrete Symmetry From Split-UED
Kong, Kyoungchul; /SLAC; Park, Seong Chan; /Tokyo U., IPMU; Rizzo, Thomas G.; /SLAC
Split-UED allows for the possibility that the lowest lying KK excitations of the Standard Model fermions can be much lighter than the corresponding gauge or Higgs KK states. This can happen provided the fermion bulk masses are chosen to be large, in units of the inverse compactification radius, 1/R, and negative. In this setup, all of the other KK states would be effectively decoupled from low energy physics. Such a scenario would then lead to an apparent vector-like fourth generation with an associated discrete symmetry that allows us to accommodate a dark matter candidate. In this paper the rather unique phenomenology presented by this picture will be examined.
Metastring Theory and Modular Space-time
Freidel, Laurent; Minic, Djordje
String theory is canonically accompanied with a space-time interpretation which determines S-matrix-like observables, and connects to the standard physics at low energies in the guise of local effective field theory. Recently, we have introduced a reformulation of string theory which does not rely on an {\\it a priori} space-time interpretation or a pre-assumption of locality. This \\hlt{metastring theory} is formulated in such a way that stringy symmetries (such as T-duality) are realized linearly. In this paper, we study metastring theory on a flat background and develop a variety of technical and interpretational ideas. These include a formulation of the moduli space of Lorentzian worldsheets, a careful study of the symplectic structure and consequently consistent closed and open boundary conditions, and the string spectrum and operator algebra. What emerges from these studies is a new quantum notion of space-time that we refer to as a quantum Lagrangian or equivalently a \\hlt{modular space-time}. This conce...
Introduction Space Time Codes Space Time Coding with Feedback New Thoughts Summary Space-Time Coding for Multi-Antenna
Veeravalli, Venugopal
Introduction Space Time Codes Space Time Coding with Feedback New Thoughts Summary Space 2007 #12;Introduction Space Time Codes Space Time Coding with Feedback New Thoughts Summary MIMO: Diversity vs Multiplexing Multiplexing Diversity Pictures taken from lectures notes on Space Time Coding
Haesen, S; Haesen, Stefan; Verstraelen, Leopold
Due to the growing interest in embeddings of space-time in higher-dimensional spaces we consider a specific type of embedding. After proving an inequality between intrinsically defined curvature invariants and the squared mean curvature, we extend the notion of ideal embeddings from Riemannian geometry to the indefinite case. Ideal embeddings are such that the embedded manifold receives the least amount of tension from the surrounding space. Then it is shown that the de Sitter spaces, a Robertson-Walker space-time and some anisotropic perfect fluid metrics can be ideally embedded in a five-dimensional pseudo-Euclidean space.
Stefan Haesen; Leopold Verstraelen
Due to the growing interest in embeddings of space-time in higher-dimensional spaces we consider a specific type of embedding. After proving an inequality between intrinsically defined curvature invariants and the squared mean curvature, we extend the notion of ideal embeddings from Riemannian geometry to the indefinite case. Ideal embeddings are such that the embedded manifold receives the least amount of tension from the surrounding space. Then it is shown that the de Sitter spaces, a Robertson-Walker space-time and some anisotropic perfect fluid metrics can be ideally embedded in a five-dimensional pseudo-Euclidean space.
Space-Time Galerkin Projection of Electro-Magnetic Fields
Wang, Zifu; Hofmann, Heath
Spatial Galerkin projection transfers fields between different meshes. In the area of finite element analysis of electromagnetic fields, it provides great convenience for remeshing, multi-physics, domain decomposition methods, etc. In this paper, a space-time Galerkin projection is developed in order to transfer fields between different spatial and temporal discretization bases.
Noncommutative space-time models
N. A. Gromov; V. V. Kuratov
The FRT quantum Euclidean spaces $O_q^N$ are formulated in terms of Cartesian generators. The quantum analogs of N-dimensional Cayley-Klein spaces are obtained by contractions and analytical continuations. Noncommutative constant curvature spaces are introduced as a spheres in the quantum Cayley-Klein spaces. For N=5 part of them are interpreted as the noncommutative analogs of (1+3) space-time models. As a result the quantum (anti) de Sitter, Newton, Galilei kinematics with the fundamental length and the fundamental time are suggested.
Discrete canonical analysis of three dimensional gravity with cosmological constant
J. Berra-Montiel; J. E. Rosales-Quintero
We discuss the interplay between standard canonical analysis and canonical discretization in three-dimensional gravity with cosmological constant. By using the Hamiltonian analysis, we find that the continuum local symmetries of the theory are given by the on-shell space-time diffeomorphisms, which at the action level, corresponds to the Kalb-Ramond transformations. At the time of discretization, although this symmetry is explicitly broken, we prove that the theory still preserves certain gauge freedom generated by a constant curvature relation in terms of holonomies and the Gauss's law in the lattice approach.
Space-time Curvature of Classical Electromagnetism
R. W. M. Woodside
The space-time curvature carried by electromagnetic fields is discovered and a new unification of geometry and electromagnetism is found. Curvature is invariant under charge reversal symmetry. Electromagnetic field equations are examined with De Rham co homology theory. Radiative electromagnetic fields must be exact and co exact to preclude unobserved massless topological charges. Weyl's conformal tensor, here called ``the gravitational field'', is decomposed into a divergence-free non-local piece with support everywhere and a local piece with the same support as the matter. By tuning a local gravitational field to a Maxwell field the electromagnetic field's local gravitational field is discovered. This gravitational field carries the electromagnetic field's polarization or phase information, unlike Maxwell's stress-energy tensor. The unification assumes Einstein's equations and derives Maxwell's equations from curvature assumptions. Gravity forbids magnetic monopoles! This unification is stronger than the Einstein-Maxwell equations alone, as those equations must produce the electromagnetic field's local gravitational field and not just any conformal tensor. Charged black holes are examples. Curvature of radiative null electromagnetic fields is characterized.
Quantum Field Theory on Noncommutative Space-Times and the Persistence of Ultraviolet Divergences
M. Chaichian; A. Demichev; P. Presnajder
We study properties of a scalar quantum field theory on two-dimensional noncommutative space-times. Contrary to the common belief that noncommutativity of space-time would be a key to remove the ultraviolet divergences, we show that field theories on a noncommutative plane with the most natural Heisenberg-like commutation relations among coordinates or even on a noncommutative quantum plane with $E_q(2)$-symmetry have ultraviolet divergences, while the theory on a noncommutative cylinder is ultraviolet finite. Thus, ultraviolet behaviour of a field theory on noncommutative spaces is sensitive to the topology of the space-time, namely to its compactness. We present general arguments for the case of higher space-time dimensions and as well discuss the symmetry transformations of physical states on noncommutative space-times.
Ning Wu
When we discuss problems on gravity, we can not avoid some fundamental physical problems, such as space-time, inertia, and inertial reference frame. The goal of this paper is to discuss the logic system of gravity theory and the problems of space-time, inertia, and inertial reference frame. The goal of this paper is to set up the theory on space-time in gauge theory of gravity. Based on this theory, it is possible for human kind to manipulate physical space-time on earth, and produce a machine which can physically prolong human's lifetime.
Convergence of Space-Time Discrete Dynamics to Anisotropic ...
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Pseudo-Z symmetric space-times
Mantica, Carlo Alberto, E-mail: firstname.lastname@example.com [Physics Department, Universit� degli Studi di Milano, Via Celoria 16, 20133 Milano (Italy); Suh, Young Jin, E-mail: firstname.lastname@example.com [Department of Mathematics, Kyungpook National University, Taegu 702-701 (Korea, Republic of)
In this paper, we investigate Pseudo-Z symmetric space-time manifolds. First, we deal with elementary properties showing that the associated form A{sub k} is closed: in the case the Ricci tensor results to be Weyl compatible. This notion was recently introduced by one of the present authors. The consequences of the Weyl compatibility on the magnetic part of the Weyl tensor are pointed out. This determines the Petrov types of such space times. Finally, we investigate some interesting properties of (PZS){sub 4} space-time; in particular, we take into consideration perfect fluid and scalar field space-time, and interesting properties are pointed out, including the Petrov classification. In the case of scalar field space-time, it is shown that the scalar field satisfies a generalized eikonal equation. Further, it is shown that the integral curves of the gradient field are geodesics. A classical method to find a general integral is presented.
Space-time defects and teleparallelism
J. W. Maluf; A. Goya
We consider the class of space-time defects investigated by Puntigam and Soleng. These defects describe space-time dislocations and disclinations (cosmic strings), and are in close correspondence to the actual defects that arise in crystals and metals. It is known that in such materials dislocations and disclinations require a small and large amount of energy, respectively, to be created. The present analysis is carried out in the context of the teleparallel equivalent of general relativity (TEGR). We evaluate the gravitational energy of these space-time defects in the framework of the TEGR and find that there is an analogy between defects in space-time and in continuum material systems: the total gravitational energy of space-time dislocations and disclinations (considered as idealized defects) is zero and infinit, respectively.
Discrete Symmetries on the Light Front and a General Relation Connecting Nucleon Electric Dipole and Anomalous Magnetic Moments
Brodsky, S J; Hwang, D S
We consider the electric dipole form factor, F_3(q^2), as well as the Dirac and Pauli form factors, F_1(q^2) and F_2(q^2), of the nucleon in the light-front formalism. We derive an exact formula for F_3(q^2) to complement those known for F_1(q^2) and F_2(q^2). We derive the light-front representation of the discrete symmetry transformations and show that time-reversal- and parity-odd effects are captured by phases in the light-front wave functions. We thus determine that the contributions to F_2(q^2) and F_3(q^2), Fock-state by Fock-state, are related, independent of the fundamental mechanism through which CP violation is generated. Our relation is not specific to the nucleon, but, rather, is true of spin-1/2 systems in general, be they lepton or baryon. The empirical values of the anomalous magnetic moments, in concert with empirical bounds on the associated electric dipole moments, can better constrain theories of CP violation. In particular, we find that the neutron and proton electric dipole moments echo ...
Discrete Symmetries on the Light Front and a General Relation connecting Nucleon Electric Dipole and Anomalous Magnetic Moments
Brodsky, Stanley J.; /SLAC; Gardner, Susan; /Kentucky U.; Hwang, Dae Sung; /Sejong U.
We consider the electric dipole form factor, F{sub 3}(q{sup 2}), as well as the Dirac and Pauli form factors, F{sub 1}(q{sup 2}) and F{sub 2}(q{sup 2}), of the nucleon in the light-front formalism. We derive an exact formula for F{sub 3}(q{sup 2}) to complement those known for F{sub 1}(q{sup 2}) and F{sub 2}(q{sup 2}). We derive the light-front representation of the discrete symmetry transformations and show that time-reversal- and parity-odd effects are captured by phases in the light-front wave functions. We thus determine that the contributions to F{sub 2}(q{sup 2}) and F{sub 3}(q{sup 2}), Fock-state by Fock-state, are related, independent of the fundamental mechanism through which CP violation is generated. Our relation is not specific to the nucleon, but, rather, is true of spin-1/2 systems in general, be they lepton or baryon. The empirical values of the anomalous magnetic moments, in concert with empirical bounds on the associated electric dipole moments, can better constrain theories of CP violation. In particular, we find that the neutron and proton electric dipole moments echo the isospin structure of the anomalous magnetic moments, {kappa}{sup n} {approx} -{kappa}{sup p}.
Discrete symmetries on the light front and a general relation connecting the nucleon electric dipole and anomalous magnetic moments
Brodsky, Stanley J. [Stanford Linear Accelerator Center, Stanford University, Stanford, California 94309 (United States); Gardner, Susan [Department of Physics and Astronomy, University of Kentucky, Lexington, Kentucky 40506-0055 (United States); Hwang, Dae Sung [Department of Physics, Sejong University, Seoul 143-747 (Korea, Republic of)
We consider the electric dipole form factor, F{sub 3}(q{sup 2}), as well as the Dirac and Pauli form factors, F{sub 1}(q{sup 2}) and F{sub 2}(q{sup 2}), of the nucleon in the light-front formalism. We derive an exact formula for F{sub 3}(q{sup 2}) to complement those known for F{sub 1}(q{sup 2}) and F{sub 2}(q{sup 2}). We derive the light-front representation of the discrete symmetry transformations and show that time-reversal- and parity-odd effects are captured by phases in the light-front wave functions. We thus determine that the contributions to F{sub 2}(q{sup 2}) and F{sub 3}(q{sup 2}), Fock state by Fock state, are related, independent of the fundamental mechanism through which CP violation is generated. Our relation is not specific to the nucleon, but, rather, is true of spin-1/2 systems in general, be they lepton or baryon. The empirical values of the anomalous magnetic moments, in concert with empirical bounds on the associated electric dipole moments, can better constrain theories of CP violation. In particular, we find that the neutron and proton electric dipole moments echo the isospin structure of the anomalous magnetic moments, {kappa}{sup n}{approx}-{kappa}{sup p}.
Discrete Symmetries on the Light Front and a General Relation Connecting Nucleon Electric Dipole and Anomalous Magnetic Moments
S. J. Brodsky; S. Gardner; D. S. Hwang
We consider the electric dipole form factor, F_3(q^2), as well as the Dirac and Pauli form factors, F_1(q^2) and F_2(q^2), of the nucleon in the light-front formalism. We derive an exact formula for F_3(q^2) to complement those known for F_1(q^2) and F_2(q^2). We derive the light-front representation of the discrete symmetry transformations and show that time-reversal- and parity-odd effects are captured by phases in the light-front wave functions. We thus determine that the contributions to F_2(q^2) and F_3(q^2), Fock state by Fock state, are related, independent of the fundamental mechanism through which CP violation is generated. Our relation is not specific to the nucleon, but, rather, is true of spin-1/2 systems in general, be they lepton or baryon. The empirical values of the anomalous magnetic moments, in concert with empirical bounds on the associated electric dipole moments, can better constrain theories of CP violation. In particular, we find that the neutron and proton electric dipole moments echo the isospin structure of the anomalous magnetic moments, kappa^n ~ - kappa^p.
Boris Doubrov; Jonathan Holland; George Sparling
A Weyl structure is a bundle over space-time, whose fiber at each space-time point is a space of maximally isotropic complex tangent planes. We develop the theory of Weyl connections for Weyl structures and show that the requirement that the connection be torsion-free fixes the Weyl connection uniquely. Further we show that to each such Weyl connection, there is naturally associated a (2, 3, 5)-Pfaffian system, as first analyzed by Cartan. We determine the associated G_2-conformal structure and calculate it explicitly in the cases of the Kapadia family of space-times and of the Schwarzschild solution
Space-time singularities and the axion in the Poincare coset models ISO(2,1)/H
Roberto Casadio; Benjamin Harms
By promoting an invariant subgroup $H$ of $ISO(2,1)$ to a gauge symmetry of a WZWN action, we obtain the description of a bosonic string moving either in a curved 4-dimensional space--time with an axion field and curvature singularities or in 3-dimensional Minkowski space--time.
Relativity of Space-Time Geometry
L. V. Verozub
We argue that space-time geometry is not absolute with respect to the frame of reference being used. The space-time metric differential form $ds$ in noninertial frames of reference (NIFR) is caused by the properties of the used frames in accordance with the Berkley - Leibnitz - Mach - Poincar\\'{e} ideas about relativity of space and time . It is shown that the Sagnac effect and the existence of inertial forces in NIFR can be considered from this point of view. An experimental test is proposed.
'AdS_5' Geometry Beyond Space-time and 4D Noncommutative Space-time
Otto C. W. Kong
We discuss a 4D noncommutative space-time as suggested by the version of quantum (deformed) relativity which provides a classical geometry picture as an `AdS_5'. The 4D noncommutative space-time is more like a part of a phase space description, in accordance with the quantum notion -- quantum mechanics talks about only states but not configurations. The `AdS_5' picture also illustrates the classical 4D space-time is to be described as part of a bigger geometry beyond space-time at the quantum level. The radically new picture of quantum 'space-time' is expected to provide the basis for a (still to be formulated) new approach to quantum gravity with fundamental constants (quantum) hbar and Newton's constant G put at a similar level as c, the speed of light.
Y. M. Cho
We present a topological classification of vacuum space-time. Assuming the 3-dimensional space allows a global chart, we show that the static vacuum space-time of Einstein's theory can be classified by the knot topology $\\pi_3(S^3)=\\pi_3(S^2)$. Viewing Einstein's theory as a gauge theory of Lorentz group and identifying the gravitational connection as the gauge potential of Lorentz group, we construct all possible vacuum gravitational connections which give a vanishing curvature tensor. With this we show that the vacuum connection has the knot topology, the same topology which describes the multiple vacua of SU(2) gauge theory. We discuss the physical implications of our result in quantum gravity.
Generalised hyperbolicity in singular space-times
C J S Clarke
A new concept analogous to global hyperbolicity is introduced, based on test fields. It is shown that the space-times termed here ``curve integrable'' are globally hyperbolic in this new sense, and a plausibility argument is given suggesting that the result applies to shell crossing singularities. If the assumptions behind this last argument are valid, this provides an alternative route to the assertion that such singularities do not violate cosmic censorship.
Quantum Space-Time and Noncommutative Gauge Field Theories
Sami Saxell
The three original publications in this thesis encompass various aspects in the still developing area of noncommutative quantum field theory, ranging from fundamental concepts to model building. One of the key features of noncommutative space-time is the apparent loss of Lorentz invariance that has been addressed in different ways in the literature. One recently developed approach is to eliminate the Lorentz violating effects by integrating over the parameter of noncommutativity. Fundamental properties of such theories are investigated in this thesis. Another issue addressed is model building, which is difficult in the noncommutative setting due to severe restrictions on the possible gauge symmetries imposed by the noncommutativity of the space-time. Possible ways to relieve these restrictions are investigated and applied and a noncommutative version of the Minimal Supersymmetric Standard Model is presented. While putting the results obtained in the three original publications into their proper context, the introductory part of this thesis aims to provide an overview of the present situation in the field.
Holographic Space-time and Newton's Law
Tom Banks; Willy Fischler
We derive Newton's Law from the formalism of Holographic Space-Time (HST). More precisely, we show that for a large class of Hamiltonians of the type proposed previously for the HST description of a geodesic in Minkowski space, the eikonal for scattering of two massless particles at large impact parameter scales as expected with the impact parameter and the energies of the particles in the center of mass (CM) frame. We also discuss the criteria for black hole production in this collision, and find an estimate, purely within the HST framework, for the impact parameter at which it sets in, which coincides with the estimate based on general relativity.
Universal space-time codes from demultiplexed trellis codes
Kose, Cenk; Wesel, R D
and A. R. Calderbank, �Space-time codes for high data ratePerformance criteria and code construction,� IEEE Trans.of space�time trellis codes,� IEEE Trans. Commun. , vol. 51,
Spinorial space-time and privileged space direction (I)
Paris-Sud XI, Universit� de
Spinorial space-time and privileged space direction (I) Luis Gonzalez-Mestres Abstract Contrary of a privileged space direction are not strange phenomena from the point of view of fundamental space-time geometry. As already emphasized in our previous papers on the subject, the spinorial space-time we
On Space-Time Singularities, Holes, and Extensions
Manchak, John
On Space-Time Singularities, Holes, and Extensions John Byron Manchak*y Here, we clarify the relationship among three space-time conditions of interest: geodesic completeness, hole. In what follows, we consider three space-time conditions of interest: geodesic completeness, hole
A Survey on Space-Time Turbo Codes
Seshaiah, C V
As wireless communication systems look intently to compose the transition from voice communication to interactive Internet data, achieving higher bit rates becomes both increasingly desirable and challenging. Space-time coding (STC) is a communications technique for wireless systems that inhabit multiple transmit antennas and single or multiple receive antennas. Space-time codes make use of advantage of both the spatial diversity provided by multiple antennas and the temporal diversity available with time-varying fading. Space-time codes can be divided into block codes and trellis codes. Space-time trellis coding merges signal processing at the receiver with coding techniques appropriate to multiple transmit antennas. The advantages of space-time codes (STC) make it extremely remarkable for high-rate wireless applications. Initial STC research efforts focused on narrowband flat-fading channels. The decoding complexity of Space-time turbo codes STTC increases exponentially as a function of the diversity level ...
Space-Time as an Orderparameter Manifold in Random Networks and the Emergence of Physical Points
Manfred Requardt
In the following we are going to describe how macroscopic space-time is supposed to emerge as an orderparameter manifold or superstructure floating in a stochastic discrete network structure. As in preceeding work (mentioned below), our analysis is based on the working philosophy that both physics and the corresponding mathematics have to be genuinely discrete on the primordial (Planck scale) level. This strategy is concretely implemented in the form of cellular networks and random graphs. One of our main themes is the development of the concept of physical (proto)points as densely entangled subcomplexes of the network and their respective web, establishing something like (proto)causality. It max perhaps be said that certain parts of our programme are realisations of some old and qualitative ideas of Menger and more recent ones sketched by Smolin a couple of years ago. We briefly indicate how this two-story-concept of space-time can be used to encode the (at least in our view) existing non-local aspects of quantum theory without violating macroscopic space-time causality!
(Quantum) Space-Time as a Statistical Geometry of Lumps in Random Networks
Manfred Requardt
In the following we undertake to describe how macroscopic space-time (or rather, a microscopic protoform of it) is supposed to emerge as a superstructure of a web of lumps in a stochastic discrete network structure. As in preceding work (mentioned below), our analysis is based on the working philosophy that both physics and the corresponding mathematics have to be genuinely discrete on the primordial (Planck scale) level. This strategy is concretely implemented in the form of \\tit{cellular networks} and \\tit{random graphs}. One of our main themes is the development of the concept of \\tit{physical (proto)points} or \\tit{lumps} as densely entangled subcomplexes of the network and their respective web, establishing something like \\tit{(proto)causality}. It may perhaps be said that certain parts of our programme are realisations of some early ideas of Menger and more recent ones sketched by Smolin a couple of years ago. We briefly indicate how this \\tit{two-story-concept} of \\tit{quantum} space-time can be used to encode the (at least in our view) existing non-local aspects of quantum theory without violating macroscopic space-time causality.
BLIND RECOGNITION OF LINEAR SPACE TIME BLOCK CODES Vincent Choqueuse
Paris-Sud XI, Universit� de
BLIND RECOGNITION OF LINEAR SPACE TIME BLOCK CODES Vincent Choqueuse E3 I2 , EA 3876, ENSIETA 2 6165, UBO 6, avenue le Gorgeu, 29200 Brest Cedex 3 FRANCE ABSTRACT The blind recognition. In this paper, we investigate the problem of the blind recognition of Linear Space-Time Block Codes (STBC
Hierarchical Bayesian models for space-time air pollution data
Sahu, Sujit K
Hierarchical Bayesian models for space-time air pollution data Sujit K. Sahu June 14, 2011 sets have led to a step change in the analysis of space-time air pollution data. Accurate predictions-time air pollution data and illustrate the benefits of modeling with a real data example on monitoring
Turbo Space-Time Codes with Time Varying Linear Transformations
Haimovich, Alexander
1 Turbo Space-Time Codes with Time Varying Linear Transformations Hangjun Chen and Alexander 07102 Email: {hangjun.chen; email@example.com Abstract Turbo space-time codes with symbols in this paper. It is shown that turbo codes with TVLT achieve full diversity gain and do not require exhaustive
Wick rotation for quantum field theories on degenerate Moyal space(-time)
Grosse, Harald; Lechner, Gandalf [Department of Physics, University of Vienna, 1090 Vienna (Austria)] [Department of Physics, University of Vienna, 1090 Vienna (Austria); Ludwig, Thomas [Max-Planck-Institute for Mathematics in the Sciences, 04103 Leipzig (Germany) [Max-Planck-Institute for Mathematics in the Sciences, 04103 Leipzig (Germany); Institute for Theoretical Physics, University of Leipzig, 04009 Leipzig (Germany); Verch, Rainer [Institute for Theoretical Physics, University of Leipzig, 04009 Leipzig (Germany)] [Institute for Theoretical Physics, University of Leipzig, 04009 Leipzig (Germany)
In this paper the connection between quantum field theories on flat noncommutative space(-times) in Euclidean and Lorentzian signature is studied for the case that time is still commutative. By making use of the algebraic framework of quantum field theory and an analytic continuation of the symmetry groups which are compatible with the structure of Moyal space, a general correspondence between field theories on Euclidean space satisfying a time zero condition and quantum field theories on Moyal Minkowski space is presented ('Wick rotation'). It is then shown that field theories transferred to Moyal space(-time) by Rieffel deformation and warped convolution fit into this framework, and that the processes of Wick rotation and deformation commute.
Maximally Symmetric Minimal Unification Model SO(32) with Three Families in Ten Dimensional Space-time
Yue-Liang Wu
Based on a maximally symmetric minimal unification hypothesis and a quantum charge-dimension correspondence principle, it is demonstrated that each family of quarks and leptons belongs to the Majorana-Weyl spinor representation of 14-dimensions that relate to quantum spin-isospin-color charges. Families of quarks and leptons attribute to a spinor structure of extra 6-dimensions that relate to quantum family charges. Of particular, it is shown that 10-dimensions relating to quantum spin-family charges form a motional 10-dimensional quantum space-time with a generalized Lorentz symmetry SO(1,9), and 10-dimensions relating to quantum isospin-color charges become a motionless 10-dimensional quantum intrinsic space. Its corresponding 32-component fermions in the spinor representation possess a maximal gauge symmetry SO(32). As a consequence, a maximally symmetric minimal unification model SO(32) containing three families in ten dimensional quantum space-time is naturally obtained by choosing a suitable Majorana-Weyl spinor structure into which quarks and leptons are directly embedded. Both resulting symmetry and dimensions coincide with the ones of type I string and heterotic string SO(32) in string theory.
Space-Time Noncommutative Field Theories And Unitarity
Jaume Gomis; Thomas Mehen
We study the perturbative unitarity of noncommutative scalar field theories. Field theories with space-time noncommutativity do not have a unitary S-matrix. Field theories with only space noncommutativity are perturbatively unitary. This can be understood from string theory, since space noncommutative field theories describe a low energy limit of string theory in a background magnetic field. On the other hand, there is no regime in which space-time noncommutative field theory is an appropriate description of string theory. Whenever space-time noncommutative field theory becomes relevant massive open string states cannot be neglected.
Space--time fluctuations and the spreading of wavepackets
E. G�kl�; C. L�mmerzahl; A. Camacho; A. Macias
Using a density matrix description in space we study the evolution of wavepackets in a fluctuating space-time background. We assume that space-time fluctuations manifest as classical fluctuations of the metric. From the non-relativistic limit of a non-minimally coupled Klein-Gordon equation we derive a Schr\\"odinger equation with an additive gaussian random potential. This is transformed into an effective master equation for the density matrix. The solutions of this master equation allow to study the dynamics of wavepackets in a fluctuating space-time, depending on the fluctuation scenario. We show how different scenarios alter the diffusion properties of wavepackets.
Electrodynamics on {kappa}-Minkowski space-time
Harikumar, E.; Juric, T.; Meljanac, S. [School of Physics, University of Hyderabad, Central University P O, Hyderabad, AP, PIN 500046 (India); Rudjer Boskovic Institute, Bijenicka c.54, HR-10002 Zagreb (Croatia)
In this paper, we derive Lorentz force and Maxwell's equations on kappa-Minkowski space-time up to the first order in the deformation parameter. This is done by elevating the principle of minimal coupling to noncommutative space-time. We also show the equivalence of minimal coupling prescription and Feynman's approach. It is shown that the motion in kappa space-time can be interpreted as motion in a background gravitational field, which is induced by this noncommutativity. In the static limit, the effect of kappa deformation is to scale the electric charge. We also show that the laws of electrodynamics depend on the mass of the charged particle, in kappa space-time.
New orthogonal space-time block codes with full diversity�
Dalton, Lori Anne
It has been shown from the Hurwitz-Radon theorem that square complex orthogonal space-time code designs cannot achieve full diversity and full rate simul-taneously, except in the two transmit antenna case. However, this ...
Distributed Space-Time Cooperative Schemes for Underwater Acoustic Communications
Stojanovic, Milica
Distributed Space-Time Cooperative Schemes for Underwater Acoustic Communications Madhavan, which is a main characteristic of underwater acoustic channels. A time-reversal distributed space in oceanic research, such as [3] [4]: data collec- tion, pollution monitoring, tactical surveillance
Spinorial space-time and Friedmann-like equations (I)
to the space-time structure felt locally by standard matter at low energy [3]. At the stage considered firstname.lastname@example.com at the Cosmology Laboratory, Megatrend University, Belgrade (Serbia) and Paris (France) ; Luis
Horizons in Robinson-Trautman space-times
W. Natorf; J. Tafel
The past quasi-local horizons in vacuum Robinson-Trautman spacetimes are described. The case of a null (non-expanding) horizon is discussed. It is shown that the only Robinson-Trautman space-time admitting such a horizon with sections diffeomorphic to S_2 is the Schwarzschild space-time. Weakening this condition leads to the horizons of the C-metric. Properties of the hypersurface r=2m for finite retarded time u are examined.
Quantum Field Theory of Gravity with Spinnic $\\&$ Scaling Gauge Invariance and Space-time Dynamics with Quantum Inflation
Wu, Yue-Liang
Treating the gravitational force on the same footing as the electroweak and strong forces, we present a quantum field theory (QFT) of gravity based on spinnic and scaling gauge symmetries. The so-called Gravifield sided on both locally flat non-coordinate space-time and globally flat Minkowski space-time is an essential ingredient for gauging global spinnic and scaling symmetries. The locally flat Gravifield space-time spanned by the Gravifield is associated with a non-commutative geometry characterized by a gauge-type field strength of Gravifield. A gauge invariant and coordinate independent action for the quantum gravity is built in the Gravifield basis, we derive equations of motion for all quantum fields with including the gravitational effect and obtain basic conservation laws for all symmetries. The equation of motion for Gravifield tensor is deduced in connection directly with the energy-momentum tensor. When the spinnic and scaling gauge symmetries are broken down to a background structure that posses...
Fractal Relativity, Generalized Noether Theorem and New Research of Space-Time
Yi-Fang Chang
First, let the fractal dimension D=n(integer)+d(decimal), so the fractal dimensional matrix was represented by a usual matrix adds a special decimal row (column). We researched that mathematics, for example, the fractal dimensional linear algebra, and physics may be developed to fractal and the complex dimension extended from fractal. From this the fractal relativity is discussed, which connects with self-similarity Universe and the extensive quantum theory. The space dimension has been extended from real number to superreal and complex number. Combining the quaternion, etc., the high dimensional time is introduced. Such the vector and irreversibility of time are derived. Then the fractal dimensional time is obtained, and space and time possess completely symmetry. It may be constructed preliminarily that the higher dimensional, fractal, complex and supercomplex space-time theory covers all. We propose a generalized Noether theorem, and irreversibility of time should correspond to non-conservation of a certain quantity. Resumed reversibility of time and possible decrease of entropy are discussed. Finally, we obtain the quantitative relations between energy-mass and space-time, which is consistent with the space-time uncertainty relation in string theory.
False vacuum decay in de Sitter space-time
V. A. Rubakov; S. M. Sibiryakov
We suggest a technique that explicitly accounts for the structure of an initial state of quantum field in the semiclassical calculations of path integral in curved space-time, and consider decay of metastable state (conformal vacuum of scalar particles above false classical vacuum) in background de Sitter space-time as an example. Making use of this technique, we justify the Coleman-De Luccia approach to the calculation of the decay probability. We propose an interpretation of the Hawking-Moss instanton as a limiting case of constrained instantons. We find that an inverse process of the transition from true vacuum to false one is allowed in de Sitter space-time, and calculate the corresponding probability.
Galactic space-times in modified theories of gravity
Dipanjan Dey; Kaushik Bhattacharya; Tapobrata Sarkar
We study Bertrand space-times (BSTs), which have been proposed as viable models of space-times seeded by galactic dark matter, in modified theories of gravity. We first critically examine the issue of galactic rotation curves in General Relativity, and establish the usefulness of BSTs to fit experimental data in this context. We then study BSTs in metric $f(R)$ gravity and in Brans-Dicke theories. For the former, the nature of the Newtonian potential is established, and we also compute the effective equation of state and show that it can provide good fits to some recent experimental results. For the latter, we calculate the Brans-Dicke scalar analytically in some limits and numerically in general, and find interesting constraints on the parameters of the theory. Our results provide evidence for the physical nature of Bertrand space-times in modified theories of gravity.
Global geometry of space-time with the charged shell
V. A. Berezin; V. I. Dokuchaev
It is elaborated the complete classification of the possible types of the spherically symmetric global geometries for two types of electrically charged shells: (1) The charged shell as a single source of the gravitational field, when internal space-time is flat, and external space-time is the Reissner--Nordstr\\"om metric; (2) The neutralizing shell with an electric charge opposite to the charge of the internal source with the Reissner--Nordstr\\"om metric and with the Schwarzschild metric outside the shell.
Tensor distributions on signature-changing space-times
David Hartley; Robin W. Tucker; Philip A. Tuckey; Tevian Dray
Irregularities in the metric tensor of a signature-changing space-time suggest that field equations on such space-times might be regarded as distributional. We review the formalism of tensor distributions on differentiable manifolds, and examine to what extent rigorous meaning can be given to field equations in the presence of signature-change, in particular those involving covariant derivatives. We find that, for both continuous and discontinuous signature-change, covariant differentiation can be defined on a class of tensor distributions wide enough to be physically interesting.
Analyticity of the scattering amplitude, causality, and high-energy bounds in quantum field theory on noncommutative space-time
Tureanu, Anca [High Energy Physics Division, Department of Physical Sciences, University of Helsinki and Helsinki Institute of Physics, P.O. Box 64, FIN-00014 Helsinki (Finland)
In the framework of quantum field theory on noncommutative space-time with the symmetry group O(1,1)xSO(2), we prove that the Jost-Lehmann-Dyson representation, based on the causality condition taken in connection with this symmetry, leads to the mere impossibility of drawing any conclusion on the analyticity of the 2{yields}2-scattering amplitude in cos {theta}, {theta} being the scattering angle. Discussions on the possible ways of obtaining high-energy bounds analogous to the Froissart-Martin bound on the total cross section are also presented.
UCLA space-time area law model: A persuasive foundation for hadronization
Abachi, S; Buchanan, C; Chien, A; Chun, S; Hartfiel, B
UCLA-HEP-06-001 UCLA space-time area law model: A persuasivedominantly controlled by a Space- Time Area Law (�STAL�), anheavy quarks whose classical space-time world-lines deviate
Electromagnetic space-time crystals. II. Fractal computational approach
G. N. Borzdov
A fractal approach to numerical analysis of electromagnetic space-time crystals, created by three standing plane harmonic waves with mutually orthogonal phase planes and the same frequency, is presented. Finite models of electromagnetic crystals are introduced, which make possible to obtain various approximate solutions of the Dirac equation. A criterion for evaluating accuracy of these approximate solutions is suggested.
Neutrino flavor oscillations in a curved space-time
Luca Visinelli
Using a WKB approximation of the Dirac equation in a curved spacetime, we obtain the expression for the phase shift between two neutrino mass eigenstates in a generic gravitational field. We apply this expression to two specific space-time geometries, namely the Kerr-Newman metric describing a rotating and charged black hole, and the Friedmann-Robertson-Walker metric.
Distributional Energy-Momentum Densities of Schwarzschild Space-Time
Toshiharu Kawai; Eisaku Sakane
For Schwarzschild space-time, distributional expressions of energy-momentum densities and of scalar concomitants of the curvature tensors are examined for a class of coordinate systems which includes those of the Schwarzschild and of Kerr-Schild types as special cases. The energy-momentum density $\\tilde T_\\mu^{\
Non-commutative Einstein-Proca Space-time
Blanca G�nzales; Rom�n Linares; Marco Maceda; Oscar S�nchez-Santos
In this work we present a deformed model of Einstein-Proca space-time based on the replacement of point-like sources by non-commutative smeared distributions. We discuss the solutions to the set of non-commutative Einstein-Proca equations thus obtained, with emphasis on the issue of singularities and horizons.
Generalised hyperbolicity in space-times with conical singularities
J. P. Wilson
It is shown that the space-time with a conical singularity, which describes a thin cosmic string, is hyperbolic in the sense that a unique H^1 solution exists to the initial value problem for the wave equation with a certain class of initial data.
An extended Dirac equation in noncommutative space-time
R. Vilela Mendes
Stabilizing, by deformation, the algebra of relativistic quantum mechanics a non-commutative space-time geometry is obtained. The exterior algebra of this geometry leads to an extended massless Dirac equation which has both a massless and a large mass solution. The nature of the solutions is discussed, as well as the effects of coupling the two solutions.
An extended Dirac equation in noncommutative space-time
Mendes, R Vilela
Stabilizing, by deformation, the algebra of relativistic quantum mechanics a non-commutative space-time geometry is obtained. The exterior algebra of this geometry leads to an extended massless Dirac equation which has both a massless and a large mass solution. The nature of the solutions is discussed, as well as the effects of coupling the two solutions.
Entanglement in a multiverse with no common space-time
S. J. Robles-P�rez
Inter-universal entanglement may even exist in a multiverse in which there is no common space-time among the universes. In particular, the entanglement between the expanding and contracting branches of the universe might have observable consequences in the dynamical and thermodynamical properties of one single branch, making therefore testable the whole multiverse proposal, at least in principle.
Entanglement in a multiverse with no common space-time
Robles-P�rez, S J
Inter-universal entanglement may even exist in a multiverse in which there is no common space-time among the universes. In particular, the entanglement between the expanding and contracting branches of the universe might have observable consequences in the dynamical and thermodynamical properties of one single branch, making therefore testable the whole multiverse proposal, at least in principle.
