# Publications 2013

• ## Bragg spectroscopy of clean and disordered lattice bosons in one dimension: a spectral fingerprint of the Bose glass

### Guillaume Roux1, Anna Minguzzi2, Tommaso Roscilde3

#### New J. Phys. 15, 055003 (2013)

We study the dynamic structure factor of a one-dimensional Bose gas confined in an optical lattice and modeled by the Bose-Hubbard Hamiltonian, using a variety of numerical and analytical approaches. The dynamic structure factor, experimentally measurable by Bragg spectroscopy, is studied in three relevant cases: in the clean regime, featuring either a superfluid or a Mott phase; and in the presence of two types of (quasi-)disordered external potentials: a quasi-periodic potential obtained from a bichromatic superlattice and a random-box disorder - both featuring a Bose glass phase. In the clean case, we show the emergence of a gapped doublon mode (corresponding to a repulsively bound state) for incommensurate filling, well separated from the low-energy acoustic mode. In the disordered case, we show that the dynamic structure factor provides a direct insight into the spatial structure of the excitations, unveiling their localized nature, which represents a fundamental signature of the Bose glass phase. Furthermore, it provides a clear fingerprint of the very nature of the localization mechanism which differs for the two kinds of disorder potentials we consider. In special cases, the dynamic structure factor may provide an estimate of the position of the localization transition from superfluid to Bose glass, in a complementary manner to the information deduced from the momentum distribution.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Université Grenoble-Alpes and CNRS, Laboratoire de Physique et Modélisation des Milieux Condensés, UMR 5493, Maison des Magistères, BP 166, F-38042 Grenoble, France
• Laboratoire de Physique, CNRS UMR 5672, Ecole Normale Supérieure de Lyon, Université de Lyon, 46 Allée d'Italie, Lyon F-69364, France

• ## Influence of liquid structure on the thermodynamics of freezing

### Pierre Ronceray 1, 2, Peter Harrowell 3

#### Physical Review E 87 (2013) 052313

The ordering transitions of a 2D lattice liquid characterized by a single favoured local structure (FLS) are studied using Monte Carlo simulations. All eight distinct geometries for the FLS are considered and we find a variety of ordering transitions - first order, continuous and multi-step transitions. Using a microcanonical representation of the freezing transition we resolve the dual influence of the local structure on the ordering transition, i.e. via the energy of the crystal and the entropy cost of structure in the liquid.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Ecole Normale Supérieure de Paris (ENS Paris),
École normale supérieure [ENS] - Paris
• 3. Faculty of Sciences,
University of Sydney

• ## A method for calculating spectral statistics based on random-matrix universality with an application to the three-point correlations of the Riemann zeros

### E. Bogomolny 1, J. P. Keating 2

#### Journal of Physics A General Physics46 (2013) 305203

We illustrate a general method for calculating spectral statistics that combines the universal (Random Matrix Theory limit) and the non-universal (trace-formula-related) contributions by giving a heuristic derivation of the three-point correlation function for the zeros of the Riemann zeta function. The main idea is to construct a generalized Hermitian random matrix ensemble whose mean eigenvalue density coincides with a large but finite portion of the actual density of the spectrum or the Riemann zeros. Averaging the random matrix result over remaining oscillatory terms related, in the case of the zeta function, to small primes leads to a formula for the three-point correlation function that is in agreement with results from other heuristic methods. This provides support for these different methods. The advantage of the approach we set out here is that it incorporates the determinental structure of the Random Matrix limit.

• 1 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2 : School of Mathematics [Bristol]
University of Bristol

• ## A note on weakly discontinuous dynamical transitions

### Silvio Franz 1, Giorgio Parisi 2, Federico Ricci-Tersenghi 2, Tommaso Rizzo 2, Pierfrancesco Urbani 1

#### Journal of Chemical Physics138 (2013) 064504

We analyze Mode Coupling discontinuous transition in the limit of vanishing discontinuity, approaching the so called "$A_3$" point. In these conditions structural relaxation and fluctuations appear to have universal form independent from the details of the system. The analysis of this limiting case suggests new ways for looking at the Mode Coupling equations in the general case.

• 1 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2 : Dipartimento di Fisica and INFM
Università degli studi di Roma I - La Sapienza

• ## A stochastic model of long-range interacting particles

### Shamik Gupta 1, Thierry Dauxois 2, Stefano Ruffo 2

#### Journal of Statistical Mechanics: Theory and Experiment (2013) P11003

We introduce a model of long-range interacting particles evolving under a stochastic Monte Carlo dynamics, in which possible increase or decrease in the values of the dynamical variables is accepted with preassigned probabilities. For symmetric increments, the system at long times settles to the Gibbs equilibrium state, while for asymmetric updates, the steady state is out of equilibrium. For the associated Fokker-Planck dynamics in the thermodynamic limit, we compute exactly the phase space distribution in the nonequilibrium steady state, and find that it has a nontrivial form that reduces to the familiar Gibbsian measure in the equilibrium limit.

• 1 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2 : Laboratoire de Physique de l'ENS Lyon (Phys-ENS)
CNRS : UMR5672 – École Normale Supérieure (ENS) - Lyon

• ## Anomalous fluctuations of currents in Sinai-type random chains with strongly correlated disorder

### Gleb Oshanin 1, Alberto Rosso 2, Gregory Schehr 2

#### Physical Review Letters110 (2013) 100602

We study properties of a random walk in a generalized Sinai model, in which a quenched random potential is a trajectory of a fractional Brownian motion with arbitrary Hurst parameter H, 0< H <1, so that the random force field displays strong spatial correlations. In this case, the disorder-average mean-square displacement grows in proportion to log^{2/H}(n), n being time. We prove that moments of arbitrary order k of the steady-state current J_L through a finite segment of length L of such a chain decay as L^{-(1-H)}, independently of k, which suggests that despite a logarithmic confinement the average current is much higher than its Fickian counterpart in homogeneous systems. Our results reveal a paradoxical behavior such that, for fixed n and L, the mean square displacement decreases when one varies H from 0 to 1, while the average current increases. This counter-intuitive behavior is explained via an analysis of representative realizations of disorder.

• 1 : Laboratoire de Physique Théorique de la Matière Condensée (LPTMC)
CNRS : UMR7600 – Université Pierre et Marie Curie (UPMC) - Paris VI
• 2 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
CNRS : UMR8626 – Université Paris XI - Paris Sud

• ## Archive ouverte HAL – Mesoscopic fluctuations in the Fermi-liquid regime of the Kondo problem

### Denis Ullmo 1, * Dong E. Liu 2 Sébastien Burdin 3 Harold U. Baranger 2

#### European Physical Journal B: Condensed Matter and Complex Systems, Springer-Verlag, 2013, 86 (8), pp.353. 〈10.1140/epjb/e2013-40418-3〉

We consider the low temperature regime of the mesoscopic Kondo problem, and in particular the relevance of a Fermi-liquid description of this regime. Mesoscopic fluctuations of both the quasiparticle energy levels and the corresponding wavefunctions are large in this case. These mesoscopic fluctuations make the traditional approach to Fermi-liquids impracticable, as it assumes the existence of a limited number of relevant parameters. We show here how this difficulty can be overcome and discuss the relationship between the resulting Fermi-liquid description "à la Nozières" and the mean field slave fermion approximation.

• 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
• 2. Duke Physics
• 3. LOMA - Laboratoire Ondes et Matière d'Aquitaine