Path integral for space-time noncommutative field theory
Fujikawa, Kazuo [Institute of Quantum Science, College of Science and Technology, Nihon University, Chiyoda-ku, Tokyo 101-8308 (Japan)
The path integral for space-time noncommutative theory is formulated by means of Schwinger's action principle, which is based on the equations of motion and a suitable ansatz of asymptotic conditions. The resulting path integral has essentially the same physical basis as the Yang-Feldman formulation. It is first shown that higher derivative theories are neatly dealt with by the path integral formulation, and the underlying canonical structure is recovered by the Bjorken-Johnson-Low (BJL) prescription from correlation functions defined by the path integral. A simple theory which is nonlocal in time is then analyzed for an illustration of the complications related to quantization, unitarity, and positive energy conditions. From the viewpoint of the BJL prescription, the naive quantization in the interaction picture is justified for space-time noncommutative theory but not for the simple theory nonlocal in time. We finally show that the perturbative unitarity and the positive energy condition, in the sense that only the positive energy flows in the positive time direction for any fixed time slice in space-time, are not simultaneously satisfied for space-time noncommutative theory by the known methods of quantization.
Space time coded code division multiplexing on SC140 DSP
Menon, Murali P
The aim of this research is to design a high data rate wireless communication system for multi-path fading channels. Code-division multiplexing is proposed as a modulation scheme for a space-time coded multiple antenna system that would guarantee...
Propagation of Test Particles and Scalar Fields on a Class of Wormhole Space-Times
Peter Taylor
In this paper, we consider the problem of test particles and test scalar fields propagating on the background of a class of wormhole space-times. For test particles, we solve for arbitrary causal geodesics in terms of integrals which are solved numerically. These integrals are parametrized by the radius and shape of the wormhole throat as well as the initial conditions of the geodesic trajectory. In terms of these parameters, we compute the conditions for the geodesic to traverse the wormhole, to be reflected by the wormhole's potential or to be captured on an unstable bound orbit at the wormhole's throat. These causal geodesics are visualized by embedding plots in Euclidean space in cylindrical coordinates. For test scalar fields, we compute transmission coefficients and quasi-normal modes for arbitrary coupling of the field to the background geometry in the WKB approximation. We show that there always exists an unstable mode whenever the coupling constant is greater than 1/2. This analysis is interesting since recent computations of self-interactions of a static scalar field in wormhole space-times reveal some anomalous dependence on the coupling constant, principally, the existence of an infinite discrete set of poles. We show that this pathological behavior of the self-field is an artifact of computing the interaction for values of the coupling constant that do not lie in the domain of stability.
Entropy of Quantum Fields in de Sitter Space-time
M. V. Takook
The quantum states or Hilbert spaces for the quantum field theory in de Sitter space-time are studied on ambient space formalism. In this formalism, the quantum states are only depended $(1)$ on the topological character of the de Sitter space-time, {\\it i.e.} $\\R \\times S^3$, and $(2)$ on the homogeneous spaces which are used for construction of the unitary irreducible representation of de Sitter group. A compact homogeneous space is chosen in this paper. The unique feature of this homogeneous space is that its total number of quantum states, ${\\cal N}$, is finite although the Hilbert space has infinite dimensions. It is shown that ${\\cal N}$ is a continuous function of the Hubble constant $H$ and the eigenvalue of the Casimir operators of de Sitter group. The entropy of the quantum fields on this Hilbert space have been calculated which is finite and invariant for all inertial observers on the de Sitter hyperboloid.
The Xi-transform for conformally flat space-time
George Sparling
The Xi-transform is a new spinor transform arising naturally in Einstein's general relativity. Here the example of conformally flat space-time is discussed in detail. In particular it is shown that for this case, the transform coincides with two other naturally defined transforms: one a two-variable transform on the Lie group SU(2, C), the other a transform on the space of null split octaves. The key properties of the transform are developed.
Noncommutative of space-time and the relativistic Hydrogen atom
Slimane Zaim; Yazid Delenda
We study the Klein-Gordon equation in a non-commutative space-time as applied to the Hydrogen atom to extract the energy levels, by considering the second-order corrections in the non-commutativity paramete and by comparing to the 2S - 1S transition accuracy we get a bound on the parameter of noncommutativity. Phenomenologically we show that non-commutativity is the source of lamb shift corrections and spin electron.
Class of Einstein-Maxwell-dilaton-axion space-times
Matos, Tonatiuh; Miranda, Galaxia; Sanchez-Sanchez, Ruben; Wiederhold, Petra [Departamento de Fisica, Centro de Investigacion y de Estudios Avanzados del IPN, Apartado Postal 14-740, 07000 Distrito Federal (Mexico); Departamento de Fisica, Escuela Superior de Fisica y Matematicas del IPN, Edificio 9, 07738 Distrito Federal (Mexico); Centro de Investigacion en Ciencia Aplicada y Tecnologia Avanzada del IPN, Legaria 694, 11500 Distrito Federal (Mexico); Departamento de Control Automatico, Centro de Investigacion y de Estudios Avanzados del IPN, Apartado Postal 14-740, 07000 Distrito Federal (Mexico)
We use the harmonic maps ansatz to find exact solutions of the Einstein-Maxwell-dilaton-axion (EMDA) equations. The solutions are harmonic maps invariant to the symplectic real group in four dimensions Sp(4,R){approx}O(5). We find solutions of the EMDA field equations for the one- and two-dimensional subspaces of the symplectic group. Specially, for illustration of the method, we find space-times that generalize the Schwarzschild solution with dilaton, axion, and electromagnetic fields.
Class of Einstein-Maxwell-Dilaton-Axion Space-Times
Tonatiuh Matos; Galaxia Miranda; Ruben Sanchez-Sanchez; Petra Wiederhold
We use the harmonic maps ansatz to find exact solutions of the Einstein-Maxwell-Dilaton-Axion (EMDA) equations. The solutions are harmonic maps invariant to the symplectic real group in four dimensions $Sp(4,\\Rreal)\\sim O(5)$. We find solutions of the EMDA field equations for the one and two dimensional subspaces of the symplectic group. Specially, for illustration of the method, we find space-times that generalise the Schwarzschild solution with dilaton, axion and electromagnetic fields.
The wave equation on static singular space-times
Eberhard Mayerhofer
The first part of my thesis lays the foundations to generalized Lorentz geometry. The basic algebraic structure of finite-dimensional modules over the ring of generalized numbers is investigated. The motivation for this part of my thesis evolved from the main topic, the wave equation on singular space-times. The second and main part of my thesis is devoted to establishing a local existence and uniqueness theorem for the wave equation on singular space-times. The singular Lorentz metric subject to our discussion is modeled within the special algebra on manifolds in the sense of Colombeau. Inspired by an approach to generalized hyperbolicity of conical-space times due to Vickers and Wilson, we succeed in establishing certain energy estimates, which by a further elaborated equivalence of energy integrals and Sobolev norms allow us to prove existence and uniqueness of local generalized solutions of the wave equation with respect to a wide class of generalized metrics. The third part of my thesis treats three different point value resp. uniqueness questions in algebras of generalized functions
Relativistic helicity and link in Minkowski space-time
Yoshida, Z.; Kawazura, Y. [Graduate School of Frontier Sciences, University of Tokyo, Kashiwanoha, Kashiwa, Chiba 277-8561 (Japan)] [Graduate School of Frontier Sciences, University of Tokyo, Kashiwanoha, Kashiwa, Chiba 277-8561 (Japan); Yokoyama, T. [Department of Mathematics, Hokkaido University, Kita 10, Nishi 8, Kita-Ku, Sapporo, Hokkaido 060-0810 (Japan)] [Department of Mathematics, Hokkaido University, Kita 10, Nishi 8, Kita-Ku, Sapporo, Hokkaido 060-0810 (Japan)
A relativistic helicity has been formulated in the four-dimensional Minkowski space-time. Whereas the relativistic distortion of space-time violates the conservation of the conventional helicity, the newly defined relativistic helicity conserves in a barotropic fluid or plasma, dictating a fundamental topological constraint. The relation between the helicity and the vortex-line topology has been delineated by analyzing the linking number of vortex filaments which are singular differential forms representing the pure states of Banach algebra. While the dimension of space-time is four, vortex filaments link, because vorticities are primarily 2-forms and the corresponding 2-chains link in four dimension; the relativistic helicity measures the linking number of vortex filaments that are proper-time cross-sections of the vorticity 2-chains. A thermodynamic force yields an additional term in the vorticity, by which the vortex filaments on a reference-time plane are no longer pure states. However, the vortex filaments on a proper-time plane remain to be pure states, if the thermodynamic force is exact (barotropic), thus, the linking number of vortex filaments conserves.
Fradkin-Bacry-Ruegg-Souriau vector in kappa-deformed space-time
Guha, Partha; S, Zuhair N
We study presence of an additional symmetry of a generic central potential in the $\\kappa$-space-time. An explicit construction of Fradkin and Bacry, Ruegg, Souriau (FBRS) for a central potential is carried out and the piece-wise conserved nature of the vector is established. We also extend the study to Kepler systems with a drag term, particularly Gorringe-Leach equation is generalized to the $\\kappa$-deformed space. The possibility of mapping Gorringe-Leach equation to an equation with out drag term is exploited in associating a similar conserved vector to system with a drag term. An extension of duality between two class of central potential is introduced in the $\\kappa$-deformed space and is used to investigate the duality existing between two class of Gorringe-Leach equations. All the results obtained can be retraced to the correct commutative limit as we let $a \\rightarrow 0$.
Tolman-Bondi Space-Time in Brane World Scenario
Subenoy Chakraborty; Asit Banerjee; Ujjal Debnath
In the present work, inhomogeneous Tolman-Bondi type dust space-time is studied on the brane. There are two sets of solutions of the above model. The first solution represents either a collapsing model starting from an infinite volume at infinite past to the singularity or a model starting from a singularity and expanding for ever having a transition from decelerating phase to accelerating phase. The first solution shows that the end state of collapse may be black hole or a naked singularity depending signs of various parameters involved. The second solution represents a bouncing model where the bounce occurs at different comoving radii at different epochs.
Space-time noncommutative theories at finite temperature
Strelchenko, A. V.; Vassilevich, D. V. [Dnepropetrovsk National University, 49050 Dnepropetrovsk (Ukraine); Instituto de Fisica, Universidade de Sao Paulo Caixa Postal 66318 CEP 05315-970, Sao Paulo S.P. (Brazil)
We analyze renormalization and the high-temperature expansion of the one-loop effective action of the space-time noncommutative {phi}{sup 4} theory by using the zeta-function regularization in the imaginary-time formalism (i.e., on S{sup 1}xR{sup 3}). Interestingly enough, there are no mixed (nonplanar) contributions to the counterterms as well as to the power-law high-temperature asymptotics. We also study the Wick rotation and formulate assumptions under which the real and imaginary-time formalisms are equivalent.
Photon Green Functions in Curved Space-Time
Giuseppe Bimonte; Enrico Calloni; Luciano Di Fiore; Giampiero Esposito; Leopoldo Milano; Luigi Rosa
Quantization of electrodynamics in curved space-time in the Lorenz gauge and with arbitrary gauge parameter makes it necessary to study Green functions of non-minimal operators with variable coefficients. Starting from the integral representation of photon Green functions, we link them to the evaluation of integrals involving Gamma-functions. Eventually, the full asymptotic expansion of the Feynman photon Green function at small values of the world function, as well as its explicit dependence on the gauge parameter, are obtained without adding by hand a mass term to the Faddeev-Popov Lagrangian. Coincidence limits of second covariant derivatives of the associated Hadamard function are also evaluated, as a first step towards the energy-momentum tensor in the non-minimal case.
Effects of quantum space time foam in the neutrino sector
H. V. Klapdor-Kleingrothaus; H. P�s; U. Sarkar
We discuss violations of CPT and quantum mechanics due to interactions of neutrinos with space-time quantum foam. Neutrinoless double beta decay and oscillations of neutrinos from astrophysical sources (supernovae, active galactic nuclei) are analysed. It is found that the propagation distance is the crucial quantity entering any bounds on EHNS parameters. Thus, while the bounds from neutrinoless double beta decay are not significant, the data of the supernova 1987a imply a bound being several orders of magnitude more stringent than the ones known from the literature. Even more stringent limits may be obtained from the investigation of neutrino oscillations from active galactic nuclei sources, which have an impressive potential for the search of quantum foam interactions in the neutrino sector.
Bounds on negative energy densities in static space-times
Christopher J. Fewster; Edward Teo
Certain exotic phenomena in general relativity, such as backward time travel, appear to require the presence of matter with negative energy. While quantum fields are a possible source of negative energy densities, there are lower bounds - known as quantum inequalities - that constrain their duration and magnitude. In this paper, we derive new quantum inequalities for scalar fields in static space-times, as measured by static observers with a choice of sampling function. Unlike those previously derived by Pfenning and Ford, our results do not assume any specific sampling function. We then calculate these bounds in static three- and four-dimensional Robertson-Walker universes, the de Sitter universe, and the Schwarzschild black hole. In each case, the new inequality is stronger than that of Pfenning and Ford for their particular choice of sampling function.
LINEAR SPACE-TIME PRECODING FOR RICIAN FADING MISO CHANNELS Mai Vu, Arogyaswami Paulraj
Vu, Mai
LINEAR SPACE-TIME PRECODING FOR RICIAN FADING MISO CHANNELS Mai Vu, Arogyaswami Paulraj Stanford, Australia Email: email@example.com ABSTRACT We study a space-time precoding technique for MISO wire- less in practice. In this paper, we study a particular space-time coding scheme with memory for Rician MISO
Imperial College, London
SPACE-TIME BLOCK CODING : JOINT DETECTION AND CHANNEL ESTIMATION USING MULTIPLE MODEL THEORY Harini of Sheffield, Mappin Street, Sheffield S1 3JD. Email: email@example.com ABSTRACT A joint decoding method for space-time block codes [1, 2] is pre- sented. The space-time coded signals can be viewed as a first
A SpaceTime Finite Element Method for the Exterior Structural Acoustics Problem
Thompson, Lonny L.
A Space�Time Finite Element Method for the Exterior Structural Acoustics Problem: Time�discontinuous Galerkin space�time finite element method is formu� lated for the exterior structural acoustics problem Introduction A space�time finite element formulation is presented for solution of the exterior struc� tural
A Space-Time Finite Element Method for the Exterior Acoustics Problem
Thompson, Lonny L.
A Space-Time Finite Element Method for the Exterior Acoustics Problem Lonny L. Thompson Department in exterior domains is discussed. The space-time formulation for the exterior acoustics problem is obtained, the development of a space-time finite element method for so- lution of the transient acoustics problem
A SpaceTime Finite Element Method for the Exterior Acoustics Problem
Thompson, Lonny L.
A Space�Time Finite Element Method for the Exterior Acoustics Problem by Lonny L. Thompson problem in exterior domains is discussed. The space�time formulation for the exterior acoustics problem acoustics problem. i #12; Contents 1 Introduction 1 2 The Exterior Acoustics Problem 3 3 Space�time finite
Space-Time Turbo Codes Youjian Liu and Michael P. Fitz
Liu, Youjian "Eugene"
Space-Time Turbo Codes Youjian Liu and Michael P. Fitz Department of Electrical Engineering. We propose a new class of scalable space{time codes based on turbo codes or turbo trellis codes 1]. They will be referred as space{time turbo codes (STT) in the sequel. The scalability implies that the code rate
Space-Time Turbo Code Using Quantized Feedback with Two Transmit Antennas
Lee, Jae Hong
Space-Time Turbo Code Using Quantized Feedback with Two Transmit Antennas Chi Hoon Yoo and Jae Hong-time turbo code with two transmit antennas in a quasi- static Rayleigh fading channel. The performance for the space-time turbo code. To improve the perform- ance of the space-time turbo code, we propose the new
The Euclid space-time diagram of the theory of relativity
W. LiMing
A conventional space-time diagram is $r-ct$ one, which satisfies the Minkowski geometry. This geometry conflict the intuition from the Euclid geometry. In this work an Euclid space-time diagram is proposed to describe relativistic world lines with an exact Euclid geometry. The relativistic effects such as the dilation of moving clocks, the contraction of moving length, and the twin paradox can be geometrically expressed in the Euclid space-time diagram. It is applied to the case of a satellite clock to correct the gravitational effect. It is found that this Euclid space-time diagram is much more intuitive than the conventional space-time diagram.
Geometry of Majorana neutrino and new symmetries
G. G. Volkov
Experimental observation of Majorana fermion matter gives a new impetus to the understanding of the Lorentz symmetry and its extension, the geometrical properties of the ambient space-time structure, matter--antimatter symmetry and some new ways to understand the baryo-genesis problem in cosmology. Based on the primordial Majorana fermion matter assumption, we discuss a possibility to solve the baryo-genesis problem through the the Majorana-Diraco genesis in which we have a chance to understand creation of Q(em) charge and its conservation in our D=1+3 Universe after the Big Bang. In the Majorana-Diraco genesis approach there appears a possibility to check the proton and electron non-stability on the very low energy scale. In particle physics and in our space-time geometry, the Majorana nature of the neutrino can be related to new types of symmetries which are lying beyond the binary Cartan-Killing-Lie algebras/superalgebras. This can just support a conjecture about the non-completeness of the SM in terms of binary Cartan--Killing--Lie symmetries/supersymmetries. As one of the very important applications of such new ternary symmetries could be related with explanation of the nature of the three families and three colour symmetry. The Majorana neutrino can directly indicate the existence of a new extra-dimensional geometry and thanks to new ternary space-time symmetries, could lead at high energies to the unextraordinary phenomenological consequences.
L. R. G. Fontes; C. M. Newman; K. Ravishankar; E. Schertzer
The dynamical discrete web (DDW), introduced in recent work of Howitt and Warren, is a system of coalescing simple symmetric one-dimensional random walks which evolve in an extra continuous dynamical parameter s. The evolution is by independent updating of the underlying Bernoulli variables indexed by discrete space-time that define the discrete web at any fixed s. In this paper, we study the existence of exceptional (random) values of s where the paths of the web do not behave like usual random walks and the Hausdorff dimension of the set of such exceptional s. Our results are motivated by those about exceptional times for dynamical percolation in high dimension by H\\"aggstrom, Peres and Steif, and in dimension two by Schramm and Steif. The exceptional behavior of the walks in DDW is rather different from the situation for dynamical random walks of Benjamini, H\\"aggstrom, Peres and Steif. In particular, we prove that there are exceptional values of s for which the walk from the origin S^s(n) has limsup S^s(n)/\\sqrt n \\leq K with a nontrivial dependence of the Hausdorff dimension on K. We also discuss how these and other results extend to the dynamical Brownian web, a natural scaling limit of DDW. The scaling limit is the focus of a paper in preparation; it was studied by Howitt and Warren and is related to the Brownian net of Sun and Swart.
Majorana-Oppenheimer approach to Maxwell electrodynamics in Riemannian space-time
A. Bogush; V. Red'kov; N. Tokarevskaya; G. Spix
The Riemann -- Silberstein -- Majorana -- Oppengeimer approach to the Maxwell electrodynamics in presence of electrical sources and arbitrary media is investigated within the matrix formalism. The symmetry of the matrix Maxwell equation under transformations of the complex rotation group SO(3.C) is demonstrated explicitly. In vacuum case, the matrix form includes four real $4 \\times 4$ matrices $\\alpha^{b}$. In presence of media matrix form requires two sets of $4 \\times 4$ matrices, $\\alpha^{b}$ and $\\beta^{b}$ -- simple and symmetrical realization of which is given. Relation of $\\alpha^{b}$ and $\\beta^{b}$ to the Dirac matrices in spinor basis is found. Minkowski constitutive relations in case of any linear media are given in a short algebraic form based on the use of complex 3-vector fields and complex orthogonal rotations from SO(3.C) group. The matrix complex formulation in the Esposito's form, based on the use of two electromagnetic 4-vector, is studied and discussed. Extension of the 3-vector complex matrix formalism to arbitrary Riemannian space-time in accordance with tetrad method by Tetrode-Weyl-Fock-Ivanenko is performed.
Quasi-orthogonal space-frequency and space-time-frequency block codes for MIMO OFDM channels
Fazel, Fatemeh; Jafarkhani, Hamid
Lu and X. Wang, �Space-time code design in OFDM systems,� inSpace-time block codes from orthogonal designs,� IEEE Trans.orthogonal space- time block codes with full diversity,�
abstract relational space-time: Topics by E-print Network
Broader source: All U.S. Department of Energy (DOE) Office Webpages (Extended Search)
geometric magnitudes. Ignacio Sanchez-Rodriguez 2008-03-13 13 Scale relativity and fractal space-time: theory and applications Physics Websites Summary: Scale relativity and...
Well-posedness of the Space-Time Fractional Diffusion Problems ...
... and dynamics of a bead in polymer network, and so on. In this talk, we consider initial boundary value problems of the space-time fractional diffusion equation�...
Alamouti Space Time Coded OFDM for Underwater Acoustic Channels Baosheng Li1
Stojanovic, Milica
the time-variation of the channel. Adaptive channel estimation for space-time block coded (STBC) OFDM], [11]. Reference [9] discusses a jointly optimized MIMO-DFE with space- time trellis codes. In [10 stay fixed over the duration of one OFDM block, but may change from one block to another. Channel
Space-time BIE methods for non homogeneous exterior wave equation problems. The Dirichlet case.
Ceragioli, Francesca
Space-time BIE methods for non homogeneous exterior wave equation problems. The Dirichlet case. S. Falletta , G. Monegato , L. Scuderi§ Abstract In this paper we consider the (2D and 3D) exterior problem; non homogeneous conditions; space-time boundary integral equations; numerical methods This work
Non-marginally bound inhomogeneous dust collapse in higher dimensional space-time
S. G. Ghosh; A. Banerjee
We investigate the occurrence and nature of a naked singularity in the gravitational collapse of an inhomogeneous dust cloud described by a self-similar higher dimensional Tolman-Bondi space-time. Bound, marginally bound and unbound space-times are analyzed. The degree of inhomogeneity of the collapsing matter necessary to form a naked singularity is given.
Hirsch, M.; Morisi, S.; Peinado, E.; Valle, J. W. F. [AHEP Group, Institut de Fisica Corpuscular--C.S.I.C./Universitat de Valencia, Edificio Institutos de Paterna, Apartado 22085, E-46071 Valencia (Spain)
We propose a new motivation for the stability of dark matter (DM). We suggest that the same non-Abelian discrete flavor symmetry which accounts for the observed pattern of neutrino oscillations, spontaneously breaks to a Z{sub 2} subgroup which renders DM stable. The simplest scheme leads to a scalar doublet DM potentially detectable in nuclear recoil experiments, inverse neutrino mass hierarchy, hence a neutrinoless double beta decay rate accessible to upcoming searches, while {theta}{sub 13}=0 gives no CP violation in neutrino oscillations.
Ilka Brunner; Nils Carqueville; Daniel Plencner
Orbifolding two-dimensional quantum field theories by a symmetry group can involve a choice of discrete torsion. We apply the general formalism of `orbifolding defects' to study and elucidate discrete torsion for topological field theories. In the case of Landau-Ginzburg models only the bulk sector had been studied previously, and we re-derive all known results. We also introduce the notion of `projective matrix factorisations', show how they naturally describe boundary and defect sectors, and we further illustrate the efficiency of the defect-based approach by explicitly computing RR charges. Roughly half of our results are not restricted to Landau-Ginzburg models but hold more generally, for any topological field theory. In particular we prove that for a pivotal bicategory, any two objects of its orbifold completion that have the same base are orbifold equivalent. Equivalently, from any orbifold theory (including those based on nonabelian groups) the original unorbifolded theory can be obtained by orbifolding via the `quantum symmetry defect'.
Modeling Space-Time Dynamics of Aerosols Using Satellite Data and Atmospheric Transport Model Output
Shi, Tao
Modeling Space-Time Dynamics of Aerosols Using Satellite Data and Atmospheric Transport Model of aerosol optical depth across mainland Southeast Asia. We include a cross validation study to assess
Dr. Shih-Lung Shaw's Research on Space-Time GIS, Human Dynamics and Big Data
Grissino-Mayer, Henri D.
1 Dr. Shih-Lung Shaw's Research on Space-Time GIS, Human Dynamics and Big Data for Geography Department's Faculty Research Highlight October 12, 2014 Shih-Lung Shaw, Ph.D. Alvin and Sally Beaman
Quantum estimation of the Schwarzschild space-time parameters of the Earth
David Edward Bruschi; Animesh Datta; Rupert Ursin; Timothy C. Ralph; Ivette Fuentes
We propose a quantum experiment to measure with high precision the Schwarzschild space-time parameters of the Earth. The scheme can also be applied to measure distances by taking into account the curvature of the Earth's space-time. As a wave-packet of (entangled) light is sent from the Earth to a satellite it is red-shifted and deformed due to the curvature of space-time. Measurements after the propagation enable the estimation of the space-time parameters. We compare our results with the state of the art, which involves classical measurement methods, and discuss what developments are required in space-based quantum experiments to improve on the current measurement of the Schwarzschild radius of the Earth.
An analysis of Texas rainfall data and asymptotic properties of space-time covariance estimators
Li, Bo
This dissertation includes two parts. Part 1 develops a geostatistical method to calibrate Texas NexRad rainfall estimates using rain gauge measurements. Part 2 explores the asymptotic joint distribution of sample space-time covariance estimators...
Space-Time Coding for the EDGE Mobile Radio System Marceau Coupechoux
Coupechoux, Marceau
28 Space-Time Coding for the EDGE Mobile Radio System Marceau Coupechoux Alcatel CorporateResearchCenter Route de Nozay, 91460 Marcoussis. France Phone: +33- 169-63-4359, e-mail: marceau
Space-Time Block Coding for Frequency-Selective and Time-Varying Channels
Langendoen, Koen
such as channel capacity and reliability [2]. Space-time block coding (STBC) [3], [4] has been introduced for a multiple-input single-output (MISO) system with 2 transmit antennas and 1 receive antenna
Space-time resolved electrokinetics in cylindrical and semi-cylindrical microchannels
Michele Campisi
It is shown show how to employ Bessel-Fourier series in order to obtain a complete space-time resolved description of electrokinetic phenomena in cylindrical and semi-cylindrical microfluidic channels.
A study of Turbo Codes across Space Time Spreading Channel 1
Ibrahim S. Raad; Peter Vial; Tad Wysocki
This study looks at the use of Turbo Codes across a space time spreading (STS) channel in the absence of multi-path. For 3 and 5 iterations, turbo codes was shown to improve the BER by up to 3%.
Spectra of disc operator for twisted acceleration-enlarged Newton-Hooke space-times
Marcin Daszkiewicz
The time-dependent spectra of disc area operator for twisted acceleration-enlarged Newton-Hooke space-times are derived. It is demonstrated that the corresponding area quanta are expanding or oscillating in time.
Semi-Blind Gradient-Newton CMA and SDD Algorithm for MIMO Space-Time Equalisation
Chen, Sheng
Semi-Blind Gradient-Newton CMA and SDD Algorithm for MIMO Space-Time Equalisation S. Chen, L. HanzoBJ, UK. E-mails: {sqc, lh, email@example.com Abstract-- Semi-blind space-time equalisation-directed scheme is then applied to adapt the STE. The proposed semi-blind adaptive STE is capable of converging
Temporal variations in space-time and progenitors of gamma ray burst and millisecond pulsars
Preston Jones
A time varying space-time metric is shown to be a source of electromagnetic radiation. The post-Newtonian approximation is used as a realistic model of the connection between the space-time metric and a time varying gravitational potential. Large temporal variations in the metric from the coalescence of colliding black holes and neutron stars are shown to be possible progenitors of gamma ray burst and millisecond pulsars.
Improved Space-time Turbo Codes with Full Spatial Diversity over Integer Ring
Lee, Jae Hong
Improved Space-time Turbo Codes with Full Spatial Diversity over Integer Ring Tae Min Kim and Jae-time turbo codes designed over integer ring for BPSK and QPSK modulation. The proposed spacetime turbo codes of 0.5 dB at FER of IO-$ over the space-time turbo codes with the iterative non-binary m a x i " D
High-Fidelity Space-Time Adaptive Multiphysics Simulations in Nuclear Engineering
Solin, Pavel; Ragusa, Jean
Monolithic adaptive multimesh hp-FEM discretization of multiphysics coupled problems Monolithic coupling of hp-FEM and hp-DG methods New modular approach to higher-order time discretization of transient PDE problems
0-7803-7442-8/02/$17.00 2002 IEEE Combined Beamforming and Space-Time Block Coding with a
Morelos-Zaragoza, Robert H.
continue our investigation of joint beamforming and transmit diversity with space-time block coding0-7803-7442-8/02/$17.00 © 2002 IEEE Combined Beamforming and Space-Time Block Coding with a Sparse or two) in conjunction with beam-space-time block coding to achieve transmit diversity. On the receiving
Compatible, energy and symmetry preserving 2D Lagrangian hydrodynamics in rz-cylindrical coordinates
Shashkov, Mikhail [Los Alamos National Laboratory; Wendroff, Burton [Los Alamos National Laboratory; Burton, Donald [Los Alamos National Laboratory; Barlow, A [AWE; Hongbin, Guo [ASU
We present a new discretization for 2D Lagrangian hydrodynamics in rz geometry (cylindrical coordinates) that is compatible, energy conserving and symmetry preserving. We describe discretization of the basic Lagrangian hydrodynamics equations.
Space-Time Models based on Random Fields with Local Interactions
Dionissios T. Hristopulos; Ivi C. Tsantili
The analysis of space-time data from complex, real-life phenomena requires the use of flexible and physically motivated covariance functions. In most cases, it is not possible to explicitly solve the equations of motion for the fields or the respective covariance functions. In the statistical literature, covariance functions are often based on mathematical constructions. We propose deriving space-time covariance functions by solving "effective equations of motion", which can be used as statistical representations of systems with diffusive behavior. In particular, we propose using the linear response theory to formulate space-time covariance functions based on an equilibrium effective Hamiltonian. The effective space-time dynamics are then generated by a stochastic perturbation around the equilibrium point of the classical field Hamiltonian leading to an associated Langevin equation. We employ a Hamiltonian which extends the classical Gaussian field theory by including a curvature term and leads to a diffusive Langevin equation. Finally, we derive new forms of space-time covariance functions.
Lifshitz field theories, Snyder noncomutative space-time and momentum dependent metric
Romero, Juan M
In this work, we propose three different modified relativistic particles. In the first case, we propose a particle with metrics depending on the momenta and we show that the quantum version of these systems includes different field theories, as anisotropic field theories. As a second case we propose a particle that implies a modified symplectic structure and we show that the quantum version of this system gives different noncommutative space-times, for example the Snyder space-time. In the third case, we combine both structures before mentioned, namely noncommutative space-times and momentum dependent metrics. In this last case, we show that anisotropic field theories can be seen as a limit of no commutative field theory.
Correspondence between Poincare symmetry of commutative QFT and twisted Poincare symmetry of noncommutative QFT
Abe, Yasumi [Institute of Particle and Nuclear Studies, High Energy Accelerator Research Organization (KEK), Tsukuba 305-0801 (Japan)
The space-time symmetry of noncommutative quantum field theories with a deformed quantization is described by the twisted Poincare algebra, while that of standard commutative quantum field theories is described by the Poincare algebra. Based on the equivalence of the deformed theory with a commutative field theory, the correspondence between the twisted Poincare symmetry of the deformed theory and the Poincare symmetry of a commutative theory is established. As a by-product, we obtain the conserved charge associated with the twisted Poincare transformation to make the twisted Poincare symmetry evident in the deformed theory. Our result implies that the equivalence between the commutative theory and the deformed theory holds in a deeper level, i.e., it holds not only in correlation functions but also in (different types of) symmetries.
Upper bound for entropy in asymptotically de Sitter space-time
Kengo Maeda; Tatsuhiko Koike; Makoto Narita; Akihiro Ishibashi
We investigate nature of asymptotically de Sitter space-times containing a black hole. We show that if the matter fields satisfy the dominant energy condition and the cosmic censorship holds in the considering space-time, the area of the cosmological event horizon for an observer approaching a future timelike infinity does not decrease, i.e. the second law is satisfied. We also show under the same conditions that the total area of the black hole and the cosmological event horizon, a quarter of which is the total Bekenstein-Hawking entropy, is less than $12\\pi/\\Lambda$, where $\\Lambda$ is a cosmological constant. Physical implications are also discussed.
Energy-momentum Prescriptions in General Spherically Symmetric Space-times
Saeed Mirshekari; Amir M. Abbassi
Einstein, Landau-Lifshitz, Papapetrou, Weinberg, and M{\\o}ller energy-momentum prescriptions in general spherically symmetric space-times are investigated. It is shown that for two special but not unusual classes of general spherically symmetric space-times several energy-momentum prescriptions in Schwarzschild Cartesian coordinates lead to some coincidences in energy distribution. It is also obtained that for a special class of spherically symmetric metrics M{\\o}ller and Einstein energy-momentum prescriptions give the same result for energy distribution if and only if it has a specific dependence on radial coordinate.
Blind Equalization and Identification for Differential Space-time Modulated Communication Systems
Schniter, Philip
Blind Equalization and Identification for Differential Space-time Modulated Communication Systems A Thesis Presented in Partial Fulfillment of the Requirements for the Degree Master of Science of blind identification and equalization for MIMO system with frequency- selective fading channels. We
New Efficient Sparse SpaceTime Algorithms for Superparameterization on Mesoscales
Xing, Yulong
New Efficient Sparse Space�Time Algorithms for Superparameterization on Mesoscales YULONG XING-scale and mesoscale processes provided by a cloud-resolving model (CRM) embedded in each column of a large-scale model for limited-area mesoscale ensemble forecasting. 1. Introduction Atmospheric processes of weather and climate
Space-Time Stereo James DavisJames Davis Honda Research InstituteHonda Research Institute
O'Brien, James F.
Space-Time Stereo James DavisJames Davis Honda Research InstituteHonda Research Institute Ravi Princeton UniversityPrinceton University DiegoDiego NehabNehab Honda & PrincetonHonda & Princeton
Powering Up With Space-Time Wind Forecasting Amanda S. HERING and Marc G. GENTON
Genton, Marc G.
Powering Up With Space-Time Wind Forecasting Amanda S. HERING and Marc G. GENTON The technology to harvest electricity from wind energy is now advanced enough to make entire cities powered by it a reality be more realistically assessed with a loss measure that depends upon the power curve relating wind speed
A space-time BIE method for wave equation exterior problems. The Neumann case.
Ceragioli, Francesca
A space-time BIE method for wave equation exterior problems. The Neumann case. S. Falletta , G. Monegato , L. Scuderi§ Abstract In this paper we consider the (2D and 3D) exterior problem for the wave equation, with a Neumann boundary condition and in general with non trivial data. First we derive a space
A Space-Time Finite Element Method for the Exterior Structural Acoustics Problem
Thompson, Lonny L.
A Space-Time Finite Element Method for the Exterior Structural Acoustics Problem: Time-time finite element method is formu- lated for the exterior structural acoustics problem in two space formulation is presented for solution of the exterior struc- tural acoustics problem in two space dimensions
Using Space-Time Constraints to Guide Model Interoperability Paul F. Reynolds Jr.
Brogan, David
to motion retargeting accurately transferring human motions to animated characters. A typical goalUsing Space-Time Constraints to Guide Model Interoperability Paul F. Reynolds Jr. Dept of Computer-924-1039 (V) , 434-982-2214 (F) email@example.com Keywords: Interoperability, Multi-Resolution Modeling
Climate Projections Using Bayesian Model Averaging and Space-Time Dependence
Haran, Murali
Climate Projections Using Bayesian Model Averaging and Space-Time Dependence K. Sham Bhat, Murali Haran, Adam Terando, and Klaus Keller. Abstract Projections of future climatic changes are a key input to the design of climate change mitiga- tion and adaptation strategies. Current climate change projections
Photon emission in a constant magnetic field in 2+1 dimensional space-time
J. T. S. Amaral; S. I. Zlatev
We calculate by the proper-time method the amplitude of the two-photon emission by a charged fermion in a constant magnetic field in (2+1)-dimensional space-time. The relevant dynamics reduces to that of a supesymmetric quantum-mechanical system with one bosonic and one fermionic degrees of freedom.
Non-trivial, static, geodesically complete, vacuum space-times with a negative cosmological constant
Avignon et des Pays de Vaucluse, Universit� de
Non-trivial, static, geodesically complete, vacuum space-times with a negative cosmological singularity-free static Lorentzian four- dimensional solutions of the vacuum Einstein equations of this paper is to show that such rigidity is false in this last situation. More precisely, for
Non-trivial, static, geodesically complete, vacuum space-times with a negative cosmological constant
Anderson, Michael
Non-trivial, static, geodesically complete, vacuum space-times with a negative solutions of the vacuum Einstein equations with a negative cosmological constant. The new families of this paper is to show that such rigidity is false in this last situation. More precisely, for
Non-trivial, static, geodesically complete, vacuum space-times with a negative cosmological constant
Anderson, Michael
Non-trivial, static, geodesically complete, vacuum space-times with a negative cosmological construct a large class of new singularity-free static Lorentzian four- dimensional solutions of the vacuum is false in this last situation. More precisely, for #3;
The stability of Killing-Cauchy horizons in colliding plane wave space-times
J. B. Griffiths
It is confirmed rigorously that the Killing-Cauchy horizons, which sometimes occur in space-times representing the collision and subsequent interaction of plane gravitational waves in a Minkowski background, are unstable with respect to bounded perturbations of the initial waves, at least for the case in which the initial waves have constant aligned polarizations.
XXII ICTAM, 2529 August 2008, Adelaide, Australia SPACE-TIME MEASUREMENTS OF BREAKING WAVE KINEMATICS
Paris-Sud XI, Université de
with light intensity. WAVE KINEMATICS Phase average vorticity In order to have a statistical evolutionXXII ICTAM, 2529 August 2008, Adelaide, Australia SPACE-TIME MEASUREMENTS OF BREAKING WAVE KINEMATICS AND VOID FRACTION IN THE SURF ZONE Olivier Kimmoun1 , 2 Hubert Branger1 1IRPHE, CNRS, Aix
Dynamics on the Way to Forming Glass: Bubbles in Space-time David Chandler1
Chandler, David
Dynamics on the Way to Forming Glass: Bubbles in Space-time David Chandler1 and Juan P. Garrahan2 1 a theoretical perspective of the dynamics of glass forming liquids and the glass tran- sition of trajectory space. This structure emerges from spatial correlations of dynamics that appear in disordered
Baras, John S.
ON-LINE DETECTION OF DISTRIBUTED ATTACKS FROM SPACE-TIME NETWORK FLOW PATTERNS J.S. Baras* , A in the network. We are interested in the "quickest detection" problem when the attack is distributed is to detect when a distributed denial of service is taking place in one sub-network of a transit (core
Iterative Spatial Sequence Estimator for Multi-Group Space Time Trellis Coded Systems
Al-Ghadhban, Samir
Iterative Spatial Sequence Estimator for Multi-Group Space Time Trellis Coded Systems Samir Al. The developed detector is called maximum a posteriori spatial sequence estimator and it has the flexibility. A novel spatial sequence estimator (SSE) for V-BLAST is proposed in [4]. The algorithm combines group
The Yang-Mills gauge theory in DFR noncommutative space-time
Abreu, Everton M C
The Doplicher-Fredenhagen-Roberts (DFR) framework for noncommutative (NC) space-times is considered as an alternative approach to describe the physics of quantum gravity, for instance. In this formalism, the NC parameter, {\\it i.e.} $\\theta^{\\mu\
Dark Energy and Tachyon Field in Bianchi Type-V Space-time
J. Sadeghi; H. Farahani
In this paper, we consider Bianchi type-V space-time and study a cosmological model of dark energy based on Tachyon scalar field. We assumed three different kinds of matter without possibility of interaction with scalar dark energy. Assuming power law Hubble parameter in terms of scale factor we obtain evolution of scalar field, scalar potential and equation of state parameter.
Performance of Turbo Coded WCDMA with Downlink Space Time Block Coding in Correlated Fading Channels
Mandayam, Narayan
Performance of Turbo Coded WCDMA with Downlink Space Time Block Coding in Correlated Fading due to potential high data rate applications such as wireless internet access. Turbo codes. In this paper, we evaluate the performance of turbo coded WCDMA systems with downlink transmit diversity
IEEE VEHICULAR TECHNOLOGY CONFERENCE SPRING, 2003 1 Space-Time Block Coding applied to Turbo Coded
Paris-Sud XI, Université de
IEEE VEHICULAR TECHNOLOGY CONFERENCE SPRING, 2003 1 Space-Time Block Coding applied to Turbo Coded and a Turbo Code (TC) as channel code. MC-CDMA is likely to be one of the most promising access technique. Then, since Turbo Coded MC-CDMA was demonstrated to be very efficient for a Single Input Single Output
Ghoniem, Nasr M.
MODELING SPACE-TIME DEPENDENT HELIUM BUBBLE EVOLUTION IN TUNGSTEN ARMOR UNDER IFE CONDITIONS Qiyang dependent Helium transport in finite geometries, including the simultaneous transient production of defects of Helium bubbles. I. INTRODUCTION Helium production and helium bubble evolution in neutron
P. Danielewicz
Examination of symmetry energy is carried out on the basis of an elementary binding-energy formula. Constraints are obtained on the energy value at the normal nuclear density and on the density dependence of the energy at subnormal densities.
${\\mathbb{Z}}_N$ graded discrete Lax pairs and discrete integrable systems
Allan P. Fordy; Pavlos Xenitidis
We introduce a class of ${\\mathbb{Z}}_N$ graded discrete Lax pairs, with $N\\times N$ matrices, linear in the spectral parameter. We give a classification scheme for such Lax pairs and the associated discrete integrable systems. We present two potential forms and completely classify the generic case. Many well known examples belong to our scheme for $N=2$, so many of our systems may be regarded as generalisations of these. Even at $N=3$, several new integrable systems arise. Many of our equations are mutually compatible, so can be used together to form "coloured" lattices. We also present continuous isospectral deformations of our Lax pairs, giving compatible differential-difference systems, which play the role of continuous symmetries of our discrete systems. We present master symmetries and a recursive formulae for their respective hierarchies, for the generic case. We present two nonlocal symmetries of our discrete systems, which have a natural representation in terms of the potential forms. These give rise to the two-dimensional Toda lattice, with our nonlinear symmetries being the B\\"acklund transformations and our discrete system being the nonlinear superposition formula (for the generic case).
Unitary Evolution on a Discrete Phase Space
E. G. Floratos; S. Nicolis
We construct unitary evolution operators on a phase space with power of two discretization. These operators realize the metaplectic representation of the modular group SL(2,Z_{2^n}). It acts in a natural way on the coordinates of the non-commutative 2-torus, T_{2^n}^2$ and thus is relevant for non-commutative field theories as well as theories of quantum space-time. The class of operators may also be useful for the efficient realization of new quantum algorithms.
Investigation of anisotropic metric in multidimensional space-time and generation of additional dimensions by scalar field
Sergey V. Yakovlev
Were investigated anisotropic metric of higher dimensional space-time with only cosmological term and scalar field. Showed, that presence of scalar field is equivalent to anisotropic metric in the multy dimensional space-time and proposed idea of dimensions generation by scalar field. Were solved Einstein's equations for higher dimensional space-time of Kazner's type and derived expressions for density of energy for scalar field, which generate additional dimensions, and proposed the procedure of renormalization of the metric.
Relativistic Spectrum of Hydrogen Atom in Space-Time Non-Commutativity
Mustafa Moumni; Achor BenSlama; Slimane Zaim
We study space-time non-commutativity applied to the hydrogen atom via the Seiberg-Witten map and its phenomenological effects. We find that it modifies the Coulomb potential in the Hamiltonian and add an r-3 part. By calculating the energies from Dirac equation using perturbation theory, we study the modifications to the hydrogen spectrum. We find that it removes the degeneracy with respect to the total angular momentum quantum number and acts like a Lamb shift. Comparing the results with experimental values from spectroscopy, we get a new bound for the space-time non-commutative parameter. N.B: In precedent works (arXiv:0907.1904, arXiv:1003.5732 and arXiv:1006.4590), we have used the Bopp Shift formulation of non-commutativity but here use it \\`a la Seiberg-Witten in the Relativistic case.
Space-time analysis of reactor-control rod-worth measurements
Moreia, J.; Lee, J.C.
An efficient method has been developed to represent the space-time behavior of neutron detector signals in nuclear reactors. The method is based on a simplified solution to the neutron shape function in the framework of a quasi-static approximation to the timedependent diffusion equation. The shape function is obtained as a sum of a modal expansion, representing the global flux perturbations, and a local function, representing the direct perturbations due to reactor parameter changes. The method was applied to the analysis of both integral and differential rod worth measurements obtained at the critical hightemperature gas-cooled reactor test facility, Kahter. The analysis of the Kahter data indicates the applicability of the proposed method in accounting for space-time effects in detector signals.
Geodesic equation in Schwarzschild--(anti-)de Sitter space--times: Analytical solutions and applications
Hackmann, Eva
The complete set of analytic solutions of the geodesic equation in a Schwarzschild--(anti-)de Sitter space--time is presented. The solutions are derived from the Jacobi inversion problem restricted to the set of zeros of the theta function, called the theta divisor. In its final form the solutions can be expressed in terms of derivatives of Kleinian sigma functions. The different types of the resulting orbits are characterized in terms of the conserved energy and angular momentum as well as the cosmological constant. Using the analytical solution, the question whether the cosmological constant could be a cause of the Pioneer Anomaly is addressed. The periastron shift and its post--Schwarzschild limit is derived. The developed method can also be applied to the geodesic equation in higher dimensional Schwarzschild space--times.
Perturbative quantization of two-dimensional space-time noncommutative QED
Ghasemkhani, M.; Sadooghi, N. [Department of Physics, Sharif University of Technology, P.O. Box 11155-9161, Tehran (Iran, Islamic Republic of)
Using the method of perturbative quantization in the first order approximation, we quantize a nonlocal QED-like theory including fermions and bosons whose interactions are described by terms containing higher order space-time derivatives. As an example, the two-dimensional space-time noncommutative QED (NC-QED) is quantized perturbatively up to O(e{sup 2},{theta}{sup 3}), where e is the NC-QED coupling constant and {theta} is the noncommutativity parameter. The resulting modified Lagrangian density is shown to include terms consisting of first order time-derivative and higher order space-derivatives of the modified field variables that satisfy the ordinary equal-time commutation relations up to O(e{sup 2},{theta}{sup 3}). Using these commutation relations, the canonical current algebra of the modified theory is also derived.
On the extension of Newton's second law to theories of gravitation in curved space-time
Mayeul Arminjon
We investigate the possibility of extending Newton's second law to the general framework of theories in which special relativity is locally valid, and in which gravitation changes the flat Galilean space-time metric into a curved metric. This framework is first recalled, underlining the possibility to uniquely define a space metric and a local time in any given reference frame, hence to define velocity and momentum in terms of the local space and time standards. It is shown that a unique consistent definition can be given for the derivative of a vector (the momentum) along a trajectory. Then the possible form of the gravitation force is investigated. It is shown that, if the motion of free particles has to follow space-time geodesics, then the expression for the gravity acceleration is determined uniquely. It depends on the variation of the metric with space and time, and it involves the velocity of the particle.
The Energy Distribution in a Static Spherically Symmetric Nonsingular Black Hole Space-Time
I. Radinschi
We calculate the energy distribution in a static spherically symmetric nonsingular black hole space-time by using the Tolman's energy-momentum complex. All the calculations are performed in quasi-Cartesian coordinates. The energy distribution is positive everywhere and be equal to zero at origin. We get the same result as obtained by Y-Ching Yang by using the Einstein's and Weinberg's prescriptions.
Space-time curvature due to quantum vacuum fluctuations: An alternative to dark energy?
Santos, Emilio
It is pointed out that quantum vacuum fluctuations may give rise to a curvature of space-time equivalent to the curvature currently attributed to dark energy. A simple calculation is made, which suggests that the value of the dark energy density is roughly given by the product of Newton constant time the quantity m^6 c^4 h^-4, m being a typical mass of elementary particles. The estimate is compatible with observations.
Space-time curvature due to quantum vacuum fluctuations: An alternative to dark energy?
Emilio Santos
It is pointed out that quantum vacuum fluctuations may give rise to a curvature of space-time equivalent to the curvature currently attributed to dark energy. A simple calculation is made, which suggests that the value of the dark energy density is roughly given by the product of Newton constant time the quantity m^6 c^4 h^-4, m being a typical mass of elementary particles. The estimate is compatible with observations.
Solution of the space-time reactor kinetics equations using the method of Laplace transforms
Rottler, Jerry Stephen
for the degree of MASTER OF SCIENCE December 1982 Major Subject: Nuclear Engineering SOLUTION OF THE SPACE-TIME REACTOR KINETICS EQUATIONS USING THE METHOD OF LAPLACE TRANSFORMS . A Thesis by JERRY STEPHEN ROTTLER Approved as to style and content by...gated in detail. ACKNOHLEDGEMENT The author would like to express gratitude to several individuals who made this work possible. First, he would like to thank his committee chairman, Dr. Clarence E. Lee, for suggesting this project and for his...
Generalized strong curvature singularities and weak cosmic censorship in cosmological space-times
W. Rudnicki; R. J. Budzynski; W. Kondracki
This paper is a further development of the approach to weak cosmic censorship proposed by the authors in Ref. 5. We state and prove a modified version of that work's main result under significantly relaxed assumptions on the asymptotic structure of space--time. The result, which imposes strong constraints on the occurrence of naked singularities of the strong curvature type, is in particular applicable to physically realistic cosmological models.
Boundary Effects on Bose-Einstein Condensation in Ultra-Static Space-Times
L. Akant; E. Ertugrul; Y. Gul; O. T. Turgut
The boundary effects on the Bose-Einstein condensation of an ideal Bose gas on an ultra-static space-time are studied by a Mellin-Barnes type asymptotic analysis of the harmonic sum representing the depletion coefficient. Small $\\beta m$ regime, which is the relevant regime for the relativistic gas, is studied through the heat kernel expansion for both Dirichlet and Neumann boundary conditions. The analysis is made for both charged bosons and neutral bosons.
Boundary Effects on Bose-Einstein Condensation in Ultra-Static Space-Times
Akant, L; Gul, Y; Turgut, O T
The boundary effects on the Bose-Einstein condensation of an ideal Bose gas on an ultra-static space-time are studied by a Mellin-Barnes type asymptotic analysis of the harmonic sum representing the depletion coefficient. Small $\\beta m$ regime, which is the relevant regime for the relativistic gas, is studied through the heat kernel expansion for both Dirichlet and Neumann boundary conditions. The analysis is made for both charged bosons and neutral bosons.
A Non-Riemannian Metric on Space-Time Emergent From Scalar Quantum Field Theory
Kar, Arnab
We show that the standard deviation \\sigma(x,x') = \\sqrt{} of a scalar quantum field theory is a metric (i.e., a symmetric positive function satisfying the triangle inequality) on space-time (with imaginary time). It is very different from the Euclidean metric |x-x'|: for four dimensional free scalar field theory, \\sigma(x,x') \\to \\frac{\\sigma_{4}}{a^{2}} -\\frac{\\sigma_{4}'}{|x-x'|^{2}} + \\mathrm{O}(|x-x'|^{-3}), as |x-x'|\\to\\infty. According to \\sigma, space-time has a finite diameter \\frac{\\sigma_{4}}{a^{2}} which is not universal (i.e., depends on the UV cut-off a and the regularization method used). The Lipschitz equivalence class of the metric is independent of the cut-off. \\sigma(x,x') is not the length of the geodesic in any Riemannian metric, as it does not have the intermediate point property: for a pair (x,x') there is in general no point x" such that \\sigma(x,x')=\\sigma(x,x")+\\sigma(x",x'). Nevertheless, it is possible to embed space-time in a higher dimensional space of negative curvature so that ...
Stress-energy tensor in colliding plane wave space-times: An approximation procedure
Miquel Dorca
In a recent work on the quantization of a massless scalar field in a particular colliding plane wave space-time, we computed the vacuum expectation value of the stress-energy tensor on the physical state which corresponds to the Minkowski vacuum before the collision of the waves. We did such a calculation in a region close to both the Killing-Cauchy horizon and the folding singularities that such a space-time contains. In the present paper, we give a suitable approximation procedure to compute this expectation value, in the conformal coupling case, throughout the causal past of the center of the collision. This will allow us to approximately study the evolution of such an expectation value from the beginning of the collision until the formation of the Killing-Cauchy horizon. We start with a null expectation value before the arrival of the waves, which then acquires nonzero values at the beginning of the collision and grows unbounded towards the Killing-Cauchy horizon. The value near the horizon is compatible with our previous result, which means that such an approximation may be applied to other colliding plane wave space-times. Even with this approximation, the initial modes propagated into the interaction region contain a function which cannot be calculated exactly and to ensure the correct regularization of the stress-energy tensor with the point-splitting technique, this function must be given up to adiabatic order four of approximation.
Asymptotically Stationary and Static Space-times and Shear-free Null Geodesic Congruences
T. M. Adamo; E. T. Newman
In classical electromagnetic theory, one formally defines the complex dipole moment (the electric plus 'i' magnetic dipole) and then computes (and defines) the complex center of charge by transforming to a complex frame where the complex dipole moment vanishes. Analogously in asymptotically flat space-times it has been shown that one can determine the complex center of mass by transforming the complex gravitational dipole (mass dipole plus 'i' angular momentum) (via an asymptotic tetrad trasnformation) to a frame where the complex dipole vanishes. We apply this procedure to such space-times which are asymptotically stationary or static, and observe that the calculations can be performed exactly, without any use of the approximation schemes which must be employed in general. In particular, we are able to exactly calculate complex center of mass and charge world-lines for such space-times, and - as a special case - when these two complex world-lines coincide, we recover the Dirac value of the gyromagnetic ratio.
TASI Lectures on Holographic Space-Time, SUSY and Gravitational Effective Field Theory
Tom Banks
I argue that the conventional field theoretic notion of vacuum state is not valid in quantum gravity. The arguments use gravitational effective field theory, as well as results from string theory, particularly the AdS/CFT correspondence. Different solutions of the same low energy gravitational field equations correspond to different quantum systems, rather than different states in the same system. I then introduce {\\it holographic space-time} a quasi-local quantum mechanical construction based on the holographic principle. I argue that models of quantum gravity in asymptotically flat space-time will be exactly super-Poincare invariant, because the natural variables of holographic space-time for such a system, are the degrees of freedom of massless superparticles. The formalism leads to a non-singular quantum Big Bang cosmology, in which the asymptotic future is required to be a de Sitter space, with cosmological constant (c.c.) determined by cosmological initial conditions. It is also approximately SUSic in the future, with the gravitino mass $K \\Lambda^{1/4}$.
Cosmological perturbations in the (1+3+6)-dimensional space-times
Kenji Tomita
Cosmological perturbations in the (1+3+6)-dimensional space-times including photon gas without viscous processes are studied on the basis of Abbott et al.'s formalism. Space-times consist of the outer space (the 3-dimensional expanding section) and the inner space (the 6-dimensional section). The inner space expands initially and contracts later. Abbott et al. derived only power-type solutions in the small wave-number limit which appear at the final stage of the space-times. In this paper, we derive not only small wave-number solutions, but also large wave-number solutions. It is found that the latter solutions depend on the two wave-numbers k_r and k_R (which are defined in the outer and inner spaces, respectively), and that the k_r-dependent and k_R-dependent parts dominate the total perturbations when (k_r/r(t))/(k_R/R(t)) >> 1 or spaces. By comparing the behaviors of these perturbations, moreover, changes in the spectrum of perturbations in the outer space with time are discussed.
Field Theory on Newton-Cartan Backgrounds and Symmetries of the Lifshitz Vacuum
Hartong, Jelle; Obers, Niels A
Holography for Lifshitz space-times corresponds to dual field theories on a fixed torsional Newton-Cartan (TNC) background. We examine the coupling of non-relativistic field theories to TNC backgrounds and uncover a novel mechanism by which a global U(1) can become local. This involves the TNC vector $M_\\mu$ which sources a particle number current, and which for flat NC space-time satisfies $M_{\\mu}=\\partial_{\\mu}M$ with a Schroedinger symmetry realized on $M$. We discuss various toy model field theories on flat NC space-time for which the new mechanism leads to extra global space-time symmetries beyond the generic Lifshitz symmetry, allowing for an enhancement to Schroedinger symmetry. On the holographic side, the source $M$ also appears in the Lifshitz vacuum with exactly the same properties as for flat NC space-time. In particular, the bulk diffeomorphisms that preserve the boundary conditions realize a Schroedinger algebra on $M$, allowing for a conserved particle number current. Finally, we present a pro...
- Physics, as we know it, attempts to interpret the diverse natural phenomena as particular manifestations of general laws. This vision of a world ruled by general testable laws is relatively recent in the history of mankind. Basically it was initiated by the Galilean inertial principle. The subsequent rapid development of large-scale physics is certainly tributary to the fact that gravitational and electromagnetic forces are long-range and hence can be perceived directly without the mediation of highly sophisticated technical devices. - The discovery of subatomic structures and of the concomitant weak and strong short-range forces raised the question of how to cope with short-range forces in relativistic quantum field theory. The Fermi theory of weak interactions, formulated in terms of point-like current-current interaction, was well-defined in lowest order perturbation theory and accounted for existing experimental data.However, it was inconsistent in higher orders because of uncontrollable divergent quantum fluctuations. In technical terms, in contradistinction to quantum electrodynamics, the Fermi theorywas not ?renormalizable?. This difficulty could not be solved by smoothing the point-like interaction by a massive, and therefore short-range, charged ?vector? particle exchange: theories with massive charged vector bosons were not renormalizable either. In the early nineteen sixties, there seemed to be insuperable obstacles to formulating a consistent theory with short-range forces mediated by massive vectors. - The breakthrough came from the notion of spontaneous symmetry breaking which arose in the study of phase transitions and was introduced in field theory by Nambu in 1960. - Ferromagnets illustrate the notion in phase transitions. Although no direction is dynamically preferred, the magnetization selects a global orientation. This is a spontaneous broken symmetry(SBS)of rotational invariance. Such continuous SBS imply the existence of ?massless? modes (here spin-waves), which are the ancestors of the NG bosons discussed below. Fluctuations of the order parameter (the magnetization) are described by a ?massive? SBS mode. - In field theory, Nambu showed that broken chiral symmetry from a spontaneous generation of hadron masses induces massless pseudoscalar modes (identified with a massless limit of pion fields). This illustrates a general phenomenon made explicit by Goldstone: massless Nambu-Goldstone (NG) bosons are a necessary concomitant of spontaneously broken continuous symmetries. Massive SBS scalars bosons describe, as in phase transitions, the fluctuations of the SBS order parameters. - In 1964, with Robert Brout, we discovered a mechanism based on SBS by which short range interactions are generated from long range ones. A similar proposal was then made independently by Higgs in a different approach. Qualitatively, our mechanism works as follows. The long range fundamental electromagnetic and gravitational interactions are governed by extended symmetries,called gauge symmetries, which were supposed to guarantee that the elementary field constituents which transmit the forces, photons or gravitons, be massless. We considered a generalization of the electromagnetic ?vector? field, known as Yang-Mills fields, and coupled them to fields which acquire from SBS constant values in the vacuum. These fields pervade space, as did magnetization, but they have no spatial orientation: they are ?scalar?? fields. The vector Yang-Mills fields which interact with the scalar fields become massive and hence the forces they mediate become short ranged. We also showed that the mechanism can survive in absence of elementary scalar fields. - Because of the extended symmetries, the nature of SBS is profoundly altered: the NG fields are absorbed into the massive vector Yang-Mills fields and restore the gauge symmetry. This has a dramatic consequence. To confront precision experiments, the mechanism should be consistent at the quantum mechanical level, or in technical terms, should yield a ?renormalizable? theory. From our analysi
A covariantly foliated higher dimensional space-time: Implications for short distance gravity and BSM physics
Cao H. Nam
We consider the space-time at short distances in which it is described by a $D$-dimensional manifold (bulk) carrying out the principal bundle structure. As a result, this space-time manifold is foliated in the covariant way by the $(D-4)$-dimensional submanifolds, realized as the space-like internal spaces, that are smooth copies of the Lie group $G$ considered in this paper as the special unitary group. The submanifolds being transversal to the internal spaces are realized as the external spaces and in fact identified as the usual $4$-dimensional world. The fundamental degrees of freedom determining the geometrical dynamics of the bulk corresponding with short distance gravity are given by the gauge fields, the external metric field and the modulus fields setting dynamically the volume of the internal spaces. These gauge fields laying the bulk is to point precisely out the local directions of the external spaces which depend on the topological non-triviality of the space-time principal bundle. The physical size of the internal spaces is fixed dynamically by the moduli stabilization potential which completely arise from the intrinsic geometry of the bulk. A detail description of the low energy bulk gravity in the weak field limit is given around the classical ground state of the bulk. Additionally, we investigate the dynamics of the fundamentally $4$-dimensional Weyl spinor fields and the fields of carrying out the non-trivial representations of the Lie group $G$ propagating in the bulk in a detail study. These results suggest naturally the possible solutions to some the experimental problems of Standard Model, the smallness of the observed neutrino masses and a dark matter candidate.
Infrared problem for the Nelson model on static space-times
Christian G�rard; Fumio Hiroshima; Annalisa Panati; Akito Suzuki
We consider the Nelson model with variable coefficients and investigate the problem of existence of a ground state and the removal of the ultraviolet cutoff. Nelson models with variable coefficients arise when one replaces in the usual Nelson model the flat Minkowski metric by a static metric, allowing also the boson mass to depend on position. A physical example is obtained by quantizing the Klein-Gordon equation on a static space-time coupled with a non-relativistic particle. We investigate the existence of a ground state of the Hamiltonian in the presence of the infrared problem, i.e. assuming that the boson mass tends to 0 at infinity.
Clock rates, clock settings and the physics of the space-time Lorentz transformation
J. H. Field
A careful study is made of the operational meaning of the time symbols appearing in the space-time Lorentz transformation. Four distinct symbols, with different physical meanings, are needed to describe reciprocal measurements involving stationary and uniformly-moving clocks. Physical predictions concern only the observed rate of a clock as a function of its relative speed, not its setting. How the failure to make this distinction leads to the conventional predictions of spurious `relativity of simultaneity' and `length contraction' effects in special relativity is explained.
Biquaternion Electrodynamics and Weyl-Cartan Geometry of Space-Time
V. V. Kassandrov
The generalized Cauchy-Riemann equations (GCRE) in biquaternion algebra appear to be Lorentz-invariant. The Laplace equation is in this case replaced by a nonlinear (complexified) eikonal equation. GCRE contain the 2-spinor and the gauge structures, and their integrability conditions take the form of free-source Maxwell and Yang-Mills equations. For the value of electric charge from GCRE only the quantization rule follows, as well as the treatment of Coulomb law as a stereographic map. The equivalent geometrodynamics in a Weyl-Cartan affine space and the conjecture of a complex-quaternion structure of space-time are discussed.
Fuzzy Geometry via the Spinor Bundle, with Applications to Holographic Space-time and Matrix Theory
Tom Banks; John Kehayias
We present a new framework for defining fuzzy approximations to geometry in terms of a cutoff on the spectrum of the Dirac operator, and a generalization of it that we call the Dirac-Flux operator. This framework does not require a symplectic form on the manifold, and is completely rotation invariant on an arbitrary n-sphere. The framework is motivated by the formalism of Holographic Space-Time (HST), whose fundamental variables are sections of the spinor bundle over a compact Euclidean manifold. The strong holographic principle (SHP) requires the space of these sections to be finite dimensional. We discuss applications of fuzzy spinor geometry to HST and to Matrix Theory.
Knot Topology of Vacuum Space-Time and Vacuum Decomposition of Einstein's Theory
Y. M. Cho; Franklin H. Cho
Viewing Einstein's theory as the gauge theory of Lorentz group, we construct the most general vacuum connections which have vanishing curvature tensor and show that the vacuum space-time can be classified by the knot topology $\\pi_3(S^3)\\simeq \\pi_3(S^2)$ of $\\pi_3(SO(3,1))$. With this we obtain the gauge independent vacuum decomposition of Einstein's theory to the vacuum and gauge covariant physical parts. We discuss the physical implications of our result in quantum gravity.
Strings in Background Electric Field, Space/Time Noncommutativity and A New Noncritical String Theory
N. Seiberg; L. Susskind; N. Toumbas
Searching for space/time noncommutativity we reconsider open strings in a constant background electric field. The main difference between this situation and its magnetic counterpart is that here there is a critical electric field beyond which the theory does not make sense. We show that this critical field prevents us from finding a limit in which the theory becomes a field theory on a noncommutative spacetime. However, an appropriate limit toward the critical field leads to a novel noncritical string theory on a noncommutative spacetime.
Energy of gravitational radiation in plane-symmetric space-times
Sean A. Hayward
Gravitational radiation in plane-symmetric space-times can be encoded in a complex potential, satisfying a non-linear wave equation. An effective energy tensor for the radiation is given, taking a scalar-field form in terms of the potential, entering the field equations in the same way as the matter energy tensor. It reduces to the Isaacson energy tensor in the linearized, high-frequency approximation. An energy conservation equation is derived for a quasi-local energy, essentially the Hawking energy. A transverse pressure exerted by interacting low-frequency gravitational radiation is predicted.
Fractal space-times under the microscope: A Renormalization Group view on Monte Carlo data
Martin Reuter; Frank Saueressig
The emergence of fractal features in the microscopic structure of space-time is a common theme in many approaches to quantum gravity. In this work we carry out a detailed renormalization group study of the spectral dimension $d_s$ and walk dimension $d_w$ associated with the effective space-times of asymptotically safe Quantum Einstein Gravity (QEG). We discover three scaling regimes where these generalized dimensions are approximately constant for an extended range of length scales: a classical regime where $d_s = d, d_w = 2$, a semi-classical regime where $d_s = 2d/(2+d), d_w = 2+d$, and the UV-fixed point regime where $d_s = d/2, d_w = 4$. On the length scales covered by three-dimensional Monte Carlo simulations, the resulting spectral dimension is shown to be in very good agreement with the data. This comparison also provides a natural explanation for the apparent puzzle between the short distance behavior of the spectral dimension reported from Causal Dynamical Triangulations (CDT), Euclidean Dynamical Triangulations (EDT), and Asymptotic Safety.
Self-force on an arbitrarily coupled static scalar particle in a wormhole space-time
Peter Taylor
In this paper, we consider the problem of computing the self-force and self-energy for a static scalar charge in a wormhole space-time with throat profile $r(\\rho)=\\sqrt{\\rho^{2}+a^{2}}$ for arbitrary coupling of the field to the curvature. This calculation has previously been considered numerically by Bezerra and Khusnutdinov, while analytic results have been obtained in the special cases of minimal ($\\xi=0$) coupling and conformal coupling ($\\xi=1/8$ in three dimensions). We present here a closed form expression for the static Green's function for arbitrary coupling and hence we obtain an analytic expression for the self-force. The self-force depends crucially on the coupling of the field to the curvature of the space-time and hence it is useful to determine the dependence explicitly. The numerical computation can identify some qualitative aspects of this dependence such as the change in the sign of the force as it passes through the conformally coupled value, as well as the fact that the self-force diverges for $\\xi=1/2$. From the closed form expression, it is straight-forward to see that there is an infinite set of values of the coupling constant for which the self-force diverges, but we also see that there is an infinite set of values for which the self-force vanishes.
Spectrum of Hydrogen Atom in Space-Time Non-Commutativity
M. Moumni; A. BenSlama; S. Zaim
We study space-time noncommutativity applied to the hydrogen atom and its phenomenological effects. We find that it modifies the potential part of the Hamiltonian in such a way we get the Kratzer potential instead of the Coulomb one and this is similar to add a dipole potential or to consider the extended charged nature of the proton in the nucleus. By calculating the energies from the Schr\\"odinger equation analytically and computing the fine structure corrections using perturbation theory, we study the modifications of the hydrogen spectrum. We find that it removes the degeneracy with respect to both the orbital quantum number l and the total angular momentum quantum number j; it acts here like a Lamb shift. Comparing the results with the experimental values from spectroscopy, we get a new bound for the space-time non-commutative parameter. We do the same perturbative calculation for the relativistic case and compute the corrections of the Dirac energies; we find that in this case too, the corrections are similar to a Lamb shift and they remove the degeneracy with respect to j ; we get an other bound for the parameter of non-commutativity.
QFT, String Temperature and the String Phase of de Sitter Space-time
Medrano, M R
The density of mass levels \\rho(m) and the critical temperature for strings in de Sitter space-time are found. QFT and string theory in de Sitter space are compared. A `Dual'-transform is introduced which relates classical to quantum string lengths, and more generally, QFT and string domains. Interestingly, the string temperature in De Sitter space turns out to be the Dual transform of the QFT-Hawking-Gibbons temperature. The back reaction problem for strings in de Sitter space is addressed selfconsistently in the framework of the `string analogue' model (or thermodynamical approach), which is well suited to combine QFT and string study.We find de Sitter space-time is a self-consistent solution of the semiclassical Einstein equations in this framework. Two branches for the scalar curvature R(\\pm) show up: a classical, low curvature solution (-), and a quantum high curvature solution (+), enterely sustained by the strings. There is a maximal value for the curvature R_{\\max} due to the string back reaction. Int...
Spherically symmetric curved space times from quantum fields backreaction corrections in two dimensional analogue
Hossein Ghaffarnejad
Aim of the paper is to obtain 2d analogue of the backreaction equation which will be useful to study final state of quantum perturbed spherically symmetric curved space times. Thus we take Einstein-massless-scalar $\\psi$ tensor gravity model described on class of spherically symmetric curved space times. We rewrite the action functional in 2d analogue in terms of dimensionless dilaton-matter field $(\\chi=\\Phi\\psi)$ where dilaton field $\\Phi$ is conformal factor of 2-sphere. Then we seek renormalized expectation value of quantum dilaton-matter field stress tensor operator by applying Hadamard rennormalization prescription. Singularity of the Green function is assumed to be has logarithmic form. Covariantly conservation condition on the renormalized quantum dilaton-matter stress tensor demands to input a variable cosmological parameter $\\lambda(x)$. Energy conditions (weak, strong and null) is studied on the obtained renormalized stress tensor leading to dynamical equations for $\\lambda(x), \\Phi$ and quantum vacuum state $W_0(x)=_{ren}.$ In weak quantum field limits our obtained trace anomaly corresponds to one which obtained from zeta function regularization method. Setting null-like apparent horizon equation $\
3526 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 7, NO. 9, SEPTEMBER 2008 Hierarchical Space-Time Block Code Recognition
Brest, Université de
at low signal-to-noise ratios. Index Terms--MIMO, space-time coding, electronic warfare. I. INTRODUCTION electronic warfare, surveillance and threat analysis. Some algorithms devoted to the blind recognition
Space-time power schedule for distributed MIMO links without instantaneous channel state information at the transmitting nodes
Rong, Yue; Hua, Yingbo; Swami, Ananthram; Swindlehurst, A. Lee
We have proposed a space�time optimal power schedulingin [4]�[7]. In [4], a space-only (i.e. , time-invariant)are all and . Scheme A5 space-only schemes. Here, RONG et
Classical Gluon Radiation in Ultrarelativistic Nuclear Collisions: Space-Time Structure, Instabilities, and Thermalization
S. G. Matinyan; B. Mueller; D. H. Rischke
We investigate the space-time structure of the classical gluon field produced in an ultrarelativistic collision between color charges. The classical solution which was computed previously in a perturbative approach is shown to become unstable on account of the non-Abelian self-interaction neglected in the perturbative solution scheme. The time scale for growth of the instabilities is found to be of the order of the distance between the colliding color charges. We argue that these instabilities will eventually lead to thermalization of gluons produced in an ultrarelativistic collision between heavy nuclei. The rate of thermalization is estimated to be of order $g^2 \\mu$, where $g$ is the strong coupling constant and $\\mu^2$ the transverse color charge density of an ultrarelativistic nucleus.
Energy dependence of space-time extent of pion source in nuclear collisions
Okorokov, V A
Energy dependence of space-time parameters of pion emission region at freeze-out is studied for collisions of various ions and for all experimentally available energies. The using of femtoscopic radii scaled on the averaged radius of colliding ions is suggested. This approach allows the expansion of the set of interaction types, in particular, on collisions of non-symmetrical ion beams which can be studied within the framework of common treatment. There is no sharp changing of femtoscopic parameter values with increasing of initial energy. Analytic functions suggested for smooth approximations of energy dependence of femtoscopic parameters demonstrate reasonable agreement with most of experimental data at $\\sqrt{s_{NN}} \\geq 5$ GeV. Estimations of some observables are obtained for energies of the LHC and FCC project.
Renormalized Free Energy on Space-time with Compact Hyperbolic Spatial Part
Rosevaldo de Oliveira
In this paper we found the renormalized free energy of a interacting scalar field on a compact hyperbolic manifold explicitly. We have shown a complete expression of the free energy and entropy as a function of the curvature and the temperature. Carefully analyzing the free energy we have shown that there exist a minimum with respect to the curvature that depend on the temperature. The principle of minimum free energy give us an estimate of the connection between stationary curvature and temperature. As a result we obtain that the stationary curvature increases when the temperature increases too. If we start from an universe with very high curvature and temperature in the beginning, because of the principle of minimum free energy, the universe will reach a new situation of equilibrium for low temperature and low curvature. Consequently, the flat space-time is obtained for low temperature.
Five-Dimensional Tangent Vectors in Space-Time: IV. Generalization of Exterior Calculus
Alexander Krasulin
This part of the series is devoted to the generalization of exterior differential calculus. I give definition to the integral of a five-vector form over a limited space-time volume of appropriate dimension; extend the notion of the exterior derivative to the case of five-vector forms; and formulate the corresponding analogs of the generalized Stokes theorem and of the Poincare theorem about closed forms. I then consider the five-vector generalization of the exterior derivative itself; prove a statement similar to the Poincare theorem; define the corresponding five-vector generalization of flux; and derive the analog of the formula for integration by parts. I illustrate the ideas developed in this paper by reformulating the Lagrange formalism for classical scalar fields in terms of five-vector forms. In conclusion, I briefly discuss the five-vector analog of the Levi-Civita tensor and dual forms.
Energy dependence of space-time extent of pion source in nuclear collisions
V. A. Okorokov
Energy dependence of space-time parameters of pion emission region at freeze-out is studied for collisions of various ions and for all experimentally available energies. The using of femtoscopic radii scaled on the averaged radius of colliding ions is suggested. This approach allows the expansion of the set of interaction types, in particular, on collisions of non-symmetrical ion beams which can be studied within the framework of common treatment. There is no sharp changing of femtoscopic parameter values with increasing of initial energy. Analytic functions suggested for smooth approximations of energy dependence of femtoscopic parameters demonstrate reasonable agreement with most of experimental data at $\\sqrt{s_{NN}} \\geq 5$ GeV. Estimations of some observables are obtained for energies of the LHC and FCC project.