• ## Asymmetric Lévy flights in the presence of absorbing boundaries

### Clélia de Mulatier 1, 2, Alberto Rosso 1, Gregory Schehr 1

#### Journal of Statistical Mechanics: Theory and Experiment (2013) P10006

We consider a one dimensional asymmetric random walk whose jumps are identical, independent and drawn from a distribution \phi(\eta) displaying asymmetric power law tails (i.e. \phi(\eta) \sim c/\eta^{\alpha +1} for large positive jumps and \phi(\eta) \sim c/(\gamma |\eta|^{\alpha +1}) for large negative jumps, with 0 < \alpha < 2). In absence of boundaries and after a large number of steps n, the probability density function (PDF) of the walker position, x_n, converges to an asymmetric Lévy stable law of stability index \alpha and skewness parameter \beta=(\gamma-1)/(\gamma+1). In particular the right tail of this PDF decays as c n/x_n^{1+\alpha}. Much less is known when the walker is confined, or partially confined, in a region of the space. In this paper we first study the case of a walker constrained to move on the positive semi-axis and absorbed once it changes sign. In this case, the persistence exponent \theta_+, which characterizes the algebraic large time decay of the survival probability, can be computed exactly and we show that the tail of the PDF of the walker position decays as c \, n/[(1-\theta_+) \, x_n^{1+\alpha}]. This last result can be generalized in higher dimensions such as a planar Lévy walker confined in a wedge with absorbing walls. Our results are corroborated by precise numerical simulations.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Département de Modélisation des Systèmes et Structures (DM2S),
CEA : DEN/DM2S

• ## Asymmetric Lévy flights in the presence of absorbing boundaries

### Clélia de Mulatier 1, 2, Alberto Rosso 1, Gregory Schehr 1

#### Journal of Statistical Mechanics: Theory and Experiment (2013) P10006

We consider a one dimensional asymmetric random walk whose jumps are identical, independent and drawn from a distribution \phi(\eta) displaying asymmetric power law tails (i.e. \phi(\eta) \sim c/\eta^{\alpha +1} for large positive jumps and \phi(\eta) \sim c/(\gamma |\eta|^{\alpha +1}) for large negative jumps, with 0 < \alpha < 2). In absence of boundaries and after a large number of steps n, the probability density function (PDF) of the walker position, x_n, converges to an asymmetric Lévy stable law of stability index \alpha and skewness parameter \beta=(\gamma-1)/(\gamma+1). In particular the right tail of this PDF decays as c n/x_n^{1+\alpha}. Much less is known when the walker is confined, or partially confined, in a region of the space. In this paper we first study the case of a walker constrained to move on the positive semi-axis and absorbed once it changes sign. In this case, the persistence exponent \theta_+, which characterizes the algebraic large time decay of the survival probability, can be computed exactly and we show that the tail of the PDF of the walker position decays as c \, n/[(1-\theta_+) \, x_n^{1+\alpha}]. This last result can be generalized in higher dimensions such as a planar Lévy walker confined in a wedge with absorbing walls. Our results are corroborated by precise numerical simulations.

• 1 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2 : Département de Modélisation des Systèmes et Structures (DM2S)
CEA : DEN/DM2S

• ## Belief Propagation Reconstruction for Discrete Tomography

### Emmanuelle Gouillart 1, Florent Krzakala 2, Marc Mezard 3, Lenka Zdeborová 4

#### Inverse Problems29, 3 (2013) 035003

We consider the reconstruction of a two-dimensional discrete image from a set of tomographic measurements corresponding to the Radon projection. Assuming that the image has a structure where neighbouring pixels have a larger probability to take the same value, we follow a Bayesian approach and introduce a fast message-passing reconstruction algorithm based on belief propagation. For numerical results, we specialize to the case of binary tomography. We test the algorithm on binary synthetic images with different length scales and compare our results against a more usual convex optimization approach. We investigate the reconstruction error as a function of the number of tomographic measurements, corresponding to the number of projection angles. The belief propagation algorithm turns out to be more efficient than the convex-optimization algorithm, both in terms of recovery bounds for noise-free projections, and in terms of reconstruction quality when moderate Gaussian noise is added to the projections.

• 1 : Surface du Verre et Interfaces (SVI)
CNRS : UMR125
• 2 : Laboratoire de Physico-Chimie Théorique (LPCT)
CNRS : UMR7083 – ESPCI ParisTech
• 3 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 4 : Institut de Physique Théorique (ex SPhT) (IPHT)
CNRS : URA2306 – CEA : DSM/IPHT

• ## Calculation of mean spectral density for statistically uniform tree-like random models

### E. Bogomolny 1, O. Giraud 1

#### Physical Review E88 (2013) 062811

For random matrices with tree-like structure there exists a recursive relation for the local Green functions whose solution permits to find directly many important quantities in the limit of infinite matrix dimensions. The purpose of this note is to investigate and compare expressions for the spectral density of random regular graphs, based on easy approximations for real solutions of the recursive relation valid for trees with large coordination number. The obtained formulas are in a good agreement with the results of numerical calculations even for small coordination number.