The causal structure of Minkowski space time: possibilities and impossibilities of secure positioning
Muhammad Nadeem
Secure positioning, a prover located at a specified position convinces a set of verifiers at distant reference stations that he/she is indeed at the specific position, is considered to be impossible if the prover and verifiers have no pre-shared data while dishonest provers have an arbitrary amount of pre-shared entanglement [Nature 479, 307-308 (2011)]. We argue here that current impossibility results for secure positioning are the upshot of not utilizing full powers of relativistic quantum information theory and show that secure positioning and hence position-based quantum cryptography is possible if causal structure of Minkowski space time and quantum non-locality is used properly.
Higher Dimensional Szekeres' Space-time in Brans-Dicke Scalar Tensor Theory
Asit Banerjee; Ujjal Debnath; Subenoy Chakraborty
The generalized Szekeres family of solution for quasi-spherical space-time of higher dimensions are obtained in the scalar tensor theory of gravitation. Brans-Dicke field equations expressed in Dicke's revised units are exhaustively solved for all the subfamilies of the said family. A particular group of solutions may also be interpreted as due to the presence of the so-called C-field of Hoyle and Narlikar and for a chosen sign of the coupling parameter. The models show either expansion from a big bang type of singularity or a collapse with the turning point at a lower bound. There is one particular case which starts from the big bang, reaches a maximum and collapses with the in course of time to a crunch.
Holographic Space-time and Black Holes: Mirages As Alternate Reality
Tom Banks; Willy Fischler; Sandipan Kundu; Juan F. Pedraza
We revisit our investigation of the claim of [1] that old black holes contain a firewall, i.e. an in-falling observer encounters highly excited states at a time much shorter than the light crossing time of the Schwarzschild radius. We used the formalism of Holographic Space-time (HST) where there is no dramatic change in particle physics inside the horizon until a time of order the Schwarzschild radius. We correct our description of the interior of the black hole . HST provides a complete description of the quantum mechanics along any time-like trajectory, even those which fall through the black hole horizon. The latter are described as alternative factorizations of the description of an external observer, turning the mirage of the interior provided by that observer's membrane paradigm on the stretched horizon, into reality.
Doppler Effects from Bending of Light Rays in Curved Space-Times
Matteo Luca Ruggiero; Angelo Tartaglia; Lorenzo Iorio
We study Doppler effects in curved space-time, i.e. the frequency shifts induced on electromagnetic signals propagating in the gravitational field. In particular, we focus on the frequency shift due to the bending of light rays in weak gravitational fields. We consider, using the PPN formalism, the gravitational field of an axially symmetric distribution of mass. The zeroth order, i.e. the sphere, is studied then passing to the contribution of the quadrupole moment, and finally to the case of a rotating source. We give numerical estimates for situations of physical interest, and by a very preliminary analysis, we argue that analyzing the Doppler effect could lead, in principle, in the foreseeable future, to the measurement of the quadrupole moment of the giant planets of the Solar System.
Cosmological entropy production and viscous processes in the (1+3+6)-dimensional space-times
Kenji Tomita
The cosmological entropy production is studied in the (1+3+6)-dimensional space-times consisting of the outer space (the 3-dimensional expanding section) and the inner space (the 6-dimensional section). The inner space expands initially and contracts later. First it is shown how the production of the 3-dimensional entropy S_3 within the horizon is strengthened by the dissipation due to viscous processes between the two spaces, in which we consider the viscosity caused by the gravitational-wave transport. Next it is shown under what conditions we can have the critical epoch when S_3 reaches the value 10^{88} in the Guth level and at the same time the outer space is decoupled from the inner space. Moreover, the total entropy S_9 in the 9-dimensional space at the primeval expanding stage is also shown corresponding to S_3.
The geometry of the space-time and motion of the spinning bodies
Kostadin Trencevski
In this paper an alternative theory about space-time is given. First some preliminaries about 3-dimensional time and the reasons for its introduction are presented. Alongside the 3-dimensional space (S) the 3-dimensional space of spatial rotations (SR) is considered independently from the 3-dimensional space. Then it is given a model of the universe, based on the Lie groups of real and complex orthogonal 3x3 matrices in this 3+3+3-dimensional space. Special attention is dedicated for introduction and study of the space SxSR, which appears to be isomorphic to SO(3,R)xSO(3,R) or S^3xS^3. The influence of the gravitational acceleration to the spinning bodies is considered. Some important applications of these results about spinning bodies are given, which naturally lead to violation of Newton's third law in its classical formulation. The precession of the spinning axis is also considered.
Origin of matter and space-time in the big bang
Mathews, G. J. [University of Notre Dame, Center for Astrophysics/JINA, Notre Dame, IN 46556, USA and Division of Theoretical Astronomy, National Astronomical Observatory of Japan, Mitaka, Tokyo 181-8588 (Japan); Kajino, T. [Division of Theoretical Astronomy, National Astronomical Observatory of Japan, Mitaka, Tokyo 181-8588, Japan and Department of Astronomy, Graduate School of Science, University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113-0033 (Japan); Yamazaki, D. [Division of Theoretical Astronomy, National Astronomical Observatory of Japan, Mitaka, Tokyo 181-8588 (Japan); Kusakabe, M. [School of Liberal Arts and Science, Korea Aerospace University, Goyang 412-791, Korea and Department of Physics, Soongsil University, Seoul 156-743 (Korea, Republic of); Cheoun, M.-K. [Department of Physics, Soongsil University, Seoul 156-743 (Korea, Republic of)
We review the case for and against a bulk cosmic motion resulting from the quantum entanglement of our universe with the multiverse beyond our horizon. Within the current theory for the selection of the initial state of the universe from the landscape multiverse there is a generic prediction that pre-inflation quantum entanglement with other universes should give rise to a cosmic bulk flow with a correlation length of order horizon size and a velocity field relative to the expansion frame of the universe. Indeed, the parameters of this motion are are tightly constrained. A robust prediction can be deduced indicating that there should be an overall motion of of about 800 km/s relative to the background space time as defined by the cosmic microwave background (CMB). This talk will summarize the underlying theoretical motivation for this hypothesis. Of course our motion relative to the background space time (CMB dipole) has been known for decades and is generally attributed to the gravitational pull of the local super cluster. However, this cosmic peculiar velocity field has been recently deduced out to very large distances well beyond that of the local super cluster by using X-ray galaxy clusters as tracers of matter motion. This is achieved via the kinematic component of the Sunyaev-Zeldovich (KSZ) effect produced by Compton scattering of cosmic microwave background photons from the local hot intracluster gas. As such, this method measures peculiar velocity directly in the frame of the cluster. Similar attempts by our group and others have attempted to independently assess this bulk flow via Type la supernova redshifts. In this talk we will review the observation case for and against the existence of this bulk flow based upon the observations and predictions of the theory. If this interpretation is correct it has profound implications in that we may be observing for the first time both the physics that occurred before the big bang and the existence of the multiverse beyond our horizon.
Generalized discrete orbit function transforms of affine Weyl groups
Tomasz Czy?ycki; Ji?� Hrivn�k
The affine Weyl groups with their corresponding four types of orbit functions are considered. Two independent admissible shifts, which preserve the symmetries of the weight and the dual weight lattices, are classified. Finite subsets of the shifted weight and the shifted dual weight lattices, which serve as a sampling grid and a set of labels of the orbit functions, respectively, are introduced. The complete sets of discretely orthogonal orbit functions over the sampling grids are found and the corresponding discrete Fourier transforms are formulated. The eight standard one-dimensional discrete cosine and sine transforms form special cases of the presented transforms.
CMB B-modes, spinorial space-time and Pre-Big Bang (II)
Luis Gonzalez-Mestres
The BICEP2 collaboration reported recently a B-mode polarization of the cosmic microwave background (CMB) radiation inconsistent with the null hypothesis at a significance of > 5 {\\sigma}. This result has been often interpreted as a signature of primordial gravitational waves from cosmic inflation, even if actually polarized dust emission may be at the origin of such a signal. Even assuming that part of this CMB B-mode polarization really corresponds to the early Universe dynamics, its interpretation in terms of inflation and primordial gravitational waves is not the only possible one. Alternative cosmologies such as pre-Big Bang patterns and the spinorial space-time (SST) we introduced in 1996-97 can naturally account for such CMB B-modes. In particular, the SST automatically generates a privileged space direction (PSD) whose existence may have been confirmed by Planck data. If such a PSD exists, it seems normal to infer that vector perturbations have been present in the early Universe leading to CMB B-modes in suitable cosmological patterns. Inflation would not be required to explain the BICEP2 result assuming it really contains a primordial signal. More generally, pre-Big Bang cosmologies can also generate gravitational waves in the early Universe without any need for cosmic inflation. We further discuss here possible alternatives to the inflationary interpretation of a primordial B-mode polarization of cosmic microwave background radiation.
Spinning particles in vacuum space-times of different curvature types -- I
Semer�k, O
We consider the motion of spinning test particles with non-zero rest mass in the "pole-dipole" approximation, as described by the Mathisson--Papapetrou--Dixon (MPD) equations, and examine its properties in dependence on the spin supplementary condition added to close the system and on algebraic type of curvature. The MPD equation of motion is first decomposed in the orthonormal tetrad whose time-like vector is given by the four-velocity $V^\\mu$ fixing the spin condition (the "reference observer") and the first spatial vector by the corresponding spin $s^\\mu$; such MPD-equation projections do not contain the Weyl scalars $\\Psi_0$ and $\\Psi_4$ obtained in the related Newman--Penrose null tetrad. One natural option how to choose the remaining two spatial basis vectors, is shown to follow "intrinsically" whenever the reference observer $V^\\mu$ has been chosen; it is realizable if the particle's four-velocity and four-momentum are not parallel. In order to discuss the problem in dependence on space-time Petrov typ...
From Dirac theories in curved space-times to a Variation of Dirac's large-number hypothesis
U. D. Jentschura
An overview is given of recent developments in the field of Dirac equations generalized to curved space-times. An illustrative discussion is provided. We conclude with a variation of Dirac's large-number hypothesis which relates a number of physical quantities on cosmological scales.
Dr. Shih-Lung Shaw, Department of Geography, UTK A Space-Time GIS for Analyzing Human Activities
Wang, Xiaorui "Ray"
Dr. Shih-Lung Shaw, Department of Geography, UTK A Space-Time GIS for Analyzing Human Activities and Interactions in Physical and Virtual Spaces Shih-Lung Shaw, Ph.D. Department of Geography University. Shih-Lung Shaw, Department of Geography, UTK "Imagine that your business had a complete log of your
Morris, J; Johnson, S
The Distinct Element Method (also frequently referred to as the Discrete Element Method) (DEM) is a Lagrangian numerical technique where the computational domain consists of discrete solid elements which interact via compliant contacts. This can be contrasted with Finite Element Methods where the computational domain is assumed to represent a continuum (although many modern implementations of the FEM can accommodate some Distinct Element capabilities). Often the terms Discrete Element Method and Distinct Element Method are used interchangeably in the literature, although Cundall and Hart (1992) suggested that Discrete Element Methods should be a more inclusive term covering Distinct Element Methods, Displacement Discontinuity Analysis and Modal Methods. In this work, DEM specifically refers to the Distinct Element Method, where the discrete elements interact via compliant contacts, in contrast with Displacement Discontinuity Analysis where the contacts are rigid and all compliance is taken up by the adjacent intact material.
Universal adiabatic quantum computation via the space-time circuit-to-Hamiltonian construction
David Gosset; Barbara M. Terhal; Anna Vershynina
We show how to perform universal adiabatic quantum computation using a Hamiltonian which describes a set of particles with local interactions on a two-dimensional grid. A single parameter in the Hamiltonian is adiabatically changed as a function of time to simulate the quantum circuit. We bound the eigenvalue gap above the unique groundstate by mapping our model onto the ferromagnetic XXZ chain with kink boundary conditions; the gap of this spin chain was computed exactly by Koma and Nachtergaele using its $q$-deformed version of SU(2) symmetry. We also discuss a related time-independent Hamiltonian which was shown by Janzing to be capable of universal computation. We observe that in the limit of large system size, the time evolution is equivalent to the exactly solvable quantum walk on Young's lattice.
Discrete Symmetry in the EPRL Model and Neutrino Physics
Louis Crane
In \\cite{C1}, we proposed a new interpretation of the EPRL quantization of the BC model for quantum general relativity using a monoidal functor we call the time functor. In this preliminary draft we apply the theory of modules over monoidal functors \\cite{Y1} to the time functor, to propose an extension of the EPRL model which would include the standard model. This is motivated by recent advances in neutrino Physics.
$K_S$ semileptonic decays and test of $\\mathcal{CPT}$ symmetry with the KLOE detector
D. Kami?ska
Study of semileptonic decays of neutral kaons allows to perform a test of discrete symmetries, as well as basic principles of the Standard Model. In this paper a general review on dependency between charge asymmetry constructed for semileptonic decays of short- and long-lived kaons and $\\mathcal{CPT}$ symmetry is given.
Gupalo, D.; Kaganovich, A.S.; Cohen, E.G.D. (Rockefeller Univ., New York, NY (United States))
The symmetry of the spectrum of Lyapunov exponents provides a useful quantitative connection between properties of dynamical systems consisting of N interacting particles coupled to a thermostat, and nonequilibrium statistical mechanics. The authors obtain here sufficient conditions for this symmetry and analyze the structure of 1/N corrections ignored in previous studies. The relation of the Lyapunov spectrum symmetry with some other symmetries of dynamical systems is discussed.
Noncommutative Geometry and a Discretized Version of Kaluza-Klein Theory with a Finite Field Content
Nguyen Ai Viet; Kameshwar C. Wali
We consider a four-dimensional space-time supplemented by two discrete points assigned to a $Z_2$ algebraic structure and develop the formalism of noncommutative geometry. By setting up a generalised vielbein, we study the metric structure. Metric compatible torsion free connection defines a unique finite field content in the model and leads to a discretized version of Kaluza-Klein theory. We study some special cases of this model that illustrate the rich and complex structure with massive modes and the possible presence of a cosmological constant.
Majorana-Oppenheimer approach to Maxwell electrodynamics in Riemannian space-time
Bogush, A; Tokarevskaya, N; Spix, G
The Riemann -- Silberstein -- Majorana -- Oppengeimer approach to the Maxwell electrodynamics in presence of electrical sources and arbitrary media is investigated within the matrix formalism. The symmetry of the matrix Maxwell equation under transformations of the complex rotation group SO(3.C) is demonstrated explicitly. In vacuum case, the matrix form includes four real $4 \\times 4$ matrices $\\alpha^{b}$. In presence of media matrix form requires two sets of $4 \\times 4$ matrices, $\\alpha^{b}$ and $\\beta^{b}$ -- simple and symmetrical realization of which is given. Relation of $\\alpha^{b}$ and $\\beta^{b}$ to the Dirac matrices in spinor basis is found. Minkowski constitutive relations in case of any linear media are given in a short algebraic form based on the use of complex 3-vector fields and complex orthogonal rotations from SO(3.C) group. The matrix complex formulation in the Esposito's form, based on the use of two electromagnetic 4-vector, is studied and discussed. Extension of the 3-vector complex m...
Effect of the electric field on the creation of fermions in de-Sitter space-time
Haouat, S
The effect of the electric field on the creation of spin 1/2 particles from vacuum in the (1+1) dimensional de-Sitter space-time is studied. The Dirac equation with a constant electric field is solved by introducing an unitary transformation. Then the canonical method based on Bogoliubov transformation is applied to calculate the pair creation probability and the density of created particles both for positive or negative wave vector. By doing summation over all allowed states, the number of created particles per unit of time per unit of length and the imaginary part of the Schwinger effective action are expressed in closed forms. It is shown that the electric field leads to a significant enhancement of the particle creation. The weak expansion case and the limit H=0, where dS space reduces to the flat Minkowski space-time, are discussed.
N = 2 superconformal algebra in NSR string and Gepner approach to space-time supersymmetry in ten dimensions
Belavin, Alexander
The fermionic NSR string possesses a hidden N = 2 superconformal algebra on the world-sheet. In this work, we show how to use an isomorphism of this algebra, the so-called spectral flow, for construction of a subspace of physical states of the string, on which space-time supersymmetry acts. This construction is an alternative to the GSO-projection in string theory.
Evolution of Crustal Magnetic Fields in Isolated Neutron Stars : Combined Effects of Cooling and Curvature of Space-time
Sujan Sengupta
The ohmic decay of magnetic fields confined within the crust of neutron stars is considered by incorporating both the effect of neutron star cooling and the effect of space-time curvature produced by the intense gravitational field of the star. For this purpose a stationary and static gravitational field has been considered with the standard as well as the accelerated cooling models of neutron stars. It is shown that general relativistic effect reduces the magnetic field decay rate substantially. At the late stage of evolution when the field decay is mainly determined by the impurity-electron scattering, the effect of space-time curvature suppresses the role of the impurity content significantly and reduces the decay rate by more than an order of magnitude. Even with a high impurity content the decay rate is too low to be of observational interest if the accelerated cooling model along with the effect of space-time curvature is taken into account. It is, therefore, pointed out that if a decrease in the magnetic field strength by more than two orders of magnitude from its initial value is detected by observation then the existence of quark in the core of the neutron star would possibly be ruled out.
A discrete fractional random transform
Zhengjun Liu; Haifa Zhao; Shutian Liu
We propose a discrete fractional random transform based on a generalization of the discrete fractional Fourier transform with an intrinsic randomness. Such discrete fractional random transform inheres excellent mathematical properties of the fractional Fourier transform along with some fantastic features of its own. As a primary application, the discrete fractional random transform has been used for image encryption and decryption.
Discrete Fourier Transform Javier Montoya
Giger, Christine
Discrete Fourier Transform Javier Montoya Photogrammetry and Remote Sensing ETH Zurich March 16, 2012 1 Introduction The Discrete form of the Fourier transform is known as Discrete Fourier Transform domain using the Inverse Discrete Fourier Transform (IDFT): f(x) = 1 N N-1 x=0 F(u)ej 2 N ux for u = 0, 1
Topological classification of crystalline insulators with space group symmetry
Jadaun, Priyamvada [University of Texas at Austin; Xiao, Di [Carnegie Mellon University (CMU); Niu, Q. [University of Texas at Austin; Banerjee, Sanjay K. [University of Texas at Austin
We show that in crystalline insulators, space group symmetry alone gives rise to a topological classification based on the discretization of electric polarization. Using C3 rotational symmetry as an example, we first prove that the polarization is discretized into three distinct classes, i.e., it can only take three inequivalent values. We then prove that these classes are topologically distinct. Therefore, a Z3 topological classification exists, with polarization as a topological class index. A concrete tight-binding model is derived to demonstrate the Z3 topological phase transition. Using first-principles calculations, we identify graphene on a BN substrate as a possible candidate to realize these Z3 topological states. To complete our analysis, we extend the classification of band structures to all 17 two-dimensional space groups. This work will contribute to a complete theory of symmetry-conserved topological phases and also elucidate topological properties of graphenelike systems.
BLIND SYMBOL IDENTIFIABILITY OF ORTHOGONAL SPACE-TIME BLOCK CODES Wing-Kin Ma , P.C. Ching , T. N. Davidson, and B.-N. Vo
Davidson, Tim
BLIND SYMBOL IDENTIFIABILITY OF ORTHOGONAL SPACE-TIME BLOCK CODES Wing-Kin Ma , P.C. Ching , T. N Hamilton, Ont., Canada Parksville, Vic., Australia ABSTRACT This paper addresses the blind symbol. In many space-time communication schemes, achieving unique blind symbol identification requires certain
Space-time properties of Gram-Schmidt vectors in classical Hamiltonian evolution Jason R. Green,1,2,3,* Julius Jellinek,2,
Berry, R. Stephen
Space-time properties of Gram-Schmidt vectors in classical Hamiltonian evolution Jason R. Green,1 tangent space directions play equivalent roles in the local chaotic motions of classical Hamiltonian many vectors, whose statistical properties may depend on the chosen phase space-time domain of a trajec- tory
Discrete KP equation with self-consistent sources
Adam Doliwa; Runliang Lin
We show that the discrete Kadomtsev-Petviashvili (KP) equation with sources obtained recently by the "source generalization" method can be incorporated into the squared eigenfunction symmetry extension procedure. Moreover, using the known correspondence between Darboux-type transformations and additional independent variables, we demonstrate that the equation with sources can be derived from Hirota's discrete KP equations but in a space of higher dimension. In this way we uncover the origin of the source terms as coming from multidimensional consistency of the Hirota system itself.
Neutrino Masses via a Seesaw with Heavy Majorana and Dirac Neutrino Mass Matrices from Discrete Subgroup $?(27)$ of SU(3)
Asan Damanik
Neutrino mass matrix via a seesaw mechanism is constructed by assuming that the underlying symmetry of both heavy Majorana and Dirac mass matrices is the discrete subgroup $\\Delta(27)$ symmetry of SU(3). Using the experimental data of neutrino oscillation, the neutrino mass matrix exhibits maximal $\
Roy Maartens; David Taylor
We define affine transport lifts on the tangent bundle by associating a transport rule for tangent vectors with a vector field on the base manifold. The aim is to develop tools for the study of kinetic/ dynamical symmetries in relativistic particle motion. The transport lift unifies and generalises the various existing lifted vector fields, with clear geometric interpretations. We find the affine dynamical symmetries of free particle motion, and compare this to previous results and to the alternative concept of "matter symmetry".
1+1+2 gravitational perturbations on LRS class II space-times: GEM scalar harmonic amplitudes
R. B. Burston
This is the third in a series of papers which considers first-order gauge-invariant and covariant gravitational perturbations to locally rotationally symmetric (LRS) class II space-times. In this paper we complete our analysis of the first-order gravito-electromagnetic (GEM) system by showing how to derive three decoupled equations governing the GEM scalar fields. One of these is for the gravito-magnetic scalar, whereas another two arise from the 2-gradient of the gravito-electric scalar.
Sekhar Chivukula
The symmetries of a quantum field theory can be realized in a variety of ways. Symmetries can be realized explicitly, approximately, through spontaneous symmetry breaking or, via an anomaly, quantum effects can dynamically eliminate a symmetry of the theory that was present�at the classical level. �Quantum Chromodynamics (QCD),�the modern theory�of the strong interactions, exemplify each of�these possibilities.�The interplay�of these effects determine the�spectrum of particles that we observe�and, ultimately, account for�99% of the mass of ordinary matter.�
Twisted symmetries and integrable systems
G. Cicogna; G. Gaeta
Symmetry properties are at the basis of integrability. In recent years, it appeared that so called "twisted symmetries" are as effective as standard symmetries in many respects (integrating ODEs, finding special solutions to PDEs). Here we discuss how twisted symmetries can be used to detect integrability of Lagrangian systems which are not integrable via standard symmetries.
Variable Cosmological Parameter and S-channel Quantum Matter Fields Hadamard renormalization in Spherically Symmetric Curved Space Times
Hossein Ghaffarnejad
Aim of the paper is to obtain 2d analogue of the backreaction equation which will be useful to study final state of quantum perturbed spherically symmetric curved space times. Thus we take Einstein-massless-scalar $\\psi$ tensor gravity model described on class of spherically symmetric curved space times. We rewrite the action functional in 2d analogue in terms of dimensionless dilaton-matter field $(\\chi=\\Phi\\psi)$ where dilaton field $\\Phi$ is conformal factor of 2-sphere. Then we seek renormalized expectation value of quantum dilaton-matter field stress tensor operator by applying Hadamard rennormalization prescription. Singularity of the Green function is assumed to be has logarithmic form. Covariantly conservation condition on the renormalized quantum dilaton-matter stress tensor demands to input a variable cosmological parameter $\\lambda(x)$. Energy conditions (weak, strong and null) is studied on the obtained renormalized stress tensor leading to dynamical equations for $\\lambda(x), \\Phi$ and quantum vacuum state $W_0(x)=_{ren}.$ In weak quantum field limits our obtained trace anomaly corresponds to one which obtained from zeta regularization. Setting null-like apparent horizon equation $\
Semi-classical determination of exponentially small intermode transitions for 1+1 space-time scattering systems
Magali Marx; Alain Joye
We consider the semiclassical limit of systems of autonomous PDE's in 1+1 space-time dimensions in a scattering regime. We assume the matrix valued coefficients are analytic in the space variable and we further suppose that the corresponding dispersion relation admits real-valued modes only with one-dimensional polarization subspaces. Hence a BKW-type analysis of the solutions is possible. We typically consider time-dependent solutions to the PDE which are carried asymptotically in the past and as $x\\to -\\infty$ along one mode only and determine the piece of the solution that is carried for $x\\to +\\infty$ along some other mode in the future. Because of the assumed non-degeneracy of the modes, such transitions between modes are exponentially small in the semiclassical parameter; this is an expression of the Landau-Zener mechanism. We completely elucidate the space-time properties of the leading term of this exponentially small wave, when the semiclassical parameter is small, for large values of $x$ and $t$, when some avoided crossing of finite width takes place between the involved modes.
1+1+2 Electromagnetic perturbations on general LRS space-times: Regge-Wheeler and Bardeen-Press equations
R. B. Burston; A. W. C. Lun
We use the, covariant and gauge-invariant, 1+1+2 formalism developed by Clarkson and Barrett, and develop new techniques, to decouple electromagnetic (EM) perturbations on arbitrary locally rotationally symmetric (LRS) space-times. Ultimately, we derive 3 decoupled complex equations governing 3 complex scalars. One of these is a new Regge-Wheeler (RW) equation generalized for LRS space-times, whereas the remaining two are new generalizations of the Bardeen-Press (BP) equations. This is achieved by first using linear algebra techniques to rewrite the first-order Maxwell equations in a new complex 1+1+2 form which is conducive to decoupling. This new complex system immediately yields the generalized RW equation, and furthermore, we also derive a decoupled equation governing a newly defined complex EM 2-vector. Subsequently, a further decomposition of the 1+1+2 formalism into a 1+1+1+1 formalism is developed, allowing us to decompose the complex EM 2-vector, and its governing equations, into spin-weighted scalars, giving rise to the generalized BP equations.
Lorentz symmetry breaking in the noncommutative Wess-Zumino model: One loop corrections
Ferrari, A.F.; Gomes, M.; Girotti, H.O. [Instituto de Fisica, Universidade de Sao Paulo, Caixa Postal 66318, 05315-970, Sao Paulo - SP (Brazil); Instituto de Fisica, Universidade Federal do Rio Grande do Sul, Caixa Postal 15051, 91501-970 - Porto Alegre, RS (Brazil)
In this paper we deal with the issue of Lorentz symmetry breaking in quantum field theories formulated in a noncommutative space-time. We show that, unlike in some recent analysis of quantum gravity effects, supersymmetry does not protect the theory from the large Lorentz-violating effects arising from the loop corrections. We take advantage of the noncommutative Wess-Zumino model to illustrate this point.
Symmetry and Topological Order
Zohar Nussinov; Gerardo Ortiz
We prove sufficient conditions for Topological Quantum Order at both zero and finite temperatures. The crux of the proof hinges on the existence of low-dimensional Gauge-Like Symmetries (that notably extend and differ from standard local gauge symmetries) and their associated defects, thus providing a unifying framework based on a symmetry principle. These symmetries may be actual invariances of the system, or may emerge in the low-energy sector. Prominent examples of Topological Quantum Order display Gauge-Like Symmetries. New systems exhibiting such symmetries include Hamiltonians depicting orbital-dependent spin exchange and Jahn-Teller effects in transition metal orbital compounds, short-range frustrated Klein spin models, and p+ip superconducting arrays. We analyze the physical consequences of Gauge-Like Symmetries (including topological terms and charges), discuss associated braiding, and show the insufficiency of the energy spectrum, topological entanglement entropy, maximal string correlators, and fractionalization in establishing Topological Quantum Order. General symmetry considerations illustrate that not withstanding spectral gaps, thermal fluctuations may impose restrictions on certain suggested quantum computing schemes and lead to "thermal fragility". Our results allow us to go beyond standard topological field theories and engineer systems with Topological Quantum Order.
Differential Geometry: Discrete Exterior Calculus
Kazhdan, Michael
Differential Geometry: Discrete Exterior Calculus [Build Your Own DEC at Home. Elcott et al., 2006] [Discrete Differential Forms for Computational Modeling. Desbrun et al., 2005] [Discrete Exterior Calculus-simplices in : where c is a real-valued function. The space of k-chains is denoted Ck(). = k cc )( #12;Chains
Neutrino masses and mixing: a flavour symmetry roadmap
S. Morisi; J. W. F. Valle
Over the last ten years tri-bimaximal mixing has played an important role in modeling the flavour problem. We give a short review of the status of flavour symmetry models of neutrino mixing. We concentrate on non-Abelian discrete symmetries, which provide a simple way to account for the TBM pattern. We discuss phenomenological implications such as neutrinoless double beta decay, lepton flavour violation as well as theoretical aspects such as the possibility to explain quarks and leptons within a common framework, such as grand unified models.
Neutrino masses and mixing: a flavour symmetry roadmap
Morisi, S
Over the last ten years tri-bimaximal mixing has played an important role in modeling the flavour problem. We give a short review of the status of flavour symmetry models of neutrino mixing. We concentrate on non-Abelian discrete symmetries, which provide a simple way to account for the TBM pattern. We discuss phenomenological implications such as neutrinoless double beta decay, lepton flavour violation as well as theoretical aspects such as the possibility to explain quarks and leptons within a common framework, such as grand unified models.
Energy-Momentum Localization for a Space-Time Geometry Exterior to a Black Hole in the Brane World
Irina Radinschi; Theophanes Grammenos; Andromahi Spanou
In general relativity one of the most fundamental issues consists in defining a generally acceptable definition for the energy-momentum density. As a consequence, many coordinate-dependent definitions have been presented, whereby some of them utilize appropriate energy-momentum complexes. We investigate the energy-momentum distribution for a metric exterior to a spherically symmetric black hole in the brane world by applying the Landau-Lifshitz and Weinberg prescriptions. In both the aforesaid prescriptions, the energy thus obtained depends on the radial coordinate, the mass of the black hole and a parameter $\\lambda_{0}$, while all the momenta are found to be zero. It is shown that for a special value of the parameter $\\lambda_{0}$, the Schwarzschild space-time geometry is recovered. Some particular and limiting cases are also discussed.
1+1+2 gravitational perturbations on LRS class II space-times: GEM vector harmonic amplitudes
R. B. Burston
This is the second in a series of papers which considers first-order gauge-invariant and covariant gravitational perturbations to locally rotationally symmetric (LRS) class II space-times. This paper shows how to decouple a complex combination of the gravito-electromagnetic (GEM) 2-vectors with the 2-tensors describing the shear of the 2/3-sheets. An arbitrary harmonic expansion is then used along with an eigen-vector/value analysis of the first-order GEM system, analogous to the first paper in this series. This results in four real decoupled equations governing four real combinations of the harmonic amplitudes of the GEM 2-vectors and the (2/3-sheet) shear 2-tensors. Finally, these are categorized into polar and axial perturbations.
Lamb shift and fundamental length of the relativistic Hydrogen atom induced from the non-commutative space-time
Slimane Zaim
We present an important contribution to the non-commutative approach to the hydrogen atom to deal with lamb shift corrections. This can be done by studying the Klein-Gordon and Dirac equations in a non-commutative space-time up to first-order of the non-commutativity parameter using the Seiberg-Witten maps. We thus find the non-commutative modification of the energy levels and by comparing with the the current experimental results on the Lamb shift of the 2P level to extract a bound on the parameter of non-commutativity, we show that the fundamental length ($\\sqrt{\\Theta}$) is compatible with the value of the electroweak length scale ($l$). Phenomenologically, this effectively confirms the presence of gravity at this level.
Dark Energy Model in Anisotropic Bianchi Type-III Space-Time with Variable EoS Parameter
Anirudh Pradhan; Hassan Amirhashchi
A new dark energy model in anisotropic Bianchi type-III space-time with variable equation of state (EoS) parameter has been investigated in the present paper. To get the deterministic model, we consider that the expansion $\\theta$ in the model is proportional to the eigen value $\\sigma^{2}_{~2}$ of the shear tensor $\\sigma^{j}_~i$. The EoS parameter $\\omega$ is found to be time dependent and its existing range for this model is in good agreement with the recent observations of SNe Ia data (Knop et al. 2003) and SNe Ia data with CMBR anisotropy and galaxy clustering statistics (Tegmark et al. 2004). It has been suggested that the dark energy that explains the observed accelerating expansion of the universe may arise due to the contribution to the vacuum energy of the EoS in a time dependent background. Some physical aspects of dark energy model are also discussed.
Miller, G.A. [Department of Physics, FM-15, University of Washington, Seattle, Washington 98195 (United States)
Charge independence and symmetry are approximate symmetries of nature. The observations of the small charge symmetry breaking effects and the consequences of those effects are reviewed. The effects of the mass difference between up and down quarks and the off shell dependence {ital q}{sup 2} of {rho}{sup 0}-{omega} mixing are stressed. We find that models which predict a strong {ital q}{sup 2} dependence of {rho}{sup 0}-{omega} mixing seem also to predict a strong {ital q}{sup 2} variation for the {rho}{sup 0}-{gamma}* matrix element, in contradiction with experiment.
Charge splitting of directed flow and space-time picture of pion emission from the electromagnetic interactions with spectators
Andrzej Rybicki; Antoni Szczurek
We estimate the effect of the spectator-induced electromagnetic interaction on the directed flow of charged pions. For intermediate centrality Au+Au collisions at $\\sqrt{s_{NN}}=7.7$~GeV, we demonstrate that the electromagnetic interaction between spectator charges and final state pions results in charge splitting of positive and negative pion directed flow. Such a charge splitting is visible in the experimental data reported by the STAR Collaboration. The magnitude of this charge splitting appears to strongly depend on the actual distance between the pion emission site (pion at freeze-out) and the spectator system. As such, the above electromagnetic effect brings new, independent information on the space-time evolution of pion production in heavy ion collisions. From the comparison of our present analysis to our earlier studies made for pions produced at higher rapidity, we formulate conclusions on the rapidity dependence of the distance between the pion emission site and the spectator system. This distance appears to decrease with increasing pion rapidity, reflecting the longitudinal expansion of the strongly-interacting system responsible for pion emission. Thus for the first time, information on the space-time characteristics of the system is being provided by means of the spectator-induced electromagnetic interaction. The above electromagnetic effect being in fact a straight-forward consequence of the presence of spectator charges in the collision, we consider that it should be considered as a baseline for studies of other phenomena, like those related to the electric conductivity of the quark-gluon plasma.
Symmetry in Scheduling Problems
Nov 16, 2010 ... Using operating room and power generator scheduling problems ... suggested that a class of highly symmetric covering problems called Steiner Triple Systems ... The structure of symmetry present in these problems allow for.
Polymer quantization and Symmetries
Ghanashyam Date; Nirmalya Kajuri
Polymer quantization was discovered during the construction of Loop Quantum Cosmology. For the simplest quantum theory of one degree of freedom, the implications for dynamics were studied for the harmonic oscillator as well as some other potentials. For more degrees of freedom, the possibility of continuous, kinematic symmetries arises. While these are realised on the Hilbert space of polymer quantum mechanics, their infinitesimal versions are not supported. For an invariant Hamiltonian, these symmetry realizations imply infinite degeneracy suggesting that the symmetry should be spontaneously or explicitly broken. The estimation of symmetry violations in some cases have been analysed before. Here we explore the alternative of shifting the arena to the distributional states. We discuss both the polymer quantum mechanics case as well as polymer quantized scalar field.
Symmetries in Integer Programs
B�di, R
The notion of symmetry is defined in the context of Linear and Integer Programming. Symmetric integer programs are studied from a group theoretical viewpoint. We investigate the structure of integer solutions of integer programs and show that any integer program on n variables having an alternating group A_n as a group of symmetries can be solved in linear time in the number of variables.
A. M. Polyakov
These notes, based on the remarks made at the 23 Solvay Conference, collect several speculative ideas concerning gauge/ strings duality, de Sitter spaces, dimensionality and the cosmological constant.
Finite group symmetry breaking
G. Gaeta
Finite group symmetry is commonplace in Physics, in particular through crystallographic groups occurring in condensed matter physics -- but also through the inversions (C,P,T and their combinations) occurring in high energy physics and field theory. The breaking of finite groups symmetry has thus been thoroughly studied, and general approaches exist to investigate it. In Landau theory, the state of a system is described by a finite dimensional variable (the {\\it order parameter}), and physical states correspond to minima of a potential, invariant under a group. In this article we describe the basics of symmetry breaking analysis for systems described by a symmetric polynomial; in particular we discuss generic symmetry breakings, i.e. those determined by the symmetry properties themselves and independent on the details of the polynomial describing a concrete system. We also discuss how the plethora of invariant polynomials can be to some extent reduced by means of changes of coordinates, i.e. how one can reduce to consider certain types of polynomials with no loss of generality. Finally, we will give some indications on extension of this theory, i.e. on how one deals with symmetry breakings for more general groups and/or more general physical systems.
Gauge symmetry breaking in orbifold model building
Michele Trapletti
We review the gauge symmetry breaking mechanism due to orbifold projections in orbifold model building. We explicitly show the existence of a scale of breaking if such a symmetry breaking is due to freely-acting orbifold operators only, i.e. in case the breaking is realized non-locally in the internal space. We show that such a scale is related to the compactification moduli only, and that there are no extra continuous parameters, at least in semirealistic models with N=1 SUSY in four dimensions. In this sense, the mechanism is peculiarly different from the standard Higgs (or Hosotani) symmetry breaking mechanism. We show that the mechanism also differs from that present in standard orbifold models where, even in presence of discrete Wilson lines, a scale of breaking is generically missing, since the breaking is localized in specific points in the internal space. We review a set of background geometries where the described non-local breaking is realized, both in the case of two and six extra dimensions. In the latter case, relevant in string model building, we consider both heterotic and open string compactifications.
Thermodynamics of discrete quantum processes
Janet Anders; Vittorio Giovannetti
We define thermodynamic configurations and identify two primitives of discrete quantum processes between configurations for which heat and work can be defined in a natural way. This allows us to uncover a general second law for any discrete trajectory that consists of a sequence of these primitives, linking both equilibrium and non-equilibrium configurations. Moreover, in the limit of a discrete trajectory that passes through an infinite number of configurations, i.e. in the reversible limit, we recover the saturation of the second law. Finally, we show that for a discrete Carnot cycle operating between four configurations one recovers Carnot's thermal efficiency.
Neutrino Masses via a Seesaw with Heavy Majorana and Dirac Neutrino Mass Matrices from Discrete Subgroup $\\Delta (27)$ of $SU(3)$
Damanik, Asan
Neutrino mass matrix via a seesaw mechanism is constructed by assuming that the underlying symmetry of both heavy Majorana and Dirac mass matrices is the discrete subgroup $\\Delta(27)$ symmetry of $SU(3)$. Using the experimental data of neutrino oscillation, the neutrino mass matrix exhibits maximal $\
Relativistic Quantum Dynamics: A non-traditional perspective on space, time, particles, fields, and action-at-a-distance
Eugene V. Stefanovich
This book is an attempt to build a consistent relativistic quantum theory of interacting particles. In the first part of the book "Quantum electrodynamics" we follow rather traditional approach to particle physics. Our discussion proceeds systematically from the principle of relativity and postulates of quantum measurements to the renormalization in quantum electrodynamics. In the second part of the book "Quantum theory of particles" this traditional approach is reexamined. We find that formulas of special relativity should be modified to take into account particle interactions. We also suggest reinterpreting quantum field theory in the language of physical "dressed" particles. This formulation eliminates the need for renormalization and opens up a new way for studying dynamical and bound state properties of quantum interacting systems. The developed theory is applied to realistic physical objects and processes including the energy spectrum of the hydrogen atom, the decay law of moving unstable particles, and the electric field of relativistic electron beams. These results force us to take a fresh look at some core issues of modern particle theories, in particular, the Minkowski space-time unification, the role of quantum fields and renormalization as well as the alleged impossibility of action-at-a-distance. A new perspective on these issues is suggested. It can help to solve the old problem of theoretical physics -- a consistent unification of relativity and quantum mechanics.
1+1+2 gravitational perturbations on LRS class II space-times: Decoupling GEM tensor harmonic amplitudes
R. B. Burston
This paper considers gauge-invariant and covariant gravitational perturbations on arbitrary vacuum locally rotationally symmetric (LRS) class II space-times. Ultimately, we derive four decoupled equations governing four specific combinations of the gravito-electromagnetic (GEM) 2-tensor harmonic amplitudes. We use the gauge-invariant and covariant 1+1+2 formalism which Clarkson and Barrett developed for analysis of vacuum Schwarzschild perturbations. In particular we focus on the first-order 1+1+2 GEM system and use linear algebra techniques suitable for exploiting its structure. Consequently, we express the GEM system new 1+1+2 complex form by choosing new complex GEM tensors, which is conducive to decoupling. We then show how to derive a gauge-invariant and covariant decoupled equation governing a newly defined complex GEM 2-tensor. Finally, the GEM 2-tensor is expanded in terms of arbitrary tensor harmonics and linear algebra is used once again to decouple the system further into 4 real decoupled equations.
Stability of Gauss-Bonnet black holes in anti-de Sitter space-time against scalar field condensation
Brihaye, Yves [Physique-Mathematique, Universite de Mons-Hainaut, 7000 Mons (Belgium); Hartmann, Betti [School of Engineering and Science, Jacobs University Bremen, 28759 Bremen (Germany)
We study the stability of static, hyperbolic Gauss-Bonnet black holes in (4+1)-dimensional anti-de Sitter (AdS) space-time against the formation of scalar hair. Close to extremality the black holes possess a near-horizon topology of AdS{sub 2}xH{sup 3} such that within a certain range of the scalar field mass one would expect that they become unstable to the condensation of an uncharged scalar field. We confirm this numerically and observe that there exists a family of hairy black hole solutions labeled by the number of nodes of the scalar field function. We construct explicit examples of solutions with a scalar field that possesses zero nodes, one node, and two nodes, respectively, and show that the solutions with nodes persist in the limit of Einstein gravity, i.e. for vanishing Gauss-Bonnet coupling. We observe that the interval of the mass for which scalar field condensation appears decreases with increasing Gauss-Bonnet coupling and/or with increasing node number.
Constucting Discrete KSurfaces Ivan Sterling
Sterling, Ivan
Constucting Discrete K�Surfaces Ivan Sterling (joint work with Tim Ho#mann, and Ulrich Pinkall) Old it is possible to find other examples (FIGURE 4). 2 #12; Figure 4. Ho#man�Sterling Discrete K�Surface 4. Computer and examples can be found at www.jreality.de. References [1] G.T. Bennett, A new mechanism, Engineering 76
Two-dimensional symmetry-protected topological orders and their protected gapless edge excitations
Chen Xie [Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States); Liu Zhengxin; Wen Xiaogang [Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States); Institute for Advanced Study, Tsinghua University, Beijing, 100084 (China)
Topological insulators in free fermion systems have been well characterized and classified. However, it is not clear in strongly interacting boson or fermion systems what symmetry-protected topological orders exist. In this paper, we present a model in a two-dimensional (2D) interacting spin system with nontrivial onsite Z{sub 2} symmetry-protected topological order. The order is nontrivial because we can prove that the one-dimensional (1D) system on the boundary must be gapless if the symmetry is not broken, which generalizes the gaplessness of Wess-Zumino-Witten model for Lie symmetry groups to any discrete symmetry groups. The construction of this model is related to a nontrivial 3-cocycle of the Z{sub 2} group and can be generalized to any symmetry group. It potentially leads to a complete classification of symmetry-protected topological orders in interacting boson and fermion systems of any dimension. Specifically, this exactly solvable model has a unique gapped ground state on any closed manifold and gapless excitations on the boundary if Z{sub 2} symmetry is not broken. We prove the latter by developing the tool of a matrix product unitary operator to study the nonlocal symmetry transformation on the boundary and reveal the nontrivial 3-cocycle structure of this transformation. Similar ideas are used to construct a 2D fermionic model with onsite Z{sub 2} symmetry-protected topological order.
Gauging the twisted Poincare symmetry as a noncommutative theory of gravitation
Chaichian, M.; Tureanu, A. [Department of Physics, University of Helsinki, P.O. Box 64, FIN-00014 Helsinki (Finland); Helsinki Institute of Physics, P.O. Box 64, FIN-00014 Helsinki (Finland); Oksanen, M. [Department of Physics, University of Helsinki, P.O. Box 64, FIN-00014 Helsinki (Finland); Zet, G. [Department of Physics, 'Gh. Asachi' Technical University, Bd. D. Mangeron 67, 700050 Iasi (Romania)
Einstein's theory of general relativity was formulated as a gauge theory of Lorentz symmetry by Utiyama in 1956, while the Einstein-Cartan gravitational theory was formulated by Kibble in 1961 as the gauge theory of Poincare transformations. In this framework, we propose a formulation of the gravitational theory on canonical noncommutative space-time by covariantly gauging the twisted Poincare symmetry, in order to fulfil the requirement of covariance under the general coordinate transformations, an essential ingredient of the theory of general relativity. It appears that the twisted Poincare symmetry cannot be gauged by generalizing the Abelian twist to a covariant non-Abelian twist, nor by introducing a more general covariant twist element. The advantages of such a formulation as well as the related problems are discussed and possible ways out are outlined.
FPGA Acceleration of Discrete Molecular Dynamics Simulation
Herbordt, Martin
' & $ % FPGA Acceleration of Discrete Molecular Dynamics Simulation Joshua Model Thesis submitted UNIVERSITY COLLEGE OF ENGINEERING Thesis FPGA Acceleration of Discrete Molecular Dynamics Simulation Acceleration of Discrete Molecular Dynamics Simulation Joshua Model ABSTRACT Molecular dynamics simulation
Observable T{sub 7} Lepton Flavor Symmetry at the Large Hadron Collider
Cao Qinghong [High Energy Division, Argonne National Laboratory, Argonne, Illinois 60439 (United States); Enrico Fermi Institute, University of Chicago, Chicago, Illinois 60637 (United States); Khalil, Shaaban [Centre for Theoretical Physics, British University in Egypt, El Sherouk City, Postal No. 11837, P.O. Box 43 (Egypt); Department of Mathematics, Ain Shams University, Faculty of Science, Cairo 11566 (Egypt); Ma, Ernest [Department of Physics and Astronomy, University of California, Riverside, California 92521 (United States); Okada, Hiroshi [Centre for Theoretical Physics, British University in Egypt, El Sherouk City, Postal No. 11837, P.O. Box 43 (Egypt)
More often than not, models of flavor symmetry rely on the use of nonrenormalizable operators (in the guise of flavons) to accomplish the phenomenologically successful tribimaximal mixing of neutrinos. We show instead how a simple renormalizable two-parameter neutrino mass model of tribimaximal mixing can be constructed with the non-Abelian discrete symmetry T{sub 7} and the gauging of B-L. This is also achieved without the addition of auxiliary symmetries and particles present in almost all other proposals. Most importantly, it is verifiable at the Large Hadron Collider.
Emily Clader; Yongbin Ruan
These expository notes are based on lectures by Yongbin Ruan during a special semester on the B-model at the University of Michigan in Winter 2014. They outline and compare the mirror symmetry constructions of Batyrev-Borisov, Hori-Vafa, and Bergland-Hubsch-Krawitz.
Gravitational Collapse In Husain Space-time For Brans-Dicke Gravity Theory with Power-law Potential
Prabir Rudra; Ritabrata Biswas; Ujjal Debnath
The motive of this work is to study gravitational collapse in Husain space-time in Brans-Dicke gravity theory. Among many scalar-tensor theories of gravity, Brans-Dicke is the simplest and the impact of it can be regulated by two parameters associated with it, namely, the Brans-Dicke parameter, $\\omega$, and the potential-scalar field dependency parameter $n$ respectively. V. Husain's work on exact solution for null fluid collapse in 1996 has influenced many authors to follow his way to find the end-state of the homogeneous/in-homogeneous dust cloud. Vaidya's metric is used all over to follow the nature of future outgoing radial null geodesics. Detecting whether the central singularity is naked or wrapped by an event horizon, by the existence of future directed radial null geodesic emitted in past from the singularity is the basic objective. To point out the existence of positive trajectory tangent solution, both particular parametric cases(through tabular forms) and wide range contouring process have been applied. Precisely, perfect fluid's EoS satisfies a wide range of phenomena : from dust to exotic fluid like dark energy. We have used the EoS parameter $k$ to determine the end state of collapse in different cosmological era. Our main target is to check low $\\omega$ (more deviations from Einstein gravity-more Brans Dicke effect) and negative $k$ zones. This particularly throws light on the nature of the end-state of collapse in accelerated expansion in Brans Dicke gravity. It is seen that for positive values of EoS parameter $k$, the collapse results in a black hole, whereas for negative values of $k$, naked singularity is the only outcome. It is also to be noted that "low $\\omega$" leads to the possibility of getting more naked singularities even for a non-accelerating universe.
Discrete generalized multigroup theory and applications
Zhu, Lei, Ph. D. Massachusetts Institute of Technology
This study develops a fundamentally new discrete generalized multigroup energy expansion theory for the linear Boltzmann transport equation. Discrete orthogonal polynomials are used, in conjunction with the traditional ...
IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 54, NO. 3, MARCH 2008 1073 A Quasi-Random Approach to SpaceTime Codes
Ping, Li
can be used to significantly increase the reliability and spectrum efficiency of wireless approach so as to ensure reliability, such as in the vertical Bell Laboratories layered space�time (V antennas. The BLAST architectures are less effective in multiple-input�single-output (MISO) environments
Symmetry Energy in Nuclear Surface
Pawel Danielewicz; Jenny Lee
Interplay between the dependence of symmetry energy on density and the variation of nucleonic densities across nuclear surface is discussed. That interplay gives rise to the mass dependence of the symmetry coefficient in an energy formula. Charge symmetry of the nuclear interactions allows to introduce isoscalar and isovector densities that are approximately independent of the magnitude of neutron-proton asymmetry.
Discrete Structures for Computer Science
Dragan, Feodor F.
-5% Final Exam 40% #12;Why Discrete Math? Design efficient computer systems. �How did Google manage to build issues. #12;16 Sub-Category Graph No Threshold New Science of Networks NYS Electric Power Grid (Thorp
International Symposium on Discrete Mathematics
University, China Ghent University, Belgium CAS-MPG Partner Institute for Computational Biology, ChinaInternational Symposium on Discrete Mathematics and Mathematical Biology August 26�27, 2013 Find Interdisciplinary Centre for Bioinformatics #12;
Mass independent textures and symmetry
Lam, C. S. [Department of Physics, McGill University, Montreal, QC, Canada H3A 2T8 and Department of Physics and Astronomy, University of British Columbia, Vancouver, BC, V6T 1Z1 (Canada)
A mass-independent texture is a set of linear relations of the fermion mass-matrix elements which imposes no constraint on the fermionic masses nor the Majorana phases. Magic and 2-3 symmetries are examples. We discuss the general construction and the properties of these textures, as well as their relation to the quark and neutrino mixing matrices. Such a texture may be regarded as a symmetry, whose unitary generators of the symmetry group can be explicitly constructed. In particular, the symmetries connected with the tribimaximal neutrino mixing matrix are discussed, together with the physical consequence of breaking one symmetry but preserving another.
Presented by Parallel Discrete Event Simulation
of discrete event execution on high performance computing Business Sensitive � Different optimizations
Symmetries in open quantum dynamics
Thomas F. Jordan
Simple examples are used to introduce and examine a Heisenberg picture of symmetries of open quantum dynamics that can be described by unitary operators. When the symmetries are for Hamiltonian dynamics of an entire system, and the spectrum of the Hamiltonian operator has a lower bound, the symmetry operators commute with the Hamiltonian operator. An example shows that symmetry operators need not commute with the Hamiltonian operator when the spectrum of the Hamiltonian does not have a lower bound. There are many more symmetries that are only for the open dynamics of a subsystem and are described by unitary operators that do not commute with the Hamiltonian for the dynamics of the entire system. Examples show how these symmetries alone can reveal properties of the dynamics and reduce what needs to be done to work out the dynamics. A symmetry of the open dynamics of a subsystem can imply properties of the dynamics for the entire system that are not implied by the symmetries of the dynamics of the entire system. The symmetries are generally not related to constants of the motion for the open dynamics of the subsystem. There are symmetries of the open dynamics of a subsystem that depend only on the dynamics. In the simplest examples, these are also symmetries of the dynamics of the entire system. There are many more symmetries, of a new kind, that also depend on correlations, or absence of correlations, between the subsystem and the rest of the entire system, or on the state of the rest of the entire system. Symmetries that depend on correlations generally cannot be seen in the Schr\\"{o}dinger picture as symmetries of dynamical maps of density matrices for the subsystem.
COW test of the weak equivalence principle: A low-energy window to look into the noncommutative structure of space-time?
Anirban Saha
We construct the quantum mechanical model of the COW experiment assuming that the underlying space time has a granular structure, described by a canonical noncommutative algebra of coordinates $x^{\\mu}$. The time-space sector of the algebra is shown to add a mass-dependent contribution to the gravitational acceleration felt by neutron deBrogli waves measured in a COW experiment. This makes time-space noncommutativity a potential candidate for an apparent violation of WEP even if the ratio of the inertial mass $m_{i}$ and gravitational mass $m_{g}$ is a universal constant. The latest experimental result based on COW principle is shown to place an upper-bound several orders of magnitude stronger than the existing one on the time-space noncommutative parameter. We argue that the evidence of NC structure of space-time may be found if the COW-type experiment can be repeated with several particle species.
N=1 Super-symmetry Lagrangian in the de Sitter space
M. R. Masouminia
Previously, in [1], a novel N=1 super-symmetric algebra in de Sitter space-time was introduced. This paper is an attempt to build a proper N=1 super-symmetric field theory of classical level in the de Sitter space. The generators, gauge transformations and different fields in a 5-dimensional ambient space notation are defined and corresponding super-space and super-fields are introduced. Finally, the N=1 super-symmetry Lagrangian in the de Sitter ambient space notation has been
Static Kerr Green's Function in Closed Form and an Analytic Derivation of the Self-Force for a Static Scalar Charge in Kerr Space-Time
Adrian C. Ottewill; Peter Taylor
We derive a closed-form solution for the Green's function for the wave equation of a static (with respect to an undragged, static observer at infinity) scalar charge in the Kerr space-time. We employ our solution to obtain an analytic expression for the self-force on such a charge, comparing our results to those previously obtained using the mode-sum regularization prescription.
Expediting model-based optoacoustic reconstructions with tomographic symmetries
Lutzweiler, Christian; De�n-Ben, Xos� Lu�s; Razansky, Daniel, E-mail: email@example.com [Institute for Biological and Medical Imaging (IBMI), Helmholtz Center Munich, Ingolst�dter Landstrasse 1, 85764 Neuherberg (Germany) [Institute for Biological and Medical Imaging (IBMI), Helmholtz Center Munich, Ingolst�dter Landstrasse 1, 85764 Neuherberg (Germany); Faculty of Medicine, Technical University of Munich, Ismaninger Strasse 22, 81675 Munich (Germany)
Purpose: Image quantification in optoacoustic tomography implies the use of accurate forward models of excitation, propagation, and detection of optoacoustic signals while inversions with high spatial resolution usually involve very large matrices, leading to unreasonably long computation times. The development of fast and memory efficient model-based approaches represents then an important challenge to advance on the quantitative and dynamic imaging capabilities of tomographic optoacoustic imaging. Methods: Herein, a method for simplification and acceleration of model-based inversions, relying on inherent symmetries present in common tomographic acquisition geometries, has been introduced. The method is showcased for the case of cylindrical symmetries by using polar image discretization of the time-domain optoacoustic forward model combined with efficient storage and inversion strategies. Results: The suggested methodology is shown to render fast and accurate model-based inversions in both numerical simulations andpost mortem small animal experiments. In case of a full-view detection scheme, the memory requirements are reduced by one order of magnitude while high-resolution reconstructions are achieved at video rate. Conclusions: By considering the rotational symmetry present in many tomographic optoacoustic imaging systems, the proposed methodology allows exploiting the advantages of model-based algorithms with feasible computational requirements and fast reconstruction times, so that its convenience and general applicability in optoacoustic imaging systems with tomographic symmetries is anticipated.
$\\mathcal{PT}$-systems without parity symmetry: topological states, hidden symmetry, and the $\\mathcal{PT}$ phase diagram
Joglekar, Yogesh N
$\\mathcal{PT}$-symmetric systems, until now, have been characterized by a real, parity-symmetric, kinetic Hamiltonian and a non-Hermitian, balanced gain-loss potential. We present a new class of discrete models in which the tunneling Hamiltonian is not parity-symmetric, and yet the models have a nonzero $\\mathcal{PT}$-breaking threshold in presence of a pair of gain-loss impurities $\\pm i\\gamma$ located at reflection-symmetric sites. We uncover a hidden symmetry that is instrumental to the finite threshold strength. We show that such models have topological edge-states that remain robust in the $\\mathcal{PT}$-broken phase. Our predictions substantially broaden possible realizations of a $\\mathcal{PT}$ system, particularly in optical waveguide arrays or coupled microstructures, by eliminating the parity-symmetry constraint.
A gauge-theoretic description of $?$-prolongations, and $?$-symmetries of differential equations
G. Gaeta
We consider generalized (possibly depending on fields as well as on space-time variables) gauge transformations and gauge symmetries in the context of general -- that is, possibly non variational nor covariant -- differential equations. In this case the relevant principal bundle admits the first jet bundle (of the phase manifold) as an associated bundle, at difference with standard Yang-Mills theories. We also show how in this context the recently introduced operation of $\\mu$-prolongation of vector fields (which generalizes the $\\la$-prolongation of Muriel and Romero), and hence $\\mu$-symmetries of differential equations, arise naturally. This is turn suggests several directions for further development. S0ome detailed examples are also given.
Software is Discrete Mathematics University of Oklahoma
Page, Rex L.
, discrete mathematics, predicate logic, correctness proofs, formal methods, software engineering. 1Software is Discrete Mathematics Rex L Page University of Oklahoma School of Computer Science Descriptors D.2.4 [Software Engineering]: Software/Program Verification � correctness proofs, formal methods
Discrete and Hybrid Nonholonomy Antonio Bicchi1
Piccoli, Benedetto
Discrete and Hybrid Nonholonomy Antonio Bicchi1 , Alessia Marigo2 , and Benedetto Piccoli3 1 Centro such as cars, trucks with trailers, rolling 3D objects, underactuated mechanisms, satellites, etc., has made of systems, allowing for discrete and hybrid (mixed continuous and discrete) configurations and transi- tions
Numerical Valuation of Discrete Barrier Options with
Chu, Hao-hua
Numerical Valuation of Discrete Barrier Options with the Adaptive Mesh Model and Other Competing for discrete barrier options such that many methods have been suggested and declared to price discrete barrier options fast and accurately but no one can tell exactly that what method is the best. We also make
Left-right symmetric model with {mu}{r_reversible}{tau} symmetry
Gomez-Izquierdo, Juan Carlos; Perez-Lorenzana, Abdel [Departamento de Fisica, Centro de Investigacion y de Estudios Avanzados del I.P.N., Apdo. Post. 14-740, 07000 Mexico D.F. (Mexico)
We present a Left-right symmetric model with a (Z{sub 2}){sup 3} discrete symmetry which realizes softly broken {mu}{r_reversible}{tau} symmetry, which is broken at tree level in the effective neutrino mass matrix by mass difference in the diagonal Dirac mass terms. Lepton mixings arise from Majorana mass matrix. We determined {theta}{sub 13}, and the deviation from maximal value of {theta}{sub ATM} in terms of the hierarchy scale, m{sub 3}, and a single free parameter, h{sub s}.
Spontaneously broken quark helicity symmetry
Dalley, Simon [Department of Physics, University of Wales Swansea, Singleton Park, Swansea SA2 8PP (United Kingdom); McCartor, Gary [Department of Physics, SMU Dallas, TX 75275 (United States)]. E-mail: firstname.lastname@example.com
We discuss the origin of chiral-symmetry breaking in the light-cone representation of QCD. In particular, we show how quark helicity symmetry is spontaneously broken in SU (N) gauge theory with massless quarks if that theory has a condensate of fermion light-cone zero modes. The symmetry breaking appears as induced interactions in an effective light-cone Hamiltonian equation based on a trivial vacuum. The induced interaction is crucial for generating a splitting between pseudoscalar and vector meson masses, which we illustrate with spectrum calculations in some 1 + 1-dimensional reduced models of gauge theory.
Discretized configurations and partial partitions
Abrams, Aaron; Hower, Valerie
We show that the discretized configuration space of $k$ points in the $n$-simplex is homotopy equivalent to a wedge of spheres of dimension $n-k+1$. This space is homeomorphic to the order complex of the poset of ordered partial partitions of $\\{1,\\...,n+1\\}$ with exactly $k$ parts. We also compute the Euler characteristic in two different ways, thereby obtaining a topological proof of a combinatorial recurrence satisfied by the Stirling numbers of the second kind.
dimensional discrete Schr�?odinger operator. We prove that if # ess (H) # [-2, 2], then H-H 0 is compact and # ess (H V = 0. One of our main results in this paper is Theorem 1. If # ess (H) # [-2, 2], then V (n) # 0 that # ess (H) = [-2, 2] if and only if V (n) # 0. Our motivation for this result came from two sources
Crossovers between superconducting symmetry classes
V. A. Koziy; M. A. Skvortsov
We study the average density of states in a small metallic grain coupled to two superconductors with the phase difference $\\pi$, in a magnetic field. The spectrum of the low-energy excitations in the grain is described by the random matrix theory whose symmetry depends on the magnetic field strength and coupling to the superconductors. In the limiting cases, a pure superconducting symmetry class is realized. For intermediate magnetic fields or couplings to the superconductors, the system experiences a crossover between different symmetry classes. With the help of the supersymmetric sigma-model we derive the exact expressions for the average density of states in the crossovers between the symmetry classes A-C and CI-C.
Domain wall solitons and Hopf algebraic translational symmetries in noncommutative field theories
Sasai, Yuya; Sasakura, Naoki [Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502 (Japan)
Domain wall solitons are the simplest topological objects in field theories. The conventional translational symmetry in a field theory is the generator of a one-parameter family of domain wall solutions, and induces a massless moduli field which propagates along a domain wall. We study similar issues in braided noncommutative field theories possessing Hopf algebraic translational symmetries. As a concrete example, we discuss a domain wall soliton in the scalar {phi}{sup 4} braided noncommutative field theory in Lie-algebraic noncommutative space-time, [x{sup i},x{sup j}]=2i{kappa}{epsilon}{sup ijk}x{sub k} (i,j,k=1,2,3), which has a Hopf algebraic translational symmetry. We first discuss the existence of a domain wall soliton in view of Derrick's theorem, and construct explicitly a one-parameter family of solutions in perturbation of the noncommutativity parameter {kappa}. We then find the massless moduli field which propagates on the domain wall soliton. We further extend our analysis to the general Hopf algebraic translational symmetry.
Classification of constraints and degrees of freedom for quadratic discrete actions
Philipp A. Hoehn
We provide a comprehensive classification of constraints and degrees of freedom for variational discrete systems governed by quadratic actions. This classification is based on the different types of null vectors of the Lagrangian two-form and employs the canonical formalism developed in arXiv:1303.4294 [math-ph] (J. Math. Phys. 54, 093505 (2013)) and arXiv:1401.6062 [gr-qc] (J. Math. Phys. 55, 083508 (2014)). The analysis is carried out in both the classical and quantum theory and applies to systems with both temporally varying or constant discretization. In particular, it is shown explicitly how changes in the discretization, e.g. resulting from canonical coarse graining or refining operations or an evolving background geometry, change the dynamical content of the system. It is demonstrated how, on a temporally varying discretization, constraints, Dirac observables, symmetries, reduced phase spaces and physical Hilbert spaces become spacetime region dependent. These results are relevant for free field theory on an evolving lattice and linearized discrete gravity models.
Robust Hydraulic Fracture Monitoring (HFM) of Multiple Time Overlapping Events Using a Generalized Discrete Radon Transform
Ely, Gregory
In this work we propose a novel algorithm for multiple-event localization for Hydraulic Fracture Monitoring (HFM) through the exploitation of the sparsity of the observed seismic signal when represented in a basis consisting of space time propagators. We provide explicit construction of these propagators using a forward model for wave propagation which depends non-linearly on the problem parameters - the unknown source location and mechanism of fracture, time and extent of event, and the locations of the receivers. Under fairly general assumptions and an appropriate discretization of these parameters we first build an over-complete dictionary of generalized Radon propagators and assume that the data is well represented as a linear superposition of these propagators. Exploiting this structure we propose sparsity penalized algorithms and workflow for super-resolution extraction of time overlapping multiple seismic events from single well data.
Dual hidden landscapes in Anderson localization on discrete lattices
Marcelo Leite Lyra; Svitlana Mayboroda; Marcel Filoche
The localization subregions of stationary waves in continuous disordered media have been recently demonstrated to be governed by a hidden landscape that is the solution of a Dirichlet problem expressed with the wave operator. In this theory, the strength of Anderson localization confinement is determined by this landscape, and continuously decreases as the energy increases. However, this picture has to be changed in discrete lattices in which the eigenmodes close to the edge of the first Brillouin zone are as localized as the low energy ones. Here we show that in a 1D discrete lattice, the localization of low and high energy modes is governed by two different landscapes, the high energy landscape being the solution of a dual Dirichlet problem deduced from the low energy one using the symmetries of the Hamiltonian. We illustrate this feature using the one-dimensional tight-binding Hamiltonian with random on-site potentials as a prototype model. Moreover we show that, besides unveiling the subregions of Anderson localization, these dual landscapes also provide an accurate overal estimate of the localization length over the energy spectrum, especially in the weak disorder regime.
Exact solutions in (2 + 1)-dimensional anti-de Sitter space-time admitting a linear or non-linear equation of state
Ayan Banerjee; Farook Rahaman; Kanti Jotania; Ranjan Sharma; Mosiur Rahaman
Gravitational analyzes in lower dimensions has become a field of active research interest ever since Banados, Teitelboim and Zanelli (BTZ) (Phys. Rev. Lett. 69, 1849, 1992) proved the existence of a black hole solution in (2 + 1) dimensions. The BTZ metric has inspired many investigators to develop and analyze circularly symmetric stellar models which can be matched to the exterior BTZ metric. We have obtained two new classes of solutions for a (2 + 1)-dimensional anisotropic star in anti-de Sitter background space-time which have been obtained by assuming that the equation of state (EOS) describing the material composition of the star could either be linear or non-linear in nature. By matching the interior solution to the BTZ exterior metric with zero spin, we have demonstrated that the solutions provided here are regular and well-behaved at the stellar interior.
Doppler effect and Hubble effect in different models of space-time in the case of auto-parallel motion of the observer
Sawa Manoff
Doppler effect and Hubble effect in different models of space-time in the case of auto-parallel motion of the observer are considered. The Doppler effect and shift frequency parameter are specialized for the case of auto-parallel motion of the observer. The Hubble effect and shift frequency parameter are considered for the same case. It is shown that by the use of the variation of the shift frequency parameter during a time perod, considered locally in the proper frame of reference of an observer, one can directly determine the centrifugal (centripetal) relative velocity and acceleration as well as the Coriolis relative velocity and acceleration of an astronomical object moving relatively to the observer. All results are obtained on purely kinematic basis without taking into account the dynamic reasons for the considered effect. PACS numbers: 98.80.Jk; 98.62.Py; 04.90.+e; 04.80.Cc
Discrete Sets of Singular Cardinality
Fleissner, William G.
singular cardinal k and a closed, cofinal in k, set of cardinals, {kb: � �,. Throughout this paper, Y will be a discrete subset of a space X with | Y \\ = k. We say that t? = (A�)�...
Bell's Jump Process in Discrete Time
Jonathan Barrett; Matthew Leifer; Roderich Tumulka
The jump process introduced by J. S. Bell in 1986, for defining a quantum field theory without observers, presupposes that space is discrete whereas time is continuous. In this letter, our interest is to find an analogous process in discrete time. We argue that a genuine analog does not exist, but provide examples of processes in discrete time that could be used as a replacement.
Symmetry energy from nuclear multifragmentation
Swagata Mallik; Gargi Chaudhuri
The ratio of symmetry energy coefficient to temperature $C_{sym}/T$ is extracted from different prescriptions using the isotopic as well as the isobaric yield distributions obtained in different projectile fragmentation reactions. It is found that the values extracted from our theoretical calculation agree with those extracted from the experimental data but they differ very much from the input value of the symmetry energy used. The best possible way to deduce the value of the symmetry energy coefficient is to use the fragment yield at the breakup stage of the reaction and it is better to use the grand canonical model for the fragmentation analysis. This is because the formulas that are used for the deduction of the symmetry energy coefficient are all derived in the framework of the grand canonical ensemble which is valid only at the break-up (equilibrium) condition. The yield of "cold" fragments either from the theoretical models or from experiments when used for extraction of the symmetry energy coefficient using these prescriptions might lead to the wrong conclusion.
Discrete particle transport in porous media : discrete observations of physical mechanisms influencing particle behavior
Yoon, Joon Sik, 1973-
An understanding of how discrete particles in the micron to submicron range behave in porous media is important to a number of environmental problems. Discrete particle behavior in the interior of a porous medium is complex ...
Chiral Symmetry Breaking in Graphene
Gordon W. Semenoff
The question of whether the Coulomb interaction is strong enough to break the sublattice symmetry of un-doped graphene is discussed. We formulate a strong coupling expansion where the ground state of the Coulomb Hamiltonian is found exactly and the kinetic hopping Hamiltonian is treated as a perturbation. We argue that many of the properties of the resulting system would be shared by graphene with a Hubbard model interaction. In particular, the best candidate sublattice symmetry breaking ground state is an antiferromagnetic Mott insulator. We discuss the results of some numerical simulations which indicate that the Coulomb interaction is indeed subcritical. We also point out the curious fact that, if the electron did not have spin degeneracy, the tendency to break chiral symmetry would be much greater and even relatively weak Coulomb interactions would likely gap the spectrum.
Unparticles and electroweak symmetry breaking
Lee, Jong-Phil [Korea Institute for Advanced Study, Seoul 130-722 (Korea, Republic of)
We investigate a scalar potential inspired by the unparticle sector for the electroweak symmetry breaking. The scalar potential contains the interaction between the standard model fields and unparticle sector. It is described by the non-integral power of fields that originates from the nontrivial scaling dimension of the unparticle operator. It is found that the electroweak symmetry is broken at tree level when the interaction is turned on. The scale invariance of unparticle sector is also broken simultaneously, resulting in a physical Higgs and a new lighter scalar particle.
Verifying Volume Rendering Using Discretization Error Analysis
Kirby, Mike
Verifying Volume Rendering Using Discretization Error Analysis Tiago Etiene, Daniel Jo�nsson, Timo--We propose an approach for verification of volume rendering correctness based on an analysis of the volume rendering integral, the basis of most DVR algorithms. With respect to the most common discretization
Introduction Discrete-time autoregressive process
Di Girolami, Cristina
Introduction Discrete-time autoregressive process Continuous-time Ornstein-Uhlenbeck process Sharp large deviations for the non-stationary Ornstein-Uhlenbeck process Bernard Bercu Bordeaux University-Uhlenbeck process 1 / 46 #12;Introduction Discrete-time autoregressive process Continuous-time Ornstein
Discrete analysis of stochastic NMR
Wong, Sam Tak-Sum
Stochastic NMR is an efficient technique for high field in vivo imaging and spectroscopic studies in cases where the peak rf power required may be prohibitively high for conventional pulsed NMR techniques. This dissertation presents a theoretical analysis of a stochastic NMR method of acquiring spectroscopy data. The spin system is excited with rf pulses where the flip angles or the phases of the pulses are samples of a discrete stochastic process. The method is formulated as a stochastic difference equation which is then converted to ordinary deterministic difference equations describing the input-output cross-correlation, average signal power and signal power spectrum. The solutions of these equations are used to evaluate the stochastic, technique in terms of peak rf power requirement, spectral distortions and signal-to-noise ratio. Experimental results are also presented which verify the results of the discrete analysis. The analysis shows that the maximum signal-to-noise ratio is achieved when the RMS flip angle is approximately the Ernst angle. When the RMS flip angle is below the Ernst angle, the input-output cross-correlation is a good estimate of the FID. Increase of excitation power causes line broadening. In addition, the use of random flip angle, fixed phase excitation causes a notch artifact and non-uniform response across the spectrum both of which are not found in two new types of excitation, the random phase excitation and the random quadrature excitation. The signal power spectrum is also a good estimate of the real spectrum. The approximation of the cross-correlation by a time average causes systematic noise. The amount of systematic noise is found to be significantly reduced when an entire maximum length sequence (MLS) is used for excitation. Noise-like distortion at high power MLS excitation is discovered to be related to the number of feedback paths in the MLS generator. 29 refs., 58 figs.
Baryon and chiral symmetry breaking
Gorsky, A. [Institute for Theoretical and Experimental Physics (ITEP), Moscow, Russia and Moscow Institute of Physics and Technology (MIPT), Dolgoprudny (Russian Federation); Krikun, A. [NORDITA, KTH Royal Institute of Technology and Stockholm University Stockholm, Sweden and Institute for Theoretical and Experimental Physics (ITEP), Moscow (Russian Federation)
We briefly review the generalized Skyrmion model for the baryon recently suggested by us. It takes into account the tower of vector and axial mesons as well as the chiral symmetry breaking. The generalized Skyrmion model provides the qualitative explanation of the Ioffe�s formula for the baryon mass.
Symmetry breaking in laser cavities
Malomed, Boris A
A brief introduction to the topic of spontaneous symmetry breaking (SSB) in conservative and dissipative nonlinear systems with an underlying double-well-potential structure is given. The reason is a discussion of a recent observation of the SSB a dual-core nanolaser cavity [5]. The effect is illustrated by means of a simple semi-analytically-tractable model (Fig. 1).
(Small) Resonant non-Gaussianities: Signatures of a Discrete Shift Symmetry
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Consistent Cosmology, Dynamic Relativity and Causal Quantum Mechanics as Unified Manifestations of the Symmetry of Complexity
Andrei P. Kirilyuk
The universal symmetry, or conservation, of complexity underlies any law or principle of system dynamics and describes the unceasing transformation of dynamic information into dynamic entropy as the unique way to conserve their sum, the total dynamic complexity. Here we describe the real world structure emergence and dynamics as manifestation of the universal symmetry of complexity of initially homogeneous interaction between two protofields. It provides the unified complex-dynamic, causally complete origin of physically real, 3D space, time, elementary particles, their properties (mass, charge, spin, etc.), quantum, relativistic, and classical behaviour, as well as fundamental interaction forces, including naturally quantized gravitation. The old and new cosmological problems (including "dark" mass and energy) are basically solved for this explicitly emerging, self-tuning world structure characterised by strictly positive (and large) energy-complexity. A general relation is obtained between the numbers of world dimensions and fundamental forces, excluding plausible existence of hidden dimensions. The unified, causally explained quantum, classical, and relativistic properties (and types of behaviour) are generalised to all higher levels of complex world dynamics. The real world structure, dynamics, and evolution are exactly reproduced by the probabilistic dynamical fractal, which is obtained as the truly complete general solution of a problem and the unique structure of the new mathematics of complexity. We outline particular, problem-solving applications of always exact, but irregularly structured symmetry of unreduced dynamic complexity to microworld dynamics, including particle physics, genuine quantum chaos, real nanobiotechnology, and reliable genomics.