• 1 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
CNRS : UMR8626 – Université Paris XI - Paris Sud

• ## Coherent topological defect dynamics and collective modes in superconductors and electronic crystals

### Dragan Mihailovic 1, 2, Tomaz Mertelj 1, Viktor V Kabanov 1, Serguei Brazovskii 3

#### Journal of Physics: Condensed Matter25 (2013) 404206

The control of condensed matter systems out of equilibrium by laser pulses allows us to investigate the system trajectories through symmetry-breaking phase transitions. Thus the evolution of both collective modes and single particle excitations can be followed through diverse phase transitions with femtosecond resolution. Here we present experimental observations of the order parameter trajectory in the normal-superconductor transition and charge-density wave ordering transitions. Of particular interest is the coherent evolution of topological defects forming during the transition via the Kibble-Zurek mechanism, which appears to be measurable in optical pump probe experiments. Experiments on CDW systems reveal some new phenomena, such as coherent oscillations of the order parameter, the creation and emission of dispersive amplitudon modes upon the annihilation of topological defects, and mixing with weakly coupled finite-frequency (massive) bosons.

• 1 : Jozef Stefan Institute
Jozef Stefan Institute
• 2 : CENN Nanocenter
CENN Nanocenter
• 3 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
CNRS : UMR8626 – Université Paris XI - Paris Sud

• ## Conformal Field Theory of Critical Casimir Interactions in 2D

### G. Bimonte 1, T. Emig 2, M. Kardar 3

#### Europhysics Letters104 (2013) 21001

Thermal fluctuations of a critical system induce long-ranged Casimir forces between objects that couple to the underlying field. For two dimensional (2D) conformal field theories (CFT) we derive an exact result for the Casimir interaction between two objects of arbitrary shape, in terms of (1) the free energy of a circular ring whose radii are determined by the mutual capacitance of two conductors with the objects' shape; and (2) a purely geometric energy that is proportional to conformal charge of the CFT, but otherwise super-universal in that it depends only on the shapes and is independent of boundary conditions and other details.

• 1 : Istituto Nazionale di Fisica Nucleare, Sezione di Napoli (INFN, Sezione di Napoli)
INFN
• 2 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 3 : Department of Physics
Massachusetts Institute of Technology

• ## Connectivities of Potts Fortuin-Kasteleyn clusters and time-like Liouville correlator

### Marco Picco 1, Raoul Santachiara 2, Jacopo Viti 3, Gesualdo Delfino 4

#### Nuclear Physics B875, 3 (2013) 719

Recently, two of us argued that the probability that an FK cluster in the Q-state Potts model connects three given points is related to the time-like Liouville three-point correlation function. Moreover, they predicted that the FK three-point connectivity has a prefactor which unveils the effects of a discrete symmetry, reminiscent of the S_Q permutation symmetry of the Q=2,3,4 Potts model. Their theoretical prediction has been checked numerically for the case of percolation, corresponding to Q=1. We introduce the time-like Liouville correlator as the only consistent analytic continuation of the minimal model structure constants and present strong numerical tests of the relation between the time-like Liouville correlator and percolative properties of the FK clusters for real values of Q.

• 1 : Laboratoire de Physique Théorique et Hautes Energies (LPTHE)
CNRS : UMR7589 – Université Pierre et Marie Curie (UPMC) - Paris VI – Université Paris VII - Paris Diderot
• 2 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 3 : Laboratoire de Physique Théorique de l'ENS (LPTENS)
CNRS : UMR8549 – Université Pierre et Marie Curie (UPMC) - Paris VI – École normale supérieure [ENS] - Paris
• 4 : Scuola Internazionale Superiore di Studi Avanzati / International School for Advanced Studies (SISSA / ISAS)
Scuola Internazionale Superiore di Studi Avanzati/International School for Advanced Studies (SISSA/ISAS)

• ## Counter-ion density profile around charged cylinders: the strong-coupling needle limit

### Emmanuel Trizac 1, Gabriel Tellez 2, Juan Pablo Mallarino 2

#### Journal of Physical Chemistry B117, 42 (2013) 12702-12716

Charged rod-like polymers are not able to bind all their neutralizing counter-ions: a fraction of them evaporates while the others are said to be condensed. We study here counter-ion