Symmetry Breaking Revisited Jean-Francois Puget
Flener, Pierre
Symmetry Breaking Revisited Jean-Fran�cois Puget ILOG, 9 avenue de Verdun, 94253 Gentilly, France, email@example.com Abstract. Symmetries in constraint satisfaction problems (CSPs) are one
Identification and Estimation of a Discrete Game of Complete Information
Bajari, Patrick
We discuss the identification and estimation of discrete games of complete information. Following Bresnahan and Reiss (1990, 1991), a discrete game is a generalization of a standard discrete choice model where utility ...
Resonance and web structure in discrete soliton systems: the two-dimensional Toda lattice and its fully discrete and ultra-discrete versions
Ken-ichi Maruno; Gino Biondini
We present a class of solutions of the two-dimensional Toda lattice equation, its fully discrete analogue and its ultra-discrete limit. These solutions demonstrate the existence of soliton resonance and web-like structure in discrete integrable systems such as differential-difference equations, difference equations and cellular automata (ultra-discrete equations).
1+1+2 Electromagnetic perturbations on non-vacuum LRS class II space-times: Decoupling scalar and 2-vector harmonic amplitudes
R B Burston
We use the covariant and gauge-invariant 1+1+2 formalism of Clarkson and Barrett \\cite{Clarkson2003} to analyze electromagnetic (EM) perturbations on non-vacuum {\\it locally rotationally symmetric} (LRS) class II space-times. Ultimately, we show how to derive six real decoupled equations governing the total of six EM scalar and 2-vector harmonic amplitudes. Four of these are new, and result from expanding the complex EM 2-vector which we defined in \\cite{Burston2007} in terms of EM 2-vector harmonic amplitudes. We are then able to show that there are four precise combinations of the amplitudes that decouple, two of these are polar perturbations whereas the remaining two are axial. The remaining two decoupled equations are the generalized Regge-Wheeler equations which were developed previously in \\cite{Betschart2004}, and these govern the two EM scalar harmonic amplitudes. However, our analysis generalizes this by including a full description and classification of energy-momentum sources, such as charges and currents.
From Additional Symmetries to Linearization of Virasoro Symmetries
Chao-Zhong Wu
We construct the additional symmetries and derive the Adler-Shiota-van Moerbeke formula for the two-component BKP hierarchy. We also show that the Drinfeld-Sokolov hierarchies of type D, which are reduced from the two-component BKP hierarchy, possess symmetries written as the action of a series of linear Virasoro operators on the tau function. It results in that the Drinfeld-Sokolov hierarchies of type D coincide with Dubrovin and Zhang's hierarchies associated to the Frobenius manifolds for Coxeter groups of type D, and that every solution of such a hierarchy together with the string equation is annihilated by certain combinations of the Virasoro operators and the time derivations of the hierarchy.
Symmetry examples in open quantum dynamics
Thomas F. Jordan; San Ha Seo
Dependent symmetries, a new kind of symmetry of the open quantum dynamics of a subsystem, symmetries that depend on the situation of the subsystem in a larger closed system, are explored by looking at simple examples. Each symmetry implies a particular form for the results of the open dynamics. The forms exhibit the symmetries very simply. It is shown directly, without assuming anything about the symmetry, that the dynamics produces the form, but knowing the symmetry and the form it implies can reduce what needs to be done to work out the dynamics; pieces can be deduced from the symmetry rather that calculated from the dynamics. Symmetries can be related to constants of the motion in new ways. A quantity might be a dependent constant of the motion, constant only for particular situations of the subsystem in the larger system. In particular, a generator of dependent symmetries could represent a quantity that is a dependent constant of the motion for the same situations as for the symmetries. The examples present a variety of possibilities. Sometimes a generator of dependent symmetries does represent a dependent constant of the motion. Sometimes it does not. Sometimes no quantity is a dependent constant of the motion. Sometimes every quantity is.
Localization and chiral symmetry in 2+1 flavor domain wall QCD
David J. Antonio; Kenneth C. Bowler; Peter A. Boyle; Norman H. Christ; Michael A. Clark; Saul D. Cohen; Chris Dawson; Alistair Hart; Balint Jo�; Chulwoo Jung; Richard D. Kenway; Shu Li; Meifeng Lin; Robert D. Mawhinney; Christopher M. Maynard; Shigemi Ohta; Robert J. Tweedie; Azusa Yamaguchi
We present results for the dependence of the residual mass of domain wall fermions (DWF) on the size of the fifth dimension and its relation to the density and localization properties of low-lying eigenvectors of the corresponding hermitian Wilson Dirac operator relevant to simulations of 2+1 flavor domain wall QCD. Using the DBW2 and Iwasaki gauge actions, we generate ensembles of configurations with a $16^3\\times 32$ space-time volume and an extent of 8 in the fifth dimension for the sea quarks. We demonstrate the existence of a regime where the degree of locality, the size of chiral symmetry breaking and the rate of topology change can be acceptable for inverse lattice spacings $a^{-1} \\ge 1.6$ GeV.
Anatomy of a deformed symmetry: Field quantization on curved momentum space
Arzano, Michele [Institute for Theoretical Physics, Utrecht University, Leuvenlaan 4, Utrecht 3584 CE (Netherlands)
In certain scenarios of deformed relativistic symmetries relevant for noncommutative field theories particles exhibit a momentum space described by a non-Abelian group manifold. Starting with a formulation of phase space for such particles which allows for a generalization to include group-valued momenta we discuss quantization of the corresponding field theory. Focusing on the particular case of {kappa}-deformed phase space we construct the one-particle Hilbert space and show how curvature in momentum space leads to an ambiguity in the quantization procedure reminiscent of the ambiguities one finds when quantizing fields in curved space-times. The tools gathered in the discussion on quantization allow for a clear definition of the basic deformed field mode operators and two-point function for {kappa}-quantum fields.
Peccei-Quinn Symmetry from Dynamical Supersymmetry Breaking
Harigaya, Keisuke; Schmitz, Kai; Yanagida, Tsutomu T
The proximity of the Peccei-Quinn scale to the scale of supersymmetry breaking in models of pure gravity mediation hints at a common dynamical origin of these two scales. To demonstrate how to make such a connection manifest, we embed the Peccei-Quinn mechanism into the vector-like model of dynamical supersymmetry breaking a la IYIT. Here, we rely on the anomaly-free discrete Z4R symmetry required in models of pure gravity mediation to solve the mu problem to protect the Peccei-Quinn symmetry from the dangerous effect of higher-dimensional operators. This results in a rich phenomenology featuring a QCD axion with a decay constant of O(10^10) GeV and mixed WIMP/axion dark matter. In addition, exactly five pairs of extra 5 and 5* matter multiplets, directly coupled to the supersymmetry breaking sector and with masses close to the gravitino mass, m3/2 ~ 100 TeV, are needed to cancel the Z4R anomalies.
Peccei-Quinn Symmetry from Dynamical Supersymmetry Breaking
Keisuke Harigaya; Masahiro Ibe; Kai Schmitz; Tsutomu T. Yanagida
The proximity of the Peccei-Quinn scale to the scale of supersymmetry breaking in models of pure gravity mediation hints at a common dynamical origin of these two scales. To demonstrate how to make such a connection manifest, we embed the Peccei-Quinn mechanism into the vector-like model of dynamical supersymmetry breaking a la IYIT. Here, we rely on the anomaly-free discrete Z4R symmetry required in models of pure gravity mediation to solve the mu problem to protect the Peccei-Quinn symmetry from the dangerous effect of higher-dimensional operators. This results in a rich phenomenology featuring a QCD axion with a decay constant of O(10^10) GeV and mixed WIMP/axion dark matter. In addition, exactly five pairs of extra 5 and 5* matter multiplets, directly coupled to the supersymmetry breaking sector and with masses close to the gravitino mass, m3/2 ~ 100 TeV, are needed to cancel the Z4R anomalies.
Clifford modules and symmetries of topological insulators
Gilles Abramovici; Pavel Kalugin
We complete the classification of symmetry constraints on gapped quadratic fermion hamiltonians proposed by Kitaev. The symmetry group is supposed compact and can include arbitrary unitary or antiunitary operators in the Fock space that conserve the algebra of quadratic observables. We analyze the multiplicity spaces of {\\em real} irreducible representations of unitary symmetries in the Nambu space. The joint action of intertwining operators and antiunitary symmetries provides these spaces with the structure of Clifford module: we prove a one-to-one correspondence between the ten Altland-Zirnbauer symmetry classes of fermion systems and the ten Morita equivalence classes of real and complex Clifford algebras. The antiunitary operators, which occur in seven classes, are projectively represented in the Nambu space by unitary "chiral symmetries". The space of gapped symmetric hamiltonians is homotopically equivalent to the product of classifying spaces indexed by the dual object of the group of unitary symmetries.
Spatially Discrete FitzHugh-Nagumo Equations
Elmer, Christopher E.; Van Vleck, Erik
We consider pulse and front solutions to a spatially discrete FitzHugh--Nagumo equation that contains terms to represent both depolarization and hyperpolarization of the nerve axon. We demonstrate a technique for deriving ...
Xiaoning Wu
In this paper, we consider the discrete AKNS-D hierarchy, find the construction of the hierarchy, prove the bilinear identity and give the construction of the $\\tau$-functions of this hierarchy.
Energy Levels of "Hydrogen Atom" in Discrete Time Dynamics
Andrei Khrennikov; Yaroslav Volovich
We analyze dynamical consequences of a conjecture that there exists a fundamental (indivisible) quant of time. In particular we study the problem of discrete energy levels of hydrogen atom. We are able to reconstruct potential which in discrete time formalism leads to energy levels of unperturbed hydrogen atom. We also consider linear energy levels of quantum harmonic oscillator and show how they are produced in the discrete time formalism. More generally, we show that in discrete time formalism finite motion in central potential leads to discrete energy spectrum, the property which is common for quantum mechanical theory. Thus deterministic (but discrete time!) dynamics is compatible with discrete energy levels.
Symmetry and Dirac points in graphene spectrum
Gregory Berkolaiko; Andrew Comech
Existence and stability of Dirac points in the dispersion relation of operators periodic with respect to the hexagonal lattice is investigated for different sets of additional symmetries. The following symmetries are considered: rotation by $2\\pi/3$ and inversion, rotation by $2\\pi/3$ and horizontal reflection, inversion or reflection with weakly broken rotation symmetry, and the case where no Dirac points arise: rotation by $2\\pi/3$ and vertical reflection. All proofs are based on symmetry considerations and are elementary in nature. In particular, existence of degeneracies in the spectrum is proved by a transplantation argument (which is deduced from the (co)representation of the relevant symmetry group). The conical shape of the dispersion relation is obtained from its invariance under rotation by $2\\pi/3$. Persistence of conical points when the rotation symmetry is weakly broken is proved using a geometric phase in one case and parity of the eigenfunctions in the other.
Symmetry and Dirac points in graphene spectrum
Gregory Berkolaiko; Andrew Comech
Existence and stability of Dirac points in the dispersion relation of operators periodic with respect to the hexagonal lattice is investigated for different sets of additional symmetries. The following symmetries are considered: rotation by $2\\pi/3$ and inversion, rotation by $2\\pi/3$ and horizontal reflection, inversion or reflection with weakly broken rotation symmetry, and the case where no Dirac points arise: rotation by $2\\pi/3$ and vertical reflection. All proofs are based on symmetry considerations and are elementary in nature. In particular, existence of degeneracies in the spectrum is proved by a transplantation argument (which is deduced from the (co)representation of the relevant symmetry group). The conical shape of the dispersion relation is obtained from its invariance under rotation by $2\\pi/3$. Persistence of conical points when the rotation symmetry is weakly broken is proved using a geometric phase in one case and parity of the eigenfunctions in the other.
Breaking Parity Symmetry Using Extra Dimensions
R. N. Mohapatra; A. P�rez-Lorenzana
We present a new way to break parity symmetry in left-right symmetric models using boundary conditions on the fields residing in the fifth dimension. We also discuss the connection between the limits on the size of extra dimensions and the scale of right handed symmetry breaking obtained from the analysis of neutrinoless double beta decay in the case where the righthanded gauge symmetry is in the bulk.
Symmetries in Linear and Integer Programs
B�di, R
The notion of symmetry is defined in the context of Linear and Integer Programming. Symmetric linear and integer programs are studied from a group theoretical viewpoint. We show that for any linear program there exists an optimal solution in the fixed point set of its symmetry group. Using this result, we develop an algorithm that allows for reducing the dimension of any linear program having a non-trivial group of symmetries.
[Re]constructing Finite Flavour Groups: Horizontal Symmetry Scans from the Bottom-Up
Jim Talbert
We present a novel procedure for identifying discrete, leptonic flavour symmetries, given a class of unitary mixing matrices. By creating explicit 3D representations for generators of residual symmetries in both the charged lepton and neutrino sector, we reconstruct large(r) non-abelian flavour groups using the GAP language for computational finite algebra. We use experimental data to construct only those generators that yield acceptable (or preferable) mixing patterns. Such an approach is advantageous because it 1) can reproduce known groups from other 'top-down' scans while elucidating their origins from residuals, 2) find new previously unconsidered groups, and 3) serve as a powerful model building tool for theorists wishing to explore exotic flavour scenarios. We test our procedure on a generalization of the canonical tri-bimaximal (TBM) form.
Contact Symmetries and Hamiltonian Thermodynamics
A. Bravetti; C. S. Lopez-Monsalvo; F. Nettel
It has been shown that contact geometry is the proper framework underlying classical thermodynamics and that thermodynamic fluctuations are captured by an additional metric structure related to Fisher's Information Matrix. In this work we analyze several unaddressed aspects about the application of contact and metric geometry to thermodynamics. We consider here the Thermodynamic Phase Space and start by investigating the role of gauge transformations and Legendre symmetries for metric contact manifolds and their significance in thermodynamics. Then we present a novel mathematical characterization of first order phase transitions as equilibrium processes on the Thermodynamic Phase Space for which the Legendre symmetry is broken. Moreover, we use contact Hamiltonian dynamics to represent thermodynamic processes in a way that resembles the classical Hamiltonian formulation of conservative mechanics and we show that the relevant Hamiltonian coincides with the irreversible entropy production along thermodynamic processes. Therefore, we use such property to give a geometric definition of thermodynamically admissible fluctuations according to the Second Law of thermodynamics. Finally, we show that the length of a curve describing a thermodynamic process measures its entropy production.
Superconformal symmetry, NMSSM, and inflation
Ferrara, Sergio [Physics Department, Theory Unit, CERN, CH 1211, Geneva 23 (Switzerland); INFN - Laboratori Nazionali di Frascati, Via Enrico Fermi 40, 00044 Frascati (Italy); Kallosh, Renata; Linde, Andrei; Marrani, Alessio [Department of Physics, Stanford University, Stanford, California 94305 (United States); Van Proeyen, Antoine [Instituut voor Theoretische Fysica, Katholieke Universiteit Leuven, Celestijnenlaan 200D, B-3001 Leuven (Belgium)
We identify a particularly simple class of supergravity models describing superconformal coupling of matter to supergravity. In these models, which we call the canonical superconformal supergravity models, the kinetic terms in the Jordan frame are canonical, and the scalar potential is the same as in the global theory. The pure supergravity part of the total action has a local Poincare supersymmetry, whereas the chiral and vector multiplets coupled to supergravity have a larger local superconformal symmetry. The scale-free globally supersymmetric theories, such as the NMSSM with a scale-invariant superpotential, can be naturally embedded into this class of theories. After the supergravity embedding, the Jordan frame scalar potential of such theories remains scale free; it is quartic, it contains no mass terms, no nonrenormalizable terms, no cosmological constant. The local superconformal symmetry can be broken by additional terms, which, in the small field limit, are suppressed by the gravitational coupling. This can be achieved by introducing the nonminimal scalar-curvature coupling, and by taking into account interactions with a hidden sector. In this approach, the smallness of the mass parameters in the NMSSM may be traced back to the original superconformal invariance. This allows one to address the {mu} problem and the cosmological domain wall problem in this model, and to implement chaotic inflation in the NMSSM. We discuss the gravitino problem in the NMSSM inflation, as well as the possibility to obtain a broad class of new versions of chaotic inflation in supergravity.
Symmetry energy in nuclear density functional theory
W. Nazarewicz; P. -G. Reinhard; W. Satula; D. Vretenar
The nuclear symmetry energy represents a response to the neutron-proton asymmetry. In this survey we discuss various aspects of symmetry energy in the framework of nuclear density functional theory, considering both non-relativistic and relativistic self-consistent mean-field realizations side-by-side. Key observables pertaining to bulk nucleonic matter and finite nuclei are reviewed. Constraints on the symmetry energy and correlations between observables and symmetry-energy parameters, using statistical covariance analysis, are investigated. Perspectives for future work are outlined in the context of ongoing experimental efforts.
Symmetries and Renormalization of Noncommutative Field Theory
Szabo, Richard J. [Department of Mathematics, Heriot-Watt University, Colin Maclaurin Building, Riccarton, Edinburgh EH14 4AS (United Kingdom); Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Colin Maclaurin Building, Riccarton, Edinburgh EH14 4AS (United Kingdom)
An overview of recent developments in the renormalization and in the implementation of spacetime symmetries of noncommutative field theory is presented, and argued to be intimately related.
Symmetries in collective neutrino oscillations
Huaiyu Duan; George M. Fuller; Yong-Zhong Qian
We discuss the relationship between a symmetry in the neutrino flavour evolution equations and neutrino flavour oscillations in the collective precession mode. This collective precession mode can give rise to spectral swaps (splits) when conditions can be approximated as homogeneous and isotropic. Multi-angle numerical simulations of supernova neutrino flavour transformation show that when this approximation breaks down, non-collective neutrino oscillation modes decohere kinematically, but the collective precession mode still is expected to stand out. We provide a criterion for significant flavour transformation to occur if neutrinos participate in a collective precession mode. This criterion can be used to understand the suppression of collective neutrino oscillations in anisotropic environments in the presence of a high matter density. This criterion is also useful in understanding the breakdown of the collective precession mode when neutrino densities are small.
Local symmetries of non-expanding horizons
Rudranil Basu; Ayan Chatterjee; Amit Ghosh
Local symmetries of a non-expanding horizon has been investigated in the 1st order formulation of gravity. When applied to a spherically symmetric isolated horizon only a U(1) subgroup of the Lorentz group survives as residual local symmetry that one can make use of in constructing an effective theory on the horizon.
Reducing Symmetry in Matrix Models # Zeynep Kzltan
Rossi, Francesca
University, Sweden email@example.com 1 Introduction Symmetry in a CSP model is an important issue as the exploration of symmetric but essentially equivalent branches in a search tree may significantly slow down developed so as to address the issue of eliminating symmetry in CSP models. Many CSPs can be modelled
Symmetry-Breaking Constraints for Matrix Models
Flener, Pierre
-breaking constraints. Experimental re- sults confirm their value. 1 Introduction Symmetry in a CSP model is an important issue as the exploration of symmet- ric but essentially equivalent branches in a search tree may techniques have been developed to address the issue of eliminating symmetry in CSP models. An important class
Symmetries in Nuclei P. Van Isacker
Boyer, Edmond
of symmetry and dynamical symmetry in quantum mechanics are introduced and illustrated with simple examples the nineteenth century and made another leap forward in 1873 when Sophus Lie proposed the concept of a Lie group of quantum mechanics, and it became clear that group theory provides a powerful tool to understand
On systems having Poincar� and Galileo symmetry
Peter Holland
Using the wave equation in d > or = 1 space dimensions it is illustrated how dynamical equations may be simultaneously Poincar\\'e and Galileo covariant with respect to different sets of independent variables. This provides a method to obtain dynamics-dependent representations of the kinematical symmetries. When the field is a displacement function both symmetries have a physical interpretation. For d = 1 the Lorentz structure is utilized to reveal hitherto unnoticed features of the non-relativistic Chaplygin gas, including a relativistic structure with a limiting case that exhibits the Carroll group, and field-dependent symmetries and associated Noether charges. The Lorentz transformations of the potentials naturally associated with the Chaplygin system are given. These results prompt the search for further symmetries and it is shown that the Chaplygin equations support a nonlinear superposition principle. A known spacetime mixing symmetry is shown to decompose into label-time and superposition symmetries. It is shown that a quantum mechanical system in a stationary state behaves as a Chaplygin gas. The extension to d > 1 is used to illustrate how the physical significance of the dual symmetries is contingent on the context by showing that Maxwells equations exhibit an exact Galileo covariant formulation where Lorentz and gauge transformations are represented by field-dependent symmetries. A natural conceptual and formal framework is provided by the Lagrangian and Eulerian pictures of continuum mechanics.
Marius de Leeuw; Takuya Matsumoto; Sanefumi Moriyama; Vidas Regelskis; Alessandro Torrielli
We discuss special quantum group (secret) symmetries of the integrable system associated to the AdS/CFT correspondence. These symmetries have by now been observed in a variety of forms, including the spectral problem, the boundary scattering problem, n-point amplitudes, the pure-spinor formulation and quantum affine deformations.
de Leeuw, Marius; Moriyama, Sanefumi; Regelskis, Vidas; Torrielli, Alessandro
We discuss special quantum group (secret) symmetries of the integrable system associated to the AdS/CFT correspondence. These symmetries have by now been observed in a variety of forms, including the spectral problem, the boundary scattering problem, n-point amplitudes, the pure-spinor formulation and quantum affine deformations.
The Symmetry, Color, and Morphology of Galaxies
Christopher J. Conselice
The structural symmetry of forty-three face-on galaxy images in the R(65 0 nm) and J(450 nm) bands are measured to determine the usefulness of symmetry a s a morphological parameter. Each galaxy image is rotated by $180$\\deg and subtr acted from the original to obtain a quantitative value for its structural symmet ry. The symmetry numbers computed for the sample are then compared with RC3 mor phological types, color \\& absolute blue magnitudes. A strong correlation betw een color and symmetry is found, and the RC3 Hubble sequence is found to be one of increasing asymmetry. The use of symmetry as a morphological parameter, and the possible causes of the asymmetries are discussed.
Noether theorem for mu-symmetries
G. Cicogna; G. Gaeta
We give a version of Noether theorem adapted to the framework of mu-symmetries; this extends to such case recent work by Muriel, Romero and Olver in the framework of lambda-symmetries, and connects mu-symmetries of a Lagrangian to a suitably modified conservation law. In some cases this "mu-conservation law'' actually reduces to a standard one; we also note a relation between mu-symmetries and conditional invariants. We also consider the case where the variational principle is itself formulated as requiring vanishing variation under mu-prolonged variation fields, leading to modified Euler-Lagrange equations. In this setting mu-symmetries of the Lagrangian correspond to standard conservation laws as in the standard Noether theorem. We finally propose some applications and examples.
Infinite-dimensional symmetry for wave equation with additional condition
Irina Yehorchenko; Alla Vorobyova
Symmetries for wave equation with additional conditions are found. Some conditions yield infinite-dimensional symmetry algebra for the nonlinear equation. Ansatzes and solutions corresponding to the new symmetries were constructed.
Fast mix table construction for material discretization
Johnson, S. R. [Oak Ridge National Laboratory, Oak Ridge, TN 37831 (United States)
An effective hybrid Monte Carlo-deterministic implementation typically requires the approximation of a continuous geometry description with a discretized piecewise-constant material field. The inherent geometry discretization error can be reduced somewhat by using material mixing, where multiple materials inside a discrete mesh voxel are homogenized. Material mixing requires the construction of a 'mix table,' which stores the volume fractions in every mixture so that multiple voxels with similar compositions can reference the same mixture. Mix table construction is a potentially expensive serial operation for large problems with many materials and voxels. We formulate an efficient algorithm to construct a sparse mix table in O(number of voxels x log number of mixtures) time. The new algorithm is implemented in ADVANTG and used to discretize continuous geometries onto a structured Cartesian grid. When applied to an end-of-life MCNP model of the High Flux Isotope Reactor with 270 distinct materials, the new method improves the material mixing time by a factor of 100 compared to a naive mix table implementation. (authors)
Regularized Discrete Optimal Transport Sira Ferradans1
Boyer, Edmond
. firstname.lastname@example.com Abstract. This article introduces a generalization of discrete in modified images. In this article, we propose a variational formalism to relax and regularize the transport dedicated linear solvers (transportation simplex) and combinatorial algorithms (such as the Hungarian
All-optical discrete vortex switch
Desyatnikov, Anton S. [Nonlinear Physics Center, Research School of Physics and Engineering, Australian National University, Canberra, ACT 0200 (Australia); Dennis, Mark R. [H. H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL (United Kingdom); Ferrando, Albert [Interdisciplinary Modeling Group, InterTech and Departament d'Optica, Universitat de Valencia, E-46100 Burjassot (Spain)
We introduce discrete vortex solitons and vortex breathers in circular arrays of nonlinear waveguides. The simplest vortex breather in a four-waveguide coupler is a nonlinear dynamic state changing its topological charge between +1 and -1 periodically during propagation. We find the stability domain for this solution and suggest an all-optical vortex switching scheme.
Dynamic Discrete Power Control in Cellular Networks
Avrachenkov, Konstantin
1 Dynamic Discrete Power Control in Cellular Networks Eitan Altman, Konstantin Avrachenkov, Ishai. In each of the two frameworks, we consider both cooperative as well as non-cooperative power control. We utilization. It is, therefore, in the interests of the users to control their transmit powers levels so
Model Uncertainty in Discrete Event Stanley Young
Garg, Vijay
Abstract Earlier work concerning control of discrete event systems usually assumed that a correct model to test for the correct model or noti cation that the remaining models cannot be controllably distin- guished. We use the nite state machine model with controllable and uncontrollable events presented
Contributions to the development of residual discretizations
Paris-Sud XI, Universit� de
Contributions to the development of residual discretizations for hyperbolic conservation laws with application to shallow water flows Manuscript submitted in fulfillment of the requirements for the obtention;Contents 1 Overview 9 1.1 Residual schemes for hyperbolic conservation laws
Discrete profile alignment via constrained information bottleneck
Chechik, Gal
Discrete profile alignment via constrained information bottleneck Sean O'Rourke firstname.lastname@example.com Abstract Amino acid profiles, which capture position-specific mutation prob- abilities, are a richer encoding of biological sequences than the in- dividual sequences themselves. However, profile comparisons
Discrete profile alignment via constrained information bottleneck
Chechik, Gal
Discrete profile alignment via constrained information bottleneck Sean O'Rourke # firstname.lastname@example.com Abstract Amino acid profiles, which capture positionspecific mutation prob abilities, are a richer encoding of biological sequences than the in dividual sequences themselves. However, profile comparisons
Comment on ``Discrete Boltzmann Equation for Microfluidics''
Luo, Li-Shi
Comment on ``Discrete Boltzmann Equation for Microfluidics'' In a recent Letter [1], Li and Kwok use a lattice Boltzmann equation (LBE) for microfluidics. Their main claim is that an LBE model for microfluidics can be constructed based on the ``Bhatnagar-Gross-Kooky [sic]'' model by including ``the
Controller Synthesis of Discrete Linear Plants Using MATTEO SLANINA
Sankaranarayanan, Sriram
Controller Synthesis of Discrete Linear Plants Using Polyhedra MATTEO SLANINA Stanford University controllers for linear discrete systems with disturbances. Given a plant description and a safety We study techniques for synthesizing synchronous controllers for affine plants with disturbances
Discretization and Algorithms for Strong Coupling in Computational Aeroelasticity
8 4.1 Flow discretization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 4.2 Structural discretization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 4.3 Mimicing the energy.4 A bifurcation at M1 = 0:95 . . . . . . . . . . . . . . . . . . . . . . . . . . 22 6.5 Stability chart
Defining Employee Perceptions of Discretion: When, Where, and How
Thompson, Rebecca Jean
discretion: choice over when, where, and how one works. Second, the influence of these three forms of discretion on both work-related outcomes (job satisfaction, burnout, and turnover intentions) and nonwork-related outcomes (life satisfaction, work...
Math 209 Discrete Mathematics Spring 2008 Instructor Amites Sarkar
Sarkar, Amites
Math 209 Discrete Mathematics Spring 2008 Instructor Amites Sarkar Text Discrete Mathematics, Tuesdays, Thursdays and Fridays, in 216 Bond Hall. My phone number is 650 7569 and my e-mail is amites.sarkar
Math 209 Discrete Mathematics Spring 2011 Instructor Dr. Amites Sarkar
Sarkar, Amites
Math 209 Discrete Mathematics Spring 2011 Instructor Dr. Amites Sarkar Text Discrete Mathematics, in 216 Bond Hall. My phone number is 650 7569 and my e-mail is email@example.com #12;
Math 209 Discrete Mathematics Winter 2009 Instructor Amites Sarkar
Sarkar, Amites
Math 209 Discrete Mathematics Winter 2009 Instructor Amites Sarkar Text Discrete Mathematics, Tuesdays, Thursdays and Fridays, in 216 Bond Hall. My phone number is 650 7569 and my e-mail is amites.sarkar
Discrete Spectral Transformations of Skew Orthogonal Polynomials and Associated Discrete Integrable Systems
Hiroshi Miki; Hiroaki Goda; Satoshi Tsujimoto
Discrete spectral transformations of skew orthogonal polynomials are presented. From these spectral transformations, it is shown that the corresponding discrete integrable systems are derived both in 1+1 dimension and in 2+1 dimension. Especially in the (2+1)-dimensional case, the corresponding system can be extended to 2x2 matrix form. The factorization theorem of the Christoffel kernel for skew orthogonal polynomials in random matrix theory is presented as a by-product of these transformations.
Discrete spectral transformations of skew orthogonal polynomials and associated discrete integral systems
Miki, Hiroshi; Tsujimoto, Satoshi
Discrete spectral transformations of skew orthognal polynomials are presented. From these spectral transformations, it is shown that the corresponding discrete integrable systems are derived both in 1+1 dimension and in 2+1 dimension. Especially in the 2+1 dimensional case, the corresponding system can be extended to 2x2 matrix form. The factorization theorem of the skew-Christoffel kernel in random matrix theory is presented as a by-product of these transformations.
Investigations into the Nature of Halogen Bonding Including Symmetry...
Broader source: All U.S. Department of Energy (DOE) Office Webpages (Extended Search)
into the Nature of Halogen Bonding Including Symmetry Adapted Perturbation Theory Analyses. Investigations into the Nature of Halogen Bonding Including Symmetry Adapted...
Optimal control, nonlinear systems, state constraints, Euler discretization, rate of ... convergence, provided with modern variational techniques, are also [25];�...
Second order symmetry-preserving conservative Lagrangian scheme for compressible Euler equations in two-dimensional cylindrical coordinates
Cheng, Juan, E-mail: email@example.com [Institute of Applied Physics and Computational Mathematics, Beijing 100094 (China); Shu, Chi-Wang, E-mail: firstname.lastname@example.com [Division of Applied Mathematics, Brown University, Providence, RI 02912 (United States)
In applications such as astrophysics and inertial confinement fusion, there are many three-dimensional cylindrical-symmetric multi-material problems which are usually simulated by Lagrangian schemes in the two-dimensional cylindrical coordinates. For this type of simulation, a critical issue for the schemes is to keep spherical symmetry in the cylindrical coordinate system if the original physical problem has this symmetry. In the past decades, several Lagrangian schemes with such symmetry property have been developed, but all of them are only first order accurate. In this paper, we develop a second order cell-centered Lagrangian scheme for solving compressible Euler equations in cylindrical coordinates, based on the control volume discretizations, which is designed to have uniformly second order accuracy and capability to preserve one-dimensional spherical symmetry in a two-dimensional cylindrical geometry when computed on an equal-angle-zoned initial grid. The scheme maintains several good properties such as conservation for mass, momentum and total energy, and the geometric conservation law. Several two-dimensional numerical examples in cylindrical coordinates are presented to demonstrate the good performance of the scheme in terms of accuracy, symmetry, non-oscillation and robustness. The advantage of higher order accuracy is demonstrated in these examples.
High density behaviour of nuclear symmetry energy
D. N. Basu; Tapan Mukhopadhyay
Role of the isospin asymmetry in nuclei and neutron stars, with an emphasis on the density dependence of the nuclear symmetry energy, is discussed. The symmetry energy is obtained using the isoscalar as well as isovector components of the density dependent M3Y effective interaction. The constants of density dependence of the effective interaction are obtained by reproducing the saturation energy per nucleon and the saturation density of spin and isospin symmetric cold infinite nuclear matter. Implications for the density dependence of the symmetry energy in case of a neutron star are discussed, and also possible constraints on the density dependence obtained from finite nuclei are compared.
Constraints on leptogenesis from a symmetry viewpoint
Gonzalez Felipe, R. [Area Cientifica de Fisica, Instituto Superior de Engenharia de Lisboa, Rua Conselheiro Emidio Navarro 1, 1959-007 Lisboa (Portugal); Departamento de Fisica and Centro de Fisica Teorica de Particulas (CFTP), Instituto Superior Tecnico, Av. Rovisco Pais, 1049-001 Lisboa (Portugal); Serodio, H. [Departamento de Fisica and Centro de Fisica Teorica de Particulas (CFTP), Instituto Superior Tecnico, Av. Rovisco Pais, 1049-001 Lisboa (Portugal)
It is shown that type I seesaw models based on the standard model Lagrangian extended with three heavy Majorana right-handed fields do not have leptogenesis in leading order, if the symmetries of mass matrices are also the residual symmetry of the Lagrangian. In particular, flavor models that lead to a mass-independent leptonic mixing have a vanishing leptogenesis CP asymmetry. Based on symmetry arguments, we prove that in these models the Dirac-neutrino Yukawa coupling combinations relevant for leptogenesis are diagonal in the physical basis where the charged leptons and heavy Majorana neutrinos are diagonal.
Constraints on leptogenesis from a symmetry viewpoint
R. Gonzalez Felipe; H. Serodio
It is shown that type I seesaw models based on the standard model Lagrangian extended with three heavy Majorana right-handed fields do not have leptogenesis in leading order, if the symmetries of mass matrices are also the residual symmetry of the Lagrangian. In particular, flavor models that lead to a mass-independent leptonic mixing have a vanishing leptogenesis CP asymmetry. Based on symmetry arguments, we prove that in these models the Dirac-neutrino Yukawa coupling combinations relevant for leptogenesis are diagonal in the physical basis where the charged leptons and heavy Majorana neutrinos are diagonal.
Constraints on leptogenesis from a symmetry viewpoint
Felipe, R Gonzalez
It is shown that type-I seesaw models based on the Standard Model Lagrangian extended with three heavy Majorana right-handed fields do not have leptogenesis in leading order, if the symmetries of mass matrices are also the residual symmetry of the Lagrangian. In particular, flavor models that lead to a mass-independent leptonic mixing have a vanishing leptogenesis CP-asymmetry. Based on symmetry arguments, we prove that in these models the Dirac-neutrino Yukawa coupling combinations relevant for leptogenesis are always real in the physical basis where the charged leptons and heavy Majorana neutrinos are diagonal.
Graphene, Lattice QFT and Symmetries
L. B Drissi; E. H Saidi; M. Bousmina
Borrowing ideas from tight binding model, we propose a board class of Lattice QFT models that are classified by the ADE Lie algebras. In the case of su(N) series, we show that the couplings between the quantum states living at the first nearest neighbor sites of the lattice $\\mathcal{L}_{su(N)}$ are governed by the complex fundamental representations \\underline{${{\\mathbf{N}}}$} and $\\bar{{\\mathbf{N}}}$ of $su(N)$; and the second nearest neighbor interactions are described by its adjoint $\\underline{\\mathbf{N}} \\otimes \\bar{\\mathbf{N}}$. The lattice models associated with the leading su(2), su(3) and su(4) cases are explicitly studied and their fermionic field realizations are given. It is also shown that the su(2) and su(3) models describe respectively the electronic properties of the acetylene chain and the graphene. It is established as well that the energy dispersion of the first nearest neighbor couplings is completely determined by the $A_{N}$ roots $ \\mathbf{\\alpha}$ through the typical dependence $N/2+\\sum_{roots}\\cos(\\mathbf{k}.\\alpha) $ with $\\mathbf{k}$ the wave vector. Other features such as DE extension and other applications are also discussed. Keywords: Tight Binding Model, Graphene, Lattice QFT, ADE Symmetries.
Does Symmetry Imply PPT Property?
Daniel Cariello
Recently, in [1], the author proved that many results that are true for PPT matrices also hold for another class of matrices with a certain symmetry in their Hermitian Schmidt decompositions. These matrices were called SPC in [1] (definition 1.1). Before that, in [9], T\\'oth and G\\"uhne proved that if a state is symmetric then it is PPT if and only if it is SPC. A natural question appeared: What is the connection between SPC matrices and PPT matrices? Is every SPC matrix PPT? Here we show that every SPC matrix is PPT in $M_2\\otimes M_2$ (theorem 4.3). This theorem is a consequence of the fact that every density matrix in $M_2\\otimes M_m$, with tensor rank smaller or equal to 3, is separable (theorem 3.2). This theorem is a generalization of the same result found in [1] for tensor rank 2 matrices in $M_k\\otimes M_m$. Although, in $M_3\\otimes M_3$, there exists a SPC matrix with tensor rank 3 that is not PPT (proposition 5.2). We shall also provide a non trivial example of a family of matrices in $M_k\\otimes M_k$, in which both, the SPC and PPT properties, are equivalent (proposition 6.2). Within this family, there exists a non trivial subfamily in which the SPC property is equivalent to separability (proposition 6.4).
Symmetry energy coefficients for asymmetric nuclear matter
F�bio L. Braghin
Symmetry energy coefficients of asymmetric nuclear matter are investigated as the inverse of nuclear matter polarizabilities with two different approaches. Firstly a general calculation shows they may depend on the neutron-proton asymmetry itself. The choice of particular prescriptions for the density fluctuations lead to certain isospin (n-p asymmetry) dependences of the polarizabilities. Secondly, with Skyrme type interactions, the static limit of the dynamical polarizability is investigated corresponding to the inverse symmetry energy coefficient which assumes different values at different asymmetries (and densities and temperatures). The symmetry energy coefficient (in the isovector channel) is found to increase as n-p asymmetries increase. The spin symmetry energy coefficient is also briefly investigated.
Localized waves with spherical harmonic symmetries
Mills, M. S.
We introduce a class of propagation invariant spatiotemporal optical wave packets with spherical harmonic symmetries in their field configurations. The evolution of these light orbitals is considered theoretically in ...
Particle-hole symmetry parameters for nuclei
Ian Bentley
Two parameters, nu and zeta, motivated by particle-hole symmetry are introduced. These parameters are determined using the number of proton (or neutron) particles and holes counted from neighboring shell closures. The new parameters can be used to evaluate particle-hole and proton-neutron symmetries of adopted B(E2) values, which indicate that both symmetries are approximate for A>100. The combined symmetries motivate empirical fits of binding energies and the energy ratio E(4_1^+)/E(2_1^+). A global binding energy fit consisting of a traditional liquid droplet and one new shell term, comprised of a function of nu and zeta, reproduces the experimental binding energies of 2353 nuclei with an r.m.s. standard deviation of 1.55 MeV.
SUSY and symmetry nonrestoration at high temperature
Bajc, Borut [J. Stefan Institute, 1001 Ljubljana (Slovenia)
The status of internal symmetry breaking at high temperature in super-symmetric models is shortly reviewed. This possibility could solve some well known cosmological problems, such as the domain wall, monopole and false vacuum problems.
Ruck, H.M.
and H.M. Ruck, Quantum field theory Potts model, J. Math.in cyclic symmetry field theories, Nucl. Phys. B167 M.J.waves in nonlinear field theories, Phys. Rev. Lett. 32. R.
Degeneracy and Discreteness in Cosmological Model Fitting
Teng, Huan-Yu; Hu, Huan-Chen; Zhang, Tong-Jie
We explore the degeneracy and discreteness problems in the standard cosmological model ({\\Lambda}CDM). We use the Observational Hubble Data (OHD) and the type Ia supernova (SNe Ia) data to study this issue. In order to describe the discreteness in fitting of data, we define a factor G to test the influence from each single data point and analyze the goodness of G. Our results indicate that a higher absolute value of G shows a better capability of distinguishing models, which means the parameters are restricted into smaller confidence intervals with a larger figure of merit evaluation. Consequently, we claim that the factor G is an effective way in model differentiation when using different models to fit the observational data.
A combinatorial approach to discrete geometry
L. Bombelli; M. Lorente
We present a paralell approach to discrete geometry: the first one introduces Voronoi cell complexes from statistical tessellations in order to know the mean scalar curvature in term of the mean number of edges of a cell. The second one gives the restriction of a graph from a regular tessellation in order to calculate the curvature from pure combinatorial properties of the graph. Our proposal is based in some epistemological pressupositions: the macroscopic continuous geometry is only a fiction, very usefull for describing phenomena at certain sacales, but it is only an approximation to the true geometry. In the discrete geometry one starts from a set of elements and the relation among them without presuposing space and time as a background.
Asymptotic symmetries in an optical lattice
G. Gaeta
It was recently remarked by Lutz [{\\it Phys. Rev. A} {\\bf 67} (2003), 051402(R)] that the equation for the marginal Wigner distribution in an optical lattice admits a scale-free distribution corresponding to Tsallis statistics. Here we show that this distribution is invariant under an asymptotic symmetry of the equation, hence that this scale-free behavior can be understood in terms of symmetry analysis.
Enhanced Coset Symmetries and Higher Derivative Corrections
Neil Lambert; Peter West
After dimensional reduction to three dimensions, the lowest order effective actions for pure gravity, M-theory and the Bosonic string admit an enhanced symmetry group. In this paper we initiate study of how this enhancement is affected by the inclusion of higher derivative terms. In particular we show that the coefficients of the scalar fields associated to the Cartan subalgebra are given by weights of the enhanced symmetry group.
Nonzero {theta}{sub 13} for neutrino mixing in a supersymmetric B-L gauge model with T{sub 7} lepton flavor symmetry
Cao Qinghong [Department of Physics and State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing 100871 (China); High Energy Physics Division, Argonne National Laboratory, Argonne, Illinois 60439, U.S.A (United States); Enrico Fermi Institute, University of Chicago, Chicago, Illinois 60637 (United States); Khalil, Shaaban [Centre for Theoretical Physics, The British University in Egypt, El Sherouk City, Postal No. 11837, P.O. Box 43 (Egypt); Department of Mathematics, Ain Shams University, Faculty of Science, Cairo 11566 (Egypt); Ma, Ernest [Department of Physics and Astronomy, University of California, Riverside, California 92521 (United States); Okada, Hiroshi [School of Physics, KIAS, Seoul 130-722 (Korea, Republic of)
We discuss how {theta}{sub 13}{ne}0 is accommodated in a recently proposed renormalizable model of neutrino mixing using the non-Abelian discrete symmetry T{sub 7} in the context of a supersymmetric extension of the standard model with gauged U(1){sub B-L}. We predict a correlation between {theta}{sub 13} and {theta}{sub 23}, as well as the effective neutrino mass m{sub ee} in neutrinoless double beta decay.
.Shechtman discovered the existence of a solid (an aluminium-manganese alloy) presenting a 5-fold symmetry in its
The Group of symmetries of a square There are eight symmetries of a square
Smith, Karen E.
The Group of symmetries of a square There are eight symmetries of a square: e = no motion r1) a product of two of its subgroups? 5. How many different (non-isomorphic) groups of order eight can you) a = reflection over anti-diagonal (the line y = -x) Complete the Cayley Table for the dihedral group D4: e r1 r2
Bilinear control of discrete spectrum Schr�dinger operators
Kais Ammari; Zied Ammari
The bilinear control problem of the Schr\\"odinger equation $i\\frac{\\partial}{\\partial t}\\psi(t)$ $=(A+u(t) B)\\psi(t)$, where $u(t)$ is the control function, is investigated through topological irreducibility of the set $\\mathfrak{M}=\\{e^{-it (A+u B)}, u\\in \\mathbb{R}, t>0\\}$ of bounded operators. This allows to prove the approximate controllability of such systems when the uncontrolled Hamiltonian $A$ has a simple discrete spectrum and under an appropriate assumption on $B$.
Quantumness of discrete Hamiltonian cellular automata
Hans-Thomas Elze
We summarize a recent study of discrete (integer-valued) Hamiltonian cellular automata (CA) showing that their dynamics can only be consistently defined, if it is linear in the same sense as unitary evolution described by the Schr\\"odinger equation. This allows to construct an invertible map between such CA and continuous quantum mechanical models, which incorporate a fundamental scale. Presently, we emphasize general aspects of these findings, the construction of admissible CA observables, and the existence of solutions of the modified dispersion relation for stationary states.
Compartmentalization analysis using discrete fracture network models
La Pointe, P.R.; Eiben, T.; Dershowitz, W. [Golder Associates, Redmond, VA (United States); Wadleigh, E. [Marathon Oil Co., Midland, TX (United States)
This paper illustrates how Discrete Fracture Network (DFN) technology can serve as a basis for the calculation of reservoir engineering parameters for the development of fractured reservoirs. It describes the development of quantitative techniques for defining the geometry and volume of structurally controlled compartments. These techniques are based on a combination of stochastic geometry, computational geometry, and graph the theory. The parameters addressed are compartment size, matrix block size and tributary drainage volume. The concept of DFN models is explained and methodologies to compute these parameters are demonstrated.
Discrete sine-Gordon dynamics on networks
Dutykh, Denys
In this study we consider the sine-Gordon equation formulated on domains which are not locally homeomorphic to any subset of the Euclidean space. More precisely, we formulate the discrete dynamics on trees and graphs. Each edge is assumed to be a 1D uniform lattice with end points identified with graph vertices. A special treatment is needed at the junctions in order to couple 1D lattices into a global communicating network. Our approach is based on considering the local conservation properties. Some preliminary numerical results are shown on a simple graph containing four loops. These results show the performance of the scheme in non-trivial realistic conditions.
Modified discrete random walk with absorption
Theo van Uem
We obtain expected number of arrivals, probability of arrival, absorption probabilities and expected time before absorption for a modified discrete random walk on the (sub)set of integers. In a [pqrs] random walk the particle can move one step forward or backward, stay for a moment in the same state or it can be absorbed immediately in the current state. M[pqrs] is a modified version, where probabilities on both sides of a multiple function barrier M are of different [pqrs] type.
SNAP:SN (Discrete Ordinates) Application Proxy
Broader source: All U.S. Department of Energy (DOE) Office Webpages (Extended Search)
AFDC Printable Version Share this resource Send a link to EERE: Alternative Fuels Data Center Home Page to someone by E-mail Share EERE: Alternative Fuels Data Center Home Page on Facebook Tweet about EERE: Alternative Fuels Data Center Home Page on Twitter Bookmark EERE: Alternative1 First Use of Energy for All Purposes (Fuel and Nonfuel), 2002; Level:Energy: Grid Integration Redefining What's PossibleRadiation Protection245C Unlimited ReleaseWelcome to theAbsorptionFinalSNAP:SN (Discrete
Collective neutrino oscillations and spontaneous symmetry breaking
Duan, Huaiyu
Neutrino oscillations in a hot and dense astrophysical environment such as a core-collapse supernova pose a challenging, seven-dimensional flavor transport problem. To make the problem even more difficult (and interesting), neutrinos can experience collective oscillations through nonlinear refraction in the dense neutrino medium in this environment. Significant progress has been made in the last decade towards the understanding of collective neutrino oscillations in various simplified neutrino gas models with imposed symmetries and reduced dimensions. However, a series of recent studies seem to have "reset" this progress by showing that these models may not be compatible with collective neutrino oscillations because the latter can break the symmetries spontaneously if they are not imposed. We review some of the key concepts of collective neutrino oscillations by using a few simple toy models. We also elucidate the breaking of spatial and directional symmetries in these models because of collective oscillation...
Viable axion from gauged flavor symmetries
Berenstein, David; Perkins, Erik [Department of Physics, University of California, Santa Barbara, California 93106 (United States)
We consider a string-inspired nonsupersymmetric extension of the standard model with gauged anomalous U(1) flavor symmetries. Consistency requires the Green-Schwarz (GS) mechanism to cancel mixed anomalies. The additional required scalars provide Stueckelberg masses for the Z{sup '} particles associated to the gauged flavor symmetry, so they decouple at low energies. Our models also include a complex scalar field {phi} to generate Froggatt-Nielsen mass terms for light particles, giving a partial solution to the fermion mass problem. A residual approximate (anomalous) global symmetry survives at low energies. The associated pseudo-Goldstone mode is the phase of the {phi} scalar field, and it becomes the dominant contribution to the physical axion. An effective field theory analysis that includes neutrino masses gives a prediction for the axion decay constant. We find a simple model where the axion decay constant is in the center of the allowed window.
Holographic Metals and Insulators with Helical Symmetry
Aristomenis Donos; Blaise Gout�raux; Elias Kiritsis
Homogeneous, zero temperature scaling solutions with Bianchi VII spatial geometry are constructed in Einstein-Maxwell-Dilaton theory. They correspond to quantum critical saddle points with helical symmetry at finite density. Assuming $AdS_{5}$ UV asymptotics, the small frequency/(temperature) dependence of the AC/(DC) electric conductivity along the director of the helix are computed. A large class of insulating and conducting anisotropic phases is found, as well as isotropic, metallic phases. Conduction can be dominated by dissipation due to weak breaking of translation symmetry or by a quantum critical current.
Chimera Death: Symmetry Breaking in Dynamical Networks
Anna Zakharova; Marie Kapeller; Eckehard Sch�ll
For a network of generic oscillators with nonlocal topology and symmetry-breaking coupling we establish novel partially coherent inhomogeneous spatial patterns, which combine the features of chimera states (coexisting incongruous coherent and incoherent domains) and oscillation death (oscillation suppression), which we call chimera death. We show that due to the interplay of nonlocality and breaking of rotational symmetry by the coupling two distinct scenarios from oscillatory behavior to a stationary state regime are possible: a transition from an amplitude chimera to chimera death via in-phase synchronized oscillations, and a direct abrupt transition for larger coupling strength.
attila discrete ordinance: Topics by E-print Network
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recurrence satisfied by the Stirling numbers of the second kind. Abrams, Aaron; Hower, Valerie 2010-01-01 428 VARIATIONAL ESTIMATES FOR DISCRETE SCHR Mathematics Websites...
attila discrete ordinates: Topics by E-print Network
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recurrence satisfied by the Stirling numbers of the second kind. Abrams, Aaron; Hower, Valerie 2010-01-01 428 VARIATIONAL ESTIMATES FOR DISCRETE SCHR Mathematics Websites...
aux ordonnees discretes: Topics by E-print Network
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recurrence satisfied by the Stirling numbers of the second kind. Abrams, Aaron; Hower, Valerie 2010-01-01 326 VARIATIONAL ESTIMATES FOR DISCRETE SCHR Mathematics Websites...
analyzing incomplete discrete: Topics by E-print Network
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Geometric Approach to ML Estimation With Incomplete Data: Application to Semi Reilly, James P. 94 Energy Levels of "Hydrogen Atom" in Discrete Time Dynamics Quantum Physics...
A quantitative description of mesh dependence for the discretization ...
that coming from a ferromagnetic spin energy. The critical case can be regarded as an interpolation between the two. Key words. spatial discretization, singularly
Efficient energy stable schemes with spectral discretization in space ...
We construct energy stable schemes for the time discretization of the highly nonlinear ... shape) in order to achieve a well-defined energy for the system.
optimization of discrete control systems with varying structure
(in russian). 4. Mansimov, K.B., Maharramov, Sh.F.: Necessary conditions of optimality for discrete system with variable structure and rolling right end of the path.
Discretization schemes for diffusion operators on general meshes
Herbin, Rapha�le
: Navier Stokes equations Flow in porous media, Darcy equation. discretization of -div( u)) A can Supplementary constraint from the oil reservoir simulation community: cell centred schemes transport equations
Lowest-rank Solutions of Continuous and Discrete Lyapunov ...
Ziyan Luo
Oct 9, 2012 ... Abstract: The low-rank solutions of continuous and discrete Lyapunov equations are of great importance but generally difficult to achieve in�...
The robust stabilization problem for discrete-time descriptor systems
Claudiu Dinicu
Sep 23, 2014 ... Abstract: We investigate the robust stabilization problem for the descriptor discrete-time systems and build an optimal solution in the case when�...
Group Momentum Space and Hopf Algebra Symmetries of Point Particles Coupled to 2+1 Gravity
Michele Arzano; Danilo Latini; Matteo Lotito
We present an in-depth investigation of the ${\\rm SL}(2,\\mathbb{R})$ momentum space describing point particles coupled to Einstein gravity in three space-time dimensions. We introduce different sets of coordinates on the group manifold and discuss their properties under Lorentz transformations. In particular we show how a certain set of coordinates exhibits an upper bound on the energy under deformed Lorentz boosts which saturate at the Planck energy. We discuss how this deformed symmetry framework is generally described by a quantum deformation of the Poincar\\'e group: the quantum double of ${\\rm SL}(2,\\mathbb{R})$. We then illustrate how the space of functions on the group manifold momentum space has a dual representation on a non-commutative space of coordinates via a (quantum) group Fourier transform. In this context we explore the connection between Weyl maps and different notions of (quantum) group Fourier transform appeared in the literature in the past years and establish relations between them.
Generalised CP and $\\Delta (6n^2)$ Family Symmetry in Semi-Direct Models of Leptons
Ding, Gui-Jun; Neder, Thomas
We perform a detailed analysis of $\\Delta (6n^2)$ family symmetry combined with a generalised CP symmetry in the lepton sector, breaking to different remnant symmetries $G_{\
ccsd00003868, Symmetry and interactivity in
interplay is about, before we enter into the more speci#12;c topic we have in mind here, namely symmetry in which computation is proof search. I am speaking here of the larger match between two kinds of wide proofs { interesting ones rely on various lemmas, sublem- mas, etc... {, checking them, or searching them
Weyl-Gauge Symmetry of Graphene
Alfredo Iorio
The conformal invariance of the low energy limit theory governing the electronic properties of graphene is explored. In particular, it is noted that the massless Dirac theory in point enjoys local Weyl symmetry, a very large symmetry. Exploiting this symmetry in the two spatial dimensions and in the associated three dimensional spacetime, we find the geometric constraints that correspond to specific shapes of the graphene sheet for which the electronic density of states is the same as that for planar graphene, provided the measurements are made in accordance to the inner reference frame of the electronic system. These results rely on the (surprising) general relativistic-like behavior of the graphene system arising from the combination of its well known special relativistic-like behavior with the less explored Weyl symmetry. Mathematical structures, such as the Virasoro algebra and the Liouville equation, naturally arise in this three-dimensional context and can be related to specific profiles of the graphene sheet. Speculations on possible applications of three-dimensional gravity are also proposed.
Symmetries in k-Symplectic Field Theories
Roman-Roy, Narciso [Departamento de Matematica Aplicada IV. Edificio C-3, Campus Norte UPC, C/Jordi Girona 1.08034 Barcelona (Spain); Salgado, Modesto; Vilarino, Silvia [Departamento de Xeometria e Topoloxia, Facultade de Matematicas, Universidade de Santiago de Compostela. 15782 Santiago de Compostela (Spain)
k-symplectic geometry provides the simplest geometric framework for describing certain class of first-order classical field theories. Using this description we analyze different kinds of symmetries for the Hamiltonian and Lagrangian formalisms of these field theories, including the study of conservation laws associated to them and stating Noether's theorem.
Noncommutative gauge theories and Lorentz symmetry
Banerjee, Rabin; Chakraborty, Biswajit; Kumar, Kuldeep [S.N. Bose National Centre for Basic Sciences, JD Block, Sector 3, Salt Lake, Kolkata 700098 (India)
We explicitly derive, following a Noether-like approach, the criteria for preserving Poincare invariance in noncommutative gauge theories. Using these criteria we discuss the various spacetime symmetries in such theories. It is shown that, interpreted appropriately, Poincare invariance holds. The analysis is performed in both the commutative as well as noncommutative descriptions and a compatibility between the two is also established.
/ http://www.sciencemag.org/content/early/recent / 3 April 2014 / Page 1 / 10.1126/science.1248253 Since the 1970s, space-time "supersymmetry" (SUSY) has been actively
Napp, Nils
Majorana modes at their boundary; the modes are protected by time-reversal symmetry from acquiring, contains a pair of Majorana modes ,R L that propagate in op- posite directions. The aforementioned) with 1d = , [ ]T R L = , and we have used the conventional Dirac gamma matrices for the relativistic
Sets of Symmetry Breaking Constraints Barbara M. Smith
Smith, Barbara M.
Sets of Symmetry Breaking Constraints Barbara M. Smith Cork Constraint Computation Centre, University College Cork, Ireland firstname.lastname@example.com Abstract [Puget, 2004] has shown that if the symmetry
On Symmetry, Perspectivity, and Level-Set-Based Segmentation
Riklin-Raviv, Tammy
We introduce a novel variational method for the extraction of objects with either bilateral or rotational symmetry in the presence of perspective distortion. Information on the symmetry axis of the object and the distorting ...
Optimal Control for Holonomic and Nonholonomic Mechanical Systems with Symmetry
Marsden, Jerrold
Optimal Control for Holonomic and Nonholonomic Mechanical Systems with Symmetry and Lagrangian Nonholonomic Mechanical Systems with Symmetry . . . . . . . . . . . . . . . 5 3 Optimal Control and Lagrangian.3 Optimal Control of a Holonomic System on a Principal Bundle . . . . . . . . . . . . 13 4 Optimal Control
Gapped symmetry preserving surface state for the electron topological insulator
Wang, Chong
It is well known that the three-dimensional (3D) electronic topological insulator (TI) with charge-conservation and time-reversal symmetry cannot have a trivial insulating surface that preserves symmetry. It is often ...
Synchronous Symmetry Breaking in Neurons with Different Neurite Counts
Wissner-Gross, Zachary D.
As neurons develop, several immature processes (i.e., neurites) grow out of the cell body. Over time, each neuron breaks symmetry when only one of its neurites grows much longer than the rest, becoming an axon. This symmetry ...
Information storage capacity of discrete spin systems
Beni Yoshida
Understanding the limits imposed on information storage capacity of physical systems is a problem of fundamental and practical importance which bridges physics and information science. There is a well-known upper bound on the amount of information that can be stored reliably in a given volume of discrete spin systems which are supported by gapped local Hamiltonians. However, all the previously known systems were far below this theoretical bound, and it remained open whether there exists a gapped spin system that saturates this bound. Here, we present a construction of spin systems which saturate this theoretical limit asymptotically by borrowing an idea from fractal properties arising in the Sierpinski triangle. Our construction provides not only the best classical error-correcting code which is physically realizable as the energy ground space of gapped frustration-free Hamiltonians, but also a new research avenue for correlated spin phases with fractal spin configurations.
Discrete solitons and vortices on anisotropic lattices
Kevrekidis, P.G. [Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-4515 (United States); Frantzeskakis, D.J. [Department of Physics, University of Athens, Panepistimiopolis, Zografos, Athens 15784 (Greece); Carretero-Gonzalez, R. [Nonlinear Dynamical Systems Group, Department of Mathematics and Statistics, and Computational Science Research Center, San Diego State University, San Diego, California 92182-7720 (United States); Malomed, B.A. [Department of Interdisciplinary Studies, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978 (Israel); Bishop, A.R. [Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)
We consider the effects of anisotropy on solitons of various types in two-dimensional nonlinear lattices, using the discrete nonlinear Schroedinger equation as a paradigm model. For fundamental solitons, we develop a variational approximation that predicts that broad quasicontinuum solitons are unstable, while their strongly anisotropic counterparts are stable. By means of numerical methods, it is found that, in the general case, the fundamental solitons and simplest on-site-centered vortex solitons ('vortex crosses') feature enhanced or reduced stability areas, depending on the strength of the anisotropy. More surprising is the effect of anisotropy on the so-called 'super-symmetric' intersite-centered vortices ('vortex squares'), with the topological charge S equal to the square's size M: we predict in an analytical form by means of the Lyapunov-Schmidt theory, and confirm by numerical results, that arbitrarily weak anisotropy results in dramatic changes in the stability and dynamics in comparison with the degenerate, in this case, isotropic, limit.
XXZ scalar products, Miwa variables and discrete KP
O. Foda; G. Schrader
We revisit the quantum/classical integrable model correspondence in the context of inhomogeneous finite length XXZ spin-1/2 chains with periodic boundary conditions and show that the Bethe scalar product of an arbitrary state and a Bethe eigenstate is a discrete KP tau-function. The continuous Miwa variables of discrete KP are the rapidities of the arbitrary state.
From Discrete Specifications to Hybrid Control1 Paulo Tabuada
Pappas, George J.
@seas.upenn.edu Abstract A great challenge for modern systems theory is the de- sign of controllers for continuous systems inside physical devices has resulted in great challenges for modern and future systems and control theory given a discrete- time controllable linear system and a discrete specifica- tion (in the form
Model Transformation with Hierarchical Discrete-Event Control
Model Transformation with Hierarchical Discrete- Event Control Thomas Huining Feng Electrical permission. #12;Model Transformation with Hierarchical Discrete-Event Control by Huining Feng B.S. (Nanjing Date Date University of California, Berkeley Spring 2009 #12;Model Transformation with Hierarchical
Directed Control of Discrete Event Systems: Optimization Based Approach
Kumar, Ratnesh
Directed Control of Discrete Event Systems: Optimization Based Approach J. Huang and R. Kumar an optimal director. Keywords: Discrete event systems, optimal control, supervisory control, directed control sense for plants that are executor of controllable events. In this paper we develop an optimization
Faugeras, Blaise
EQUILIBRIUM RECONSTRUCTION FROM DISCRETE MAGNETIC MEASUREMENTS IN A TOKAMAK Blaise Faugeras (joint of the equilibrium in a Tokamak from discrete magnetic mea- surements. In order to solve this inverse problem we of a plasma in a Tokamak [1]. The state variable of interest in the modelization of such an equilibrium under
Discrete Wavelet Diffusion for Image Denoising Kashif Rajpoot1
Rajpoot, Nasir
Discrete Wavelet Diffusion for Image Denoising Kashif Rajpoot1 , Nasir Rajpoot2 , J. Alison Noble1 to iterative wavelet shrinkage, but only for (1) MallatZhong dyadic wavelet transform and (2) Haar wavelet shrinkage in the standard discrete wavelet transform (DWT) domain. Two of the major advantages
A DISCRETE WAVELET ANALYSIS OF FREAK WAVES IN THE OCEAN EN-BING LIN AND PAUL C. LIU Received 25 wavelet analysis on a freak wave. We demonstrate several applications of wavelets and discrete and continuous wavelet transforms on the study of a freak wave. A modeling setting for freak waves will also
A Discrete-Event Systems Approach to Modeling Dextrous Manipulation
Graham, Nick
A Discrete-Event Systems Approach to Modeling Dextrous Manipulation S. L. Ricker? N. Sarkar?y K-event systems. The applicability of discrete-event systems to the modeling of dextrous manipulation tasks of the manipulation task, resulting in control discontinuities. The need for tech- niques to facilitate a smooth
University of Michigan and NBER "Identification of Discrete Choice
Presenter: Jeremy Fox University of Michigan and NBER "Identification of Discrete Choice Models;Identification of Discrete Choice Models for Bundles and Binary Games Jeremy T. Fox University of Michigan and NBER Natalia Lazzati University of Michigan March 2014 Abstract We study nonparametric identification
Hefei Institute of Intelligent Machines
importantly, the recognition based on shape feature is also a central problem in those fields such as patternSHAPE MATCHING USING FUZZY DISCRETE PARTICLE SWARM OPTIMIZATION* Ji-Xiang Du1, 2 De-Shuang Huang1 based on fuzzy discrete particle swarm optimization (FDPSO) is proposed. Based on fuzzy theory and PSO
Institute of Operations Research Discrete Optimization and Logistics
Al Hanbali, Ahmad
Institute of Operations Research Discrete Optimization and Logistics 1 Prof. Dr. Stefan Nickel � Health Care Logistics: Overview Health Care Logistics 11/28/2013 #12;Institute of Operations Research Discrete Optimization and Logistics 2 Prof. Dr. Stefan Nickel � Health Care Logistics: Overview Health Care
Cryptanalysing the Critical Group: Efficiently Solving Biggs's Discrete Logarithm Problem
Cryptanalysing the Critical Group: Efficiently Solving Biggs's Discrete Logarithm Problem Simon R Kingdom firstname.lastname@example.com November 7, 2008 Abstract Biggs has recently proposed the critical group that the discrete log problem can be efficiently solved in Biggs's groups. Thus this class of groups is not suitable
Video Denoising and Simplification Via Discrete Regularization on Graphs
Paris-Sud XI, Universit� de
Video Denoising and Simplification Via Discrete Regularization on Graphs Mahmoud Ghoniem, Youssef algorithms for video de- noising and simplification based on discrete regularization on graphs. The main difference between video and image denoising is the temporal redundancy in video sequences. Recent works
ISS-Lyapunov Functions for Discontinuous Discrete-Time Systems
Paris-Sud XI, Universit� de
1 ISS-Lyapunov Functions for Discontinuous Discrete-Time Systems Lars Gr�une and Christopher M. Kellett Abstract Input-to-State Stability (ISS) and the ISS-Lyapunov function have proved to be useful- ous discrete-time dynamics, we investigate ISS-Lyapunov functions for such systems. ISS-Lyapunov
Nuclear symmetry energy at subnormal densities from measured nuclear masses
Min Liu; Ning Wang; Zhuxia Li; Fengshou Zhang
The symmetry energy coefficients for nuclei with mass number A=20~250 are extracted from more than 2000 measured nuclear masses. With the semi-empirical connection between the symmetry energy coefficients of finite nuclei and the nuclear symmetry energy at reference densities, we investigate the density dependence of symmetry energy of nuclear matter at subnormal densities. The obtained results are compared with those extracted from other methods.
Discovering the New Standard Model: Fundamental Symmetries and Neutrinos
V. Cianciolo; A. B. Balantekin; A. Bernstein; V. Cirigliano; M. D. Cooper; D. J. Dean; S. R. Elliott; B. W. Filippone; S. J. Freedman; G. L. Greene; K. M. Heeger; D. W. Hertzog; B. R. Holstein; P. Huffman; T. Ito; K. Kumar; Z. -T. Lu; J. S. Nico; G. D. Orebi Gann; K. Paschke; A. Piepke; B. Plaster; D. Pocanic; A. W. P. Poon; D. C. Radford; M. J. Ramsey-Musolf; R. G. H. Robertson; G. Savard; K. Scholberg; Y. Semertzidis; J. F. Wilkerson
This White Paper describes recent progress and future opportunities in the area of fundamental symmetries and neutrinos.
Discovering the New Standard Model: Fundamental Symmetries and Neutrinos
Cianciolo, V; Bernstein, A; Cirigliano, V; Cooper, M D; Dean, D J; Elliott, S R; Filippone, B W; Freedman, S J; Greene, G L; Heeger, K M; Hertzog, D W; Holstein, B R; Huffman, P; Ito, T; Kumar, K; Lu, Z -T; Nico, J S; Gann, G D Orebi; Paschke, K; Piepke, A; Plaster, B; Pocanic, D; Poon, A W P; Radford, D C; Ramsey-Musolf, M J; Robertson, R G H; Savard, G; Scholberg, K; Semertzidis, Y; Wilkerson, J F
This White Paper describes recent progress and future opportunities in the area of fundamental symmetries and neutrinos.
Relativistic U(3) symmetry and pseudo-U(3) symmetry of the Dirac Hamiltonian
Ginocchio, Joseph N [Los Alamos National Laboratory
The Dirac Hamiltonian with relativistic scalar and vector harmonic oscillator potentials has been solved analytically in two limits. One is the spin limit for which spin is an invariant symmetry of the the Dirac Hamiltonian and the other is the pseudo-spin limit for which pseudo-spin is an invariant symmetry of the Dirac Hamiltonian. The spin limit occurs when the scalar potential is equal to the vector potential plus a constant, and the pseudospin limit occurs when the scalar potential is equal in magnitude but opposite in sign to the vector potential plus a constant. Like the non-relativistic harmonic oscillator, each of these limits has a higher symmetry. For example, for the spherically symmetric oscillator, these limits have a U(3) and pseudo-U(3) symmetry respectively. We shall discuss the eigenfunctions and eigenvalues of these two limits and derive the relativistic generators for the U(3) and pseudo-U(3) symmetry. We also argue, that, if an anti-nucleon can be bound in a nucleus, the spectrum will have approximate spin and U(3) symmetry.
SO(4) symmetry in the relativistic hydrogen atom
Jing-Ling Chen; Dong-Ling Deng; Ming-Guang Hu
We show that the relativistic hydrogen atom possesses an SO(4) symmetry by introducing a kind of pseudo-spin vector operator. The same SO(4) symmetry is still preserved in the relativistic quantum system in presence of an U(1) monopolar vector potential as well as a nonabelian vector potential. Lamb shift and SO(4) symmetry breaking are also discussed.
Symmetry and Relativity : From Classical Mechanics to Modern Particle Physics
Paris-Sud XI, Universit� de
Symmetry and Relativity : From Classical Mechanics to Modern Particle Physics Z.J. Ajaltouni to modern particle physics will be given and some open questions will be raised. Keywords: Symmetry that symmetry represents a methodology followed by Modern Physics in order to build coherent and successful
Terazawa, Hidezumi
Exotic forms of matter such as carbon nanofoams, hexalambdas and strange stars, pentaquarks, color-balls, etc. and their relations to current problems in cosmo-particle physics such as dark matter and energy are discussed in some details.
Synthetic morphogenesis : space, time, and deformation
Brodsky, Micah Z. (Micah Zev)
Synthetic biology has presented engineers with a fascinating opportunity: can we understand the principles of our origins { animal embryonic development - by re-engineering it in the laboratory? I investigate, from an ...
Space Time Quantization and the Big Bang
B. G. Sidharth
A recent cosmological model is recapitulated which deduces the correct mass, radius and age of the universe as also the Hubble constant and other well known apparently coincidental relations. It also predicts an ever expanding accelerating universe as is confirmed by latest supernovae observations. Finally the Big Bang model is recovered as a suitable limiting case.
Space-Time Insight | Open Energy Information
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Mirror Symmetry in Physics: The Basics
Callum Quigley
These notes are aimed at mathematicians working on topics related to mirror symmetry, but are unfamiliar with the physical origins of this subject. We explain the physical concepts that enable this surprising duality to exist, using the torus as an illustrative example. Then, we develop the basic foundations of conformal field theory so that we can explain how mirror symmetry was first discovered in that context. Along the way we will uncover a deep connection between conformal field theories with (2,2) supersymmetry and Calabi-Yau manifolds. (Based on lectures given during the "Thematic Program on Calabi-Yau Varieties: Arithmetic, Geometry and Physics" at the Fields Institute in Toronto, October 10-11, 2013.)
Generalized harmonic formulation in spherical symmetry
Evgeny Sorkin; Matthew W. Choptuik
In this pedagogically structured article, we describe a generalized harmonic formulation of the Einstein equations in spherical symmetry which is regular at the origin. The generalized harmonic approach has attracted significant attention in numerical relativity over the past few years, especially as applied to the problem of binary inspiral and merger. A key issue when using the technique is the choice of the gauge source functions, and recent work has provided several prescriptions for gauge drivers designed to evolve these functions in a controlled way. We numerically investigate the parameter spaces of some of these drivers in the context of fully non-linear collapse of a real, massless scalar field, and determine nearly optimal parameter settings for specific situations. Surprisingly, we find that many of the drivers that perform well in 3+1 calculations that use Cartesian coordinates, are considerably less effective in spherical symmetry, where some of them are, in fact, unstable.
Constraining the nuclear symmetry-energy at super-density
Yong, Gao-Chan
The nuclear symmetry-energy has broad implications in both nuclear physics and astrophysics. Due to hard work of many people, the nuclear symmetry-energy around saturation density has been roughly constrained. However, the nuclear symmetry-energy at super-density is still in chaos. By considering both the effects of the nucleon-nucleon short-rang correlations and the isospin-dependent in-medium inelastic baryon-baryon scattering cross sections in the transport model, two unrelated experimental measurements are simultaneously analyzed. A soft symmetry-energy at super-density is first consistently obtained by the double comparison of the symmetry-energy sensitive observables.
Which Chiral Symmetry is Restored in High Temperature QCD?
Claude Bernard; Tom Blum; Carleton DeTar; Steven Gottlieb; Urs M. Heller; James E. Hetrick; K. Rummukainen; R. Sugar; D. Toussaint; Matthew Wingate
Sigma models for the high temperature phase transition in quantum chromodynamics (QCD) suggest that at high temperature the SU(N_f) x SU(N_f) chiral symmetry becomes exact, but the anomalous axial U(1) symmetry need not be restored. In numerical lattice simulations, traditional methods for detecting symmetry restoration have sought multiplets in the screening mass spectrum. However, these methods were imprecise and the results, so far, incomplete. With improved statistics and methodology, we are now able to offer evidence for a restoration of the SU(2) x SU(2) chiral symmetry just above the crossover, but not of the axial U(1) chiral symmetry.
Symmetry Algebra of IIB Superstring Scattering
Gordon Chalmers
The graviton scattering in IIB superstring theory is examined in the context of S-duality and symmetry. There is an algebra that generates all of the terms in the four-point function to any order in derivatives. A map from the algebra to the scattering is given; it suggests the correctness of the full four-point function with the S-duality. The higher point functions are expected to follow a similar pattern.
Conformal Scaling Gauge Symmetry and Inflationary Universe
Yue-Liang Wu
Considering the conformal scaling gauge symmetry as a fundamental symmetry of nature in the presence of gravity, a scalar field is required and used to describe the scale behavior of universe. In order for the scalar field to be a physical field, a gauge field is necessary to be introduced. A gauge invariant potential action is constructed by adopting the scalar field and a real Wilson-like line element of the gauge field. Of particular, the conformal scaling gauge symmetry can be broken down explicitly via fixing gauge to match the Einstein-Hilbert action of gravity. As a nontrivial background field solution of pure gauge has a minimal energy in gauge interactions, the evolution of universe is then dominated at earlier time by the potential energy of background field characterized by a scalar field. Since the background field of pure gauge leads to an exponential potential model of a scalar field, the universe is driven by a power-law inflation with the scale factor $a(t) \\sim t^p$. The power-law index $p$ is determined by a basic gauge fixing parameter $g_F$ via $p = 16\\pi g_F^2[1 + 3/(4\\pi g_F^2) ]$. For the gauge fixing scale being the Planck mass, we are led to a predictive model with $g_F=1$ and $p\\simeq 62$.
Radiatively broken symmetries of nonhierarchical neutrinos
Dighe, Amol; Roy, Probir
Symmetry-based ideas, such as the quark-lepton complementarity (QLC) principle and the tri-bimaximal mixing (TBM) scheme, have been proposed to explain the observed mixing pattern of neutrinos. We argue that such symmetry relations need to be imposed at a high scale $\\Lambda \\sim 10^{12}$ GeV characterizing the large masses of right-handed neutrinos required to implement the seesaw mechanism. For nonhierarchical neutrinos, renormalisation group evolution down to a laboratory energy scale $\\lambda \\sim 10^3$ GeV tends to radiatively break these symmetries at a significant level and spoil the mixing pattern predicted by them. However, for Majorana neutrinos, suitable constraints on the extra phases $\\alpha_{2,3}$ enable the retention of those high scale mixing patterns at laboratory energies. We examine this issue within the Minimal Supersymmetric Standard Model (MSSM) and demonstrate the fact posited above for two versions of QLC and two versions of TBM. The appropriate constraints are worked out for all these...
Radiatively broken symmetries of nonhierarchical neutrinos
Amol Dighe; Srubabati Goswami; Probir Roy
Symmetry-based ideas, such as the quark-lepton complementarity (QLC) principle and the tri-bimaximal mixing (TBM) scheme, have been proposed to explain the observed mixing pattern of neutrinos. We argue that such symmetry relations need to be imposed at a high scale $\\Lambda \\sim 10^{12}$ GeV characterizing the large masses of right-handed neutrinos required to implement the seesaw mechanism. For nonhierarchical neutrinos, renormalisation group evolution down to a laboratory energy scale $\\lambda \\sim 10^3$ GeV tends to radiatively break these symmetries at a significant level and spoil the mixing pattern predicted by them. However, for Majorana neutrinos, suitable constraints on the extra phases $\\alpha_{2,3}$ enable the retention of those high scale mixing patterns at laboratory energies. We examine this issue within the Minimal Supersymmetric Standard Model (MSSM) and demonstrate the fact posited above for two versions of QLC and two versions of TBM. The appropriate constraints are worked out for all these four cases. Specifically, a preference for $\\alpha_2 \\approx \\pi$ (i.e. $m_1 \\approx -m_2$) emerges in each case. We also show how a future accurate measurement of $\\theta_{13}$ may enable some discrimination among these four cases in spite of renormalization group evolution.
Symmetry and the thermodynamics of currents in open quantum systems
Daniel Manzano; Pablo I. Hurtado
Symmetry is a powerful concept in physics, and its recent application to understand nonequilibrium behavior is providing deep insights and groundbreaking exact results. Here we show how to harness symmetry to control transport and statistics in open quantum systems. Such control is enabled by a first-order-type dynamic phase transition in current statistics and the associated coexistence of different transport channels (or nonequilibrium steady states) classified by symmetry. Microreversibility then ensues, via the Gallavotti-Cohen fluctuation theorem, a twin dynamic phase transition for rare current fluctuations. Interestingly, the symmetry present in the initial state is spontaneously broken at the fluctuating level, where the quantum system selects the symmetry sector that maximally facilitates a given fluctuation. We illustrate these results in a qubit network model motivated by the problem of coherent energy harvesting in photosynthetic complexes, and introduce the concept of a symmetry-controlled quantum thermal switch, suggesting symmetry-based design strategies for quantum devices with controllable transport properties.
Multidimensional electron-photon transport with standard discrete ordinates codes
Drumm, C.R.
A method is described for generating electron cross sections that are compatible with standard discrete ordinates codes without modification. There are many advantages of using an established discrete ordinates solver, e.g. immediately available adjoint capability. Coupled electron-photon transport capability is needed for many applications, including the modeling of the response of electronics components to space and man-made radiation environments. The cross sections have been successfully used in the DORT, TWODANT and TORT discrete ordinates codes. The cross sections are shown to provide accurate and efficient solutions to certain multidimensional electronphoton transport problems.
Information storage capacity of discrete spin systems
Yoshida, Beni, E-mail: firstname.lastname@example.com
Understanding the limits imposed on information storage capacity of physical systems is a problem of fundamental and practical importance which bridges physics and information science. There is a well-known upper bound on the amount of information that can be stored reliably in a given volume of discrete spin systems which are supported by gapped local Hamiltonians. However, all the previously known systems were far below this theoretical bound, and it remained open whether there exists a gapped spin system that saturates this bound. Here, we present a construction of spin systems which saturate this theoretical limit asymptotically by borrowing an idea from fractal properties arising in the Sierpinski triangle. Our construction provides not only the best classical error-correcting code which is physically realizable as the energy ground space of gapped frustration-free Hamiltonians, but also a new research avenue for correlated spin phases with fractal spin configurations. -- Highlights: �We propose a spin model with fractal ground states and study its coding properties. �We show that the model asymptotically saturates a theoretical limit on information storage capacity. �We discuss its relations to various theoretical physics problems.
Numerical detection of symmetry enriched topological phases with space group symmetry
Ling Wang; Andrew Essin; Michael Hermele; Olexei Motrunich
Topologically ordered phases of matter, in particular so-called symmetry enriched topological (SET) phases, can exhibit quantum number fractionalization in the presence of global symmetry. In Z_2 topologically ordered states in two dimensions, fundamental translations T_x and T_y acting on anyons can either commute or anticommute. This property, crystal momentum fractionalization, can be seen in a periodicity of the excited-state spectrum in the Brillouin zone. We present a numerical method to detect the presence of this form of symmetry enrichment given a projected entangled pair state (PEPS); we study the minima of spectrum of correlation lengths of the transfer matrix for a cylinder. As a benchmark, we demonstrate our method using a modified toric code model with perturbation. An enhanced periodicity in momentum clearly reveals the anticommutation relation {T_x,T_y}=0$ for the corresponding quasiparticles in the system.
Design of discrete-time filters for efficient implementation
Wei, Dennis
The cost of implementation of discrete-time filters is often strongly dependent on the number of non-zero filter coefficients or the precision with which the coefficients are represented. This thesis addresses the design ...
Resolution of grain scale interactions using the Discrete Element Method
Johnson, Scott M. (Scott Matthew), 1978-
Granular materials are an integral part of many engineering systems. Currently, a popular tool for numerically investigating granular systems is the Discrete Element Method (DEM). Nearly all implementations of the DEM, ...
Discrete Feature Approach for Heterogeneous Reservoir Production Enhancement
Dershowitz, William S.; Curran, Brendan; Einstein, Herbert; LaPointe, Paul; Shuttle, Dawn; Klise, Kate
The report presents summaries of technology development for discrete feature modeling in support of the improved oil recovery (IOR) for heterogeneous reservoirs. In addition, the report describes the demonstration of these technologies at project study sites.
Optimization With Parity Constraints: From Binary Codes to Discrete Integration
Bejerano, Gill
Optimization With Parity Constraints: From Binary Codes to Discrete Integration Stefano Ermon guarantees on the quality of the solution found. Markov Chain Monte Carlo [17, 21, 32] and Importance
Embed and Project: Discrete Sampling with Universal Hashing
Bejerano, Gill
Embed and Project: Discrete Sampling with Universal Hashing Stefano Ermon, Carla P. Gomes Dept Markov Chain Monte Carlo (MCMC) methods. MCMC techniques are a specialized form of local search that only
Analysis of steel silo structures on discrete supports�
Li, Hongyu
The objective of this thesis is to broaden current knowledge of the strength and buckling/collapse of shells, with special reference to steel silo structures on discrete supports, and thus to provide design guidance of ...
Dirac or inverse seesaw neutrino masses with B � L gauge symmetry and S? flavor symmetry
DOE Public Access Gateway for Energy & Science Beta (PAGES Beta)
Ma, Ernest; Srivastava, Rahul
Many studies have been made on extensions of the standard model with B � L gauge symmetry. The addition of three singlet (right-handed) neutrinos renders it anomaly-free. It has always been assumed that the spontaneous breaking of B � L is accomplished by a singlet scalar field carrying two units of B � L charge. This results in a very natural implementation of the Majorana seesaw mechanism for neutrinos. However, there exists in fact another simple anomaly-free solution which allows Dirac or inverse seesaw neutrino masses. We show for the first time these new possibilities and discuss an application tomore��neutrino mixing with S? flavor symmetry.��less
Direct measurement of yield stress of discrete materials
S. H. Ebrahimnazhad Rahbari; J. Vollmer; S. Herminghaus; M. Brinkmann
We present a novel computational method for direct measurement of yield stress of discrete materials. The method is well-suited for the measurement of jamming phase diagram of a wide range of discrete particle systems such as granular materials, foams, and colloids. We further successfully apply the method to evaluate the jamming phase diagram of wet granular material in order to demonstrates the applicability of the model.
Isolation of Discrete Nanoparticle-DNA Conjugates for Plasmonic Applications
Alivisatos, Paul; Claridge, Shelley A.; Liang, Huiyang W.; Basu, Sourav Roger; Frechet, Jean M.J.; Alivisatos, A. Paul
Discrete DNA-gold nanoparticle conjugates with DNA lengths as short as 15 bases for both 5 nm and 20 nm gold particles have been purified by anion-exchange HPLC. Conjugates comprising short DNA (<40 bases) and large gold particles (>_ 20 nm) are difficult to purify by other means, and are potential substrates for plasmon coupling experiments. Conjugate purity is demonstrated by hybridizing complementary conjugates to form discrete structures, which are visualized by TEM.
Harmonic pinnacles in the Discrete Gaussian model
Eyal Lubetzky; Fabio Martinelli; Allan Sly
The 2D Discrete Gaussian model gives each height function $\\eta : \\mathbb{Z}^2\\to\\mathbb{Z}$ a probability proportional to $\\exp(-\\beta \\mathcal{H}(\\eta))$, where $\\beta$ is the inverse-temperature and $\\mathcal{H}(\\eta) = \\sum_{x\\sim y}(\\eta_x-\\eta_y)^2$ sums over nearest-neighbor bonds. We consider the model at large fixed $\\beta$, where it is flat unlike its continuous analog (the Gaussian Free Field). We first establish that the maximum height in an $L\\times L$ box with 0 boundary conditions concentrates on two integers $M,M+1$ with $M\\sim \\sqrt{(1/2\\pi\\beta)\\log L\\log\\log L}$. The key is a large deviation estimate for the height at the origin in $\\mathbb{Z}^2$, dominated by "harmonic pinnacles", integer approximations of a harmonic variational problem. Second, in this model conditioned on $\\eta\\geq 0$ (a floor), the average height rises, and in fact the height of almost all sites concentrates on levels $H,H+1$ where $H\\sim M/\\sqrt{2}$. This in particular pins down the asymptotics, and corrects the order, in results of Bricmont, El-Mellouki and Fr\\"ohlich (1986), where it was argued that the maximum and the height of the surface above a floor are both of order $\\sqrt{\\log L}$. Finally, our methods extend to other classical surface models (e.g., restricted SOS), featuring connections to $p$-harmonic analysis and alternating sign matrices.
Infrared Spectroscopy of Discrete Uranyl Anion Complexes
Gary S. Groenewold; Anita K. Gianotto; Michael E. McIlwain; Michael J. Van Stipdonk; Michael Kullman; Travis J. Cooper; David T. Moore; Nick Polfer; Jos Oomens; Ivan Infante; Lucas Visscher; Bertrand Siboulet; Wibe A. de Jong
The Free-Electron Laser for Infrared Experiments, FELIX, was used to study the wavelength-resolved multiphoton dissociation of discrete, gas phase uranyl (UO22+) complexes containing a single anionic ligand (A), with or without ligated solvent molecules (S). The apparent uranyl antisymmetric and symmetric stretching frequencies were measured for complexes with general formula [UO2A(S)n]+, where A was either hydroxide, methoxide or acetate, S was water, ammonia, acetone or acetonitrile, and n = 0-2. The values for the antisymmetric stretching frequency for uranyl ligated with only an anion ([UO2A]+) were as low or lower than measurements for [UO2]2+ ligated with as many as five strong neutral donor ligands, and are comparable to solution phase values. This result was surprising because initial DFT calculations using B3LYP predicted values that were 30 � 40 cm-1 higher, consistent with intuition but not with the data. Modification of the basis set and use of alternative functionals improved computational accuracy for the methoxide and acetate complexes, but calculated values for the hydroxide were greater than the measurement regardless of the computational method used. Attachment of a neutral donor ligand S to [UO2A]+ produced [UO2AS]+, which resulted only very modest changes to the uranyl frequency, and did not universally shift values lower. DFT calculations for [UO2AS]+ were in accord with trends in the data, and showed that attachment of the solvent was accommodated by weakening of the U-anion bond as well as the uranyl. When uranyl frequencies were compared for [UO2AS]+ species having different solvent neutrals, values decreased with increasing neutral nucleophilicity.
Infared Spectroscopy of Discrete Uranyl Anion Complexes
Groenewold, G. S.; Gianotto, Anita K.; McIIwain, Michael E.; Van Stipdonk, Michael J.; Kullman, Michael; Moore, David T.; Polfer, Nick; Oomens, Jos; Infante, Ivan A.; Visscher, Lucas; Siboulet, Bertrand; De Jong, Wibe A.
The Free-Electron Laser for Infrared Experiments (FELIX) w 1 as used to study the wavelength-resolved multiple photon photodissociation of discrete, gas phase uranyl (UO2 2 2+) complexes containing a single anionic ligand (A), with or without ligated solvent molecules (S). The uranyl antisymmetric and symmetric stretching frequencies were measured for complexes with general formula [UO2A(S)n]+, where A was either hydroxide, methoxide, or acetate; S was water, ammonia, acetone, or acetonitrile; and n = 0-3. The values for the antisymmetric stretching frequency for uranyl ligated with only an anion ([UO2A]+) were as low or lower than measurements for [UO2]2+ ligated with as many as five strong neutral donor ligands, and are comparable to solution phase values. This result was surprising because initial DFT calculations predicted values that were 30�40 cm-1 higher, consistent with intuition but not with the data. Modification of the basis sets and use of alternative functionals improved computational accuracy for the methoxide and acetate complexes, but calculated values for the hydroxide were greater than the measurement regardless of the computational method used. Attachment of a neutral donor ligand S to [UO2A]+ produced [UO2AS]+, which produced only very modest changes to the uranyl antisymmetric stretch frequency, and did not universally shift the frequency to lower values. DFT calculations for [UO2AS]+ were in accord with trends in the data, and showed that attachment of the solvent was accommodated by weakening of the U-anion bond as well as the uranyl. When uranyl frequencies were compared for [UO2AS]+ species having different solvent neutrals, values decreased with increasing neutral nucleophilicity.
Twisted supersymmetry: Twisted symmetry versus renormalizability
Dimitrijevic, Marija; Nikolic, Biljana; Radovanovic, Voja [Faculty of Physics, University of Belgrade, Studentski Trg 12, 11000 Beograd (Serbia)
We discuss a deformation of superspace based on a Hermitian twist. The twist implies a *-product that is noncommutative, Hermitian and finite when expanded in a power series of the deformation parameter. The Leibniz rule for the twisted supersymmetry transformations is deformed. A minimal deformation of the Wess-Zumino action is proposed and its renormalizability properties are discussed. There is no tadpole contribution, but the two-point function diverges. We speculate that the deformed Leibniz rule, or more generally the twisted symmetry, interferes with renormalizability properties of the model. We discuss different possibilities to render a renormalizable model.
Strengthened PT-symmetry with P $\
Miloslav Znojil
Two alternative scenarios are shown possible in Quantum Mechanics working with non-Hermitian $PT-$symmetric form of observables. While, usually, people assume that $P$ is a self-adjoint indefinite metric in Hilbert space (and that their $P-$pseudo-Hermitian Hamiltonians $H$ possess the real spectra etc), we propose to relax the constraint $P=P^\\dagger$ as redundant. Non-Hermitian triplet of coupled square wells is chosen for illustration purposes. Its solutions are constructed and the observed degeneracy of their spectrum is attributed to the characteristic nontrivial symmetry $S={P}^{-1} {P}^\\dagger \
Dynamics of Symmetry Breaking and Tachyonic Preheating
Felder, Gary; Garcia-Bellido, Juan; Greene, Patrick B.; Kofman, Lev; Linde, Andrei; Tkachev, Igor
We reconsider the old problem of the dynamics of spontaneous symmetry breaking (SSB) using 3D lattice simulations. We develop a theory of tachyonic preheating, which occurs due to the spinodal instability of the scalar field. Tachyonic preheating is so efficient that SSB typically completes within a single oscillation as the field rolls towards the minimum of its effective potential. We show that, contrary to previous expectations, preheating in hybrid inflation is typically tachyonic. Our results may also be relevant for the theory of the formation of topological defects and of disoriented chiral condensates in heavy ion collisions.
Noncommutative geometry and twisted conformal symmetry
Matlock, Peter [Institute of Mathematical Sciences, Chennai (India)
The twist-deformed conformal algebra is constructed as a Hopf algebra with twisted coproduct. This allows for the definition of conformal symmetry in a noncommutative background geometry. The twisted coproduct is reviewed for the Poincare algebra and the construction is then extended to the full conformal algebra. The case of Moyal-type noncommutativity of the coordinates is considered. It is demonstrated that conformal invariance need not be viewed as incompatible with noncommutative geometry; the noncommutativity of the coordinates appears as a consequence of the twisting, as has been shown in the literature in the case of the twisted Poincare algebra.
Spontaneous breaking of spatial symmetries in collective neutrino oscillations
Huaiyu Duan; Shashank Shalgar
A dense neutrino medium can experience collective oscillations or self-induced flavor transformation through nonlinear neutrino-neutrino refraction. To make the problem of collective neutrino oscillations more tractable, all previous studies on this subject have assumed some spatial symmetry or symmetries in the neutrino medium (e.g., translation symmetries in the early universe and spherical symmetry in core-collapse supernovae). We point out that the collective oscillation modes studied in such models are very special. Using a simple toy model we show that spatial symmetries can be broken spontaneously in collective neutrino oscillations. We also show that the spatial-symmetry-breaking (SSB) modes of neutrino oscillations can exist for both neutrino mass hierarchies and even in the regimes where collective neutrino oscillations were previously thought to be suppressed. This finding calls for study of collective neutrino oscillations in multi-dimensional models.
Spontaneous breaking of spatial symmetries in collective neutrino oscillations
Duan, Huaiyu
A dense neutrino medium can experience collective oscillations or self-induced flavor transformation through nonlinear neutrino-neutrino refraction. To make the problem of collective neutrino oscillations more tractable, all previous studies on this subject have assumed some spatial symmetry or symmetries in the neutrino medium (e.g., translation symmetries in the early universe and spherical symmetry in core-collapse supernovae). We point out that the collective oscillation modes studied in such models are very special. Using a simple toy model we show that spatial symmetries can be broken spontaneously in collective neutrino oscillations. We also show that the spatial-symmetry-breaking (SSB) modes of neutrino oscillations can exist for both neutrino mass hierarchies and even in the regimes where collective neutrino oscillations were previously thought to be suppressed. This finding calls for study of collective neutrino oscillations in multi-dimensional models.
Critical fermion density for restoring spontaneously broken symmetry
Hagen Kleinert; She-Sheng Xue
We show how the phenomenon of spontaneous symmetry breakdown is affected by the presence of a sea of fermions in the system. When its density exceeds a critical value, the broken symmetry can be restored. We calculate the critical value and discuss the consequences for three different physical systems: First, for the standard model of particle physics, where the spontaneous symmetry breakdown leads nonzero masses of intermediate gauge bosons and fermions. The symmetry restoration will greatly enhance various processes with dramatic consequences for the early universe. Second, for the Gell-Mann--L\\`evy $\\sigma$-model of nuclear physics, where the symmetry breakdown gives rise to the nucleon and meson masses. The symmetry restoration may have important consequences for formation or collapse of stellar cores. Third, for the superconductive phase of condensed-matter, where the BCS condensate at low-temperature may be destroyed by a too large electron density.
Peccei-Quinn symmetry, dark matter, and neutrino mass
Ma, Ernest [Department of Physics and Astronomy, University of California, Riverside, California 92521 (United States)
It is pointed out that a residual Z{sub 2} symmetry of the usual anomalous Peccei-Quinn U(1){sub PQ} symmetry (which solves the strong CP problem) may be used for an absolutely stable heavy dark-matter particle in addition to the long-lived axion. The same Z{sub 2} symmetry may also be used to generate radiative neutrino mass.
Testing Time Reversal Symmetry in Artificial Atoms
Frederico Brito; Francisco Rouxinol; M. D. LaHaye; Amir O. Caldeira
Over the past several decades, a rich series of experiments has repeatedly verified the quantum nature of superconducting devices, leading some of these systems to be regarded as artificial atoms. In addition to their application in quantum information processing, these `atoms' provide a test bed for studying quantum mechanics in macroscopic limits. Regarding the last point, we present here a feasible protocol for directly testing time reversal symmetry in a superconducting artificial atom. Time reversal symmetry is a fundamental property of quantum mechanics and is expected to hold if the dynamics of the artificial atom strictly follow the Schroedinger equation. However, this property has yet to be tested in any macroscopic quantum system. The test we propose is based on the verification of the microreversibility principle, providing a viable approach to verify quantum work fluctuation theorems - an outstanding challenge in quantum statistical mechanics. For this, we outline a procedure that utilizes the microreversibility test in conjunction with numerical emulations of Gibbs ensembles to verify these theorems over a large temperature range.
On Flavor Symmetry in Lattice Quantum Chromodynamics
El Hassan Saidi
Using a well established method to engineer non abelian symmetries in superstring compactifications, we study the link between the point splitting method of Creutz et al of refs [1,2] for implementing flavor symmetry in lattice QCD; and singularity theory in complex algebraic geometry. We show amongst others that Creutz flavors for naive fermions are intimately related with toric singularities of a class of complex Kahler manifolds that are explicitly built here. In the case of naive fermions of QCD$_{2N}$, Creutz flavors are shown to live at the poles of real 2-spheres and carry quantum charges of the fundamental of $[SU(2)]^{2N}$. We show moreover that the two Creutz flavors in Karsten-Wilczek model, with Dirac operator in reciprocal space of the form $i\\gamma_1 F_1+i\\gamma_2 F_2 + i\\gamma_3 F_3+\\frac{i}{\\sin \\alpha}\\gamma_4 F_4$, are related with the small resolution of conifold singularity that live at $\\sin \\alpha =0$. Other related features are also studied.
Symmetry energy at subnuclear densities deduced from nuclear masses
Kazuhiro Oyamatsu; Kei Iida
We examine how nuclear masses are related to the density dependence of the symmetry energy. Using a macroscopic nuclear model we calculate nuclear masses in a way dependent on the equation of state of asymmetric nuclear matter. We find by comparison with empirical two-proton separation energies that a smaller symmetry energy at subnuclear densities, corresponding to a larger density symmetry coefficient L, is favored. This tendency, which is clearly seen for nuclei that are neutron-rich, nondeformed, and light, can be understood from the property of the surface symmetry energy in a compressible liquid-drop picture.
Dynamical electroweak symmetry breaking and the top quark
Chivukula, R.S. [Boston Univ., MA (United States)
In this talk, I discuss theories of dynamical electroweak symmetry breaking, with emphasis on the implications of a heavy top quark on the weak interaction {rho} parameter.
Non-Hermitian Hamiltonians with unitary and antiunitary symmetries
Fern�ndez, Francisco M., E-mail: email@example.com; Garcia, Javier
We analyse several non-Hermitian Hamiltonians with antiunitary symmetry from the point of view of their point-group symmetry. It enables us to predict the degeneracy of the energy levels and to reduce the dimension of the matrices necessary for the diagonalization of the Hamiltonian in a given basis set. We can also classify the solutions according to the irreducible representations of the point group and thus analyse their properties separately. One of the main results of this paper is that some PT-symmetric Hamiltonians with point-group symmetry C{sub 2v} exhibit complex eigenvalues for all values of a potential parameter. In such cases the PT phase transition takes place at the trivial Hermitian limit which suggests that the phenomenon is not robust. Point-group symmetry enables us to explain such anomalous behaviour and to choose a suitable antiunitary operator for the PT symmetry. -- Highlights: �PT-symmetric Hamiltonians exhibit real eigenvalues when PT symmetry is unbroken. �PT-symmetric multidimensional oscillators appear to show PT phase transitions. �This transition was conjectured to be a high-energy phenomenon. �We show that point group symmetry is useful for predicting broken PT symmetry in multidimensional oscillators. �PT-symmetric oscillators with C{sub 2v} symmetry exhibit phase transitions at the trivial Hermitian limit.
Understanding the Electroweak Symmetry Breaking: The Higgs Boson...
Broader source: All U.S. Department of Energy (DOE) Office Webpages (Extended Search)
Understanding the Electroweak Symmetry Breaking: The Higgs Boson and Beyond (Monday, March 2) DATE: Monday, March 2, 4:10 pm LOCATION: Physics 0003 Understanding the Electroweak...
Symmetry in RLT cuts for the quadratic assignment and standard ...
Etienne De Klerk
Jan 2, 2012 ... Symmetry in RLT cuts for the quadratic assignment and standard quadratic ... Category 1: Linear, Cone and Semidefinite Programming.
Temperature dependence of symmetry energy of finite nuclei
J. N. De; S. K. Samaddar
The temperature dependence of the symmetry energy and the symmetry free energy coefficients of atomic nuclei is investigated in a finite temperature Thomas-Fermi framework employing the subtraction procedure. A substantial decrement in the symmetry energy coefficient is obtained for finite systems,contrary to those seen for infinite nuclear matter at normal and somewhat subnormal densities. The effect of the coupling of the surface phonons to the nucleonic motion is also considered; this is found to decrease the symmetry energies somewhat at low temperatures.
Reply to 'Comment on 'Noncommutative gauge theories and Lorentz symmetry''
Banerjee, Rabin; Chakraborty, Biswajit; Kumar, Kuldeep [S. N. Bose National Centre for Basic Sciences, JD Block, Sector 3, Salt Lake, Kolkata 700098 (India); Department of Physics, Panjab University, Chandigarh 160014 (India)
This is a reply to the preceding 'Comment on 'Noncommutative gauge theories and Lorentz symmetry'', Phys. Rev. D 77, 048701 (2008) by Alfredo Iorio.
Discrete solitons in self-defocusing systems with $\\mathcal{PT}$-symmetric defects
Chen, Zhiqiang; Chai, Jinglei; Zhang, Xiangyu; Li, Yongyao; Malomed, Boris A
We construct families of discrete solitons (DSs) in an array of self-defocusing waveguides with an embedded $\\mathcal{PT}$ (parity-time)-symmetric dimer, which is represented by a pair of waveguides carrying mutually balanced gain and loss. Four types of states attached to the embedded defect are found, namely, staggered and unstaggered bright localized modes and gray or anti-gray DSs. Their existence and stability regions expand with the increase of the strength of the coupling between the dimer-forming sites. The existence of the gray and staggered bright DSs is qualitatively explained by dint of the continuum limit. All the gray and anti-gray DSs are stable (some of them are unstable if the dimer carries the nonlinear $\\mathcal{PT}$ symmetry, represented by balanced nonlinear gain and loss; in that case, the instability does not lead to a blowup, but rather creates oscillatory dynamical states). The boundary between the gray and anti-gray DSs is predicted in an approximate analytical form.
Neutrino symmetries from high to low scales
Probir Roy
Proposed symmetry relations, e.g., quark-lepton complementarity (QLC) or tribimaximal mixing (TBM), need to be imposed at a high scale $\\wedge \\sim 10^{12}$ GeV characterising the large masses of right-handed neutrinos required to implement the seesaw mechanism. RG evolution down to the laboratory scale $\\lambda \\sim 10^3$ GeV, generically prone to spoil these relations and their predicted neutrino mixing patterns, can be made to preserve them by appropriately constraining the Majorana phases $\\alpha_{2,3}$. This is explicitly demonstrated in the MSSM for two versions of QLC and two versions of TBM. A preference for $\\alpha_2 \\simeq \\pi$ (i.e. $m_1 \\simeq - m_2$) emerges in each case. Discrimination among the four cases is shown to be possible by future measurements of $\\theta_{13}$.
QCD evolution equations from conformal symmetry
V. M. Braun; A. N. Manashov
QCD evolution equations in $\\text{MS}$-like schemes can be recovered from the same equations in a modified theory, QCD in non-integer $d=4-2\\epsilon$ dimensions, which enjoys exact scale and conformal invariance at the critical point. Restrictions imposed by the conformal symmetry of the modified theory allow one to obtain complete evolution kernels in integer (physical) dimensions at the given order of perturbation theory from the spectrum of anomalous dimensions added by the calculation of the special conformal anomaly at one order less. We use this technique to derive two-loop evolution equations for flavor-nonsinglet quark-antiquark light-ray operators that encode the scale dependence of generalized hadron parton distributions.
The M�bius Symmetry of Quantum Mechanics
Alon E. Faraggi; Marco Matone
The equivalence postulate approach to quantum mechanics aims to formulate quantum mechanics from a fundamental geometrical principle. Underlying the formulation there exists a basic cocycle condition which is invariant under $D$--dimensional M\\"obius transformations with respect to the Euclidean or Minkowski metrics. The invariance under global M\\"obius transformations implies that spatial space is compact. Furthermore, it implies energy quantisation and undefinability of quantum trajectories without assuming any prior interpretation of the wave function. The approach may be viewed as conventional quantum mechanics with the caveat that spatial space is compact, as dictated by the M\\"obius symmetry, with the classical limit corresponding to the decompactification limit. Correspondingly, there exists a finite length scale in the formalism and consequently an intrinsic regularisation scheme. Evidence for the compactness of space may exist in the cosmic microwave background radiation.
Separability and dynamical symmetry of Quantum Dots
Zhang, P.-M., E-mail: firstname.lastname@example.com [Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou (China); Zou, L.-P., E-mail: email@example.com [Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou (China); Horvathy, P.A., E-mail: firstname.lastname@example.com [Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou (China); Laboratoire de Math�matiques et de Physique Th�orique, Tours University (France); Gibbons, G.W., E-mail: email@example.com [Department of Applied Mathematics and Theoretical Physics, Cambridge University, Cambridge (United Kingdom)
The separability and Runge�Lenz-type dynamical symmetry of the internal dynamics of certain two-electron Quantum Dots, found by Simonovi? et al. (2003), are traced back to that of the perturbed Kepler problem. A large class of axially symmetric perturbing potentials which allow for separation in parabolic coordinates can easily be found. Apart from the 2:1 anisotropic harmonic trapping potential considered in Simonovi? and Nazmitdinov (2013), they include a constant electric field parallel to the magnetic field (Stark effect), the ring-shaped Hartmann potential, etc. The harmonic case is studied in detail. -- Highlights: � The separability of Quantum Dots is derived from that of the perturbed Kepler problem. � Harmonic perturbation with 2:1 anisotropy is separable in parabolic coordinates. � The system has a conserved Runge�Lenz type quantity.
Electronic Properties and Hidden Symmetries of Graphene
L. B Drissi; E. H Saidi; M. Bousmina
Using the relation between the structural and the electronic properties of honeycomb, we study the hidden SU(3) symmetry of the graphene monolayer and exhibit the link with its electronic properties. We show that the conservation law of incoming and outgoing electronic momenta at each site of graphene is solved in terms of SU(3) representations; and the Fourier waves {\\phi}(k_{x},k_{y}) of the hopping electron may be classified by SU(3) highest weight multiplets {\\phi}_{p,q}({\\xi}). It is also shown that the phases arctan((k_{y})/(k_{x})) of the waves are quantized as (((p+q))/((p-q)))sqrt(3) with p, q positive integers. Other features are also discussed.
Infrared modification of gravity from conformal symmetry
Gegenberg, Jack; Seahra, Sanjeev S
We reconsider a gauge theory of gravity in which the gauge group is the conformal group SO(4,2) and the action is of the Yang-Mills form, quadratic in the curvature. The resulting gravitational theory exhibits local conformal symmetry and reduces to Weyl-squared gravity under certain conditions. When the theory is linearized about flat spacetime, we find that matter which couples to the generators of special conformal transformations reproduces Newton's inverse square law. Conversely, matter which couples to generators of translations induces a constant and possibly repulsive force far from the source, which may be relevant for explaining the late time acceleration of the universe. The coupling constant of theory is dimensionless, which means that it is potentially renormalizable.
Energy Content of Colliding Plane Waves using Approximate Noether Symmetries
M. Sharif; Saira Waheed
This paper is devoted to study the energy content of colliding plane waves using approximate Noether symmetries. For this purpose, we use approximate Lie symmetry method of Lagrangian for differential equations. We formulate the first-order perturbed Lagrangian for colliding plane electromagnetic and gravitational waves. It is shown that in both cases, there does not exist
Symmetry breaking and low energy conformational fluctuations in
Drabold, David
Symmetry breaking and low energy conformational fluctuations in amorphous graphene Y. Li and D. A. Drabold* Department of Physics and Astronomy, Condensed Matter Surface Science Program, Ohio University Published online 21 December 2012 Keywords amorphous graphene, low-energy excitation, symmetry breaking
ess5011 Robert J. Serfling MULTIVARIATE SYMMETRY AND
Serfling, Robert
ess5011 Robert J. Serfling MULTIVARIATE SYMMETRY AND ASYMMETRY Robert J. Serfling University by modern group theory. 1 #12;ess5011 Robert J. Serfling Here we focus on the notion of symmetry and s independently distributed as chi-square with m degrees of freedom. 2 #12;ess5011 Robert J. Serfling An important
Evolution towards Symmetry Ferdinand Verhulst and Richard Huveneers
Verhulst, Ferdinand
Evolution towards Symmetry Ferdinand Verhulst and Richard Huveneers Mathematisch Instituut those of today and will the laws of tomorrow still be the same? Henri Poincar�e in `The evolution of the laws', Derni`eres Pens�ees. Abstract The dynamics of time-dependent evolution towards symmetry
Development of an Interhemispheric Symmetry Measurement in the Neonatal Brain
Development of an Interhemispheric Symmetry Measurement in the Neonatal Brain Ninah Koolen1.dereymaeker, katrien.jansen, jan.vervisch, email@example.com Keywords: Preterm Brain, Symmetry, Channel of different brain regions will allow detecting physiologic asymmetry versus pathologic asymmetry. This can
Nonequilibrium symmetry breaking and pattern formation in magnetic films
Deutsch, Josh
films. p. 7/6 #12;Applications of Ferromagnetism Doodle Pads Refrigerator Magnets NonequilibriumNonequilibrium symmetry breaking and pattern formation in magnetic films Josh Deutsch University of California Santa Cruz Nonequilibrium symmetry breaking and pattern formation in magnetic films. p. 1/6 #12
Symmetry in CSP solutions Nicoleta Neagu and Boi Faltings
Flener, Pierre
Symmetry in CSP solutions Nicoleta Neagu and Boi Faltings Artificial Intelligence Laboratory (LIA for finding symmetric solutions of in a CSP. This method is using local symmetries of the CSP structure and research upon searching CSP solutions but few of them watch the relations between CSP solutions. In certain
Exploiting symmetry in SMT problems David Deharbe1
Fontaine, Pascal
Exploiting symmetry in SMT problems David D�eharbe1 , Pascal Fontaine2 , Stephan Merz2 , and Bruno the performance of SMT- solvers by detecting symmetries in the input formulas and use them to prune the search space of the SMT algorithm. This technique is based on the concept of (syntactic) invariance
Dynamical constants of structured photons with parabolic-cylindrical symmetry
B. M. Rodriguez-Lara; R. Jauregui
Electromagnetic modes with parabolic-cylindrical symmetry and their dynamical variables are studied both in the classical and quantum realm. As a result, a new dynamical constant for the electromagnetic field is identified and linked to the symmetry operator which supports it.
New symmetries in mixed-integer linear optimization
Besides the usual permutation of variables, these symmetries can also take the ... Having a list of generators of the group of constraint symmetries we can just ... Speed has its price, since this method cannot hope to cover all the solutions that ..... lifted form, the algorithm can be custom tailored to operate only on the original
Quantum symmetry and photoreactivity of azabenzenes
Chesko, J.D.M.
The fundamental processes associated with a photochemical reaction are described with reference to experimental properties of azabenzenes. Consideration of both excitation and relaxation processes led to presentation of the symmetry propagator, a unifying principle which maps system fluctuations (perturbations acting on an initial state) with dissipations (transitions to different states), thus directing the energy flow along competing reactive and nonreactive pathways. A coherent picture of relaxation processes including chemical reactions was constructed with the aid of spectroscopic data. Pyrazine (1,4 diazine) possesses vibronically active modes which provide an efficient mechanism for internal conversion to the first excited singlet state, where other promoting modes of the correct symmetry induce both intersystem crossing to the triplet manifold, isomerization through diaza-benzvalene, and chemical reactions through cycloreversion of dewar pyrazine to yield HCN plus an azete. At higher energies simple H atom loss and internal conversion become more predominant, leading to ring opening followed by elimination of methylene nitrile and ground state reaction products. Efficiency of chemical transformations as dissipation mechanisms versus competing fluorescence, phosphorescence and radiationless relaxation was mapped from near ultraviolet to far ultraviolet by photodissociation quantum yields into reaction channels characterized by molecular beam photofragment translational spectroscopy. A reaction path model for azabenzene photochemistry was presented and tested against experiment. Presence of undiscovered channels in other azabenzene systems was predicted and verified. The dominant process, HCN elimination, was resolved into three distinct channels. Both molecular and atomic hydrogen elimination was observed, the former with significant vibrational excitation. Small yields of isomerization products, acetylene and N2, were also observed.

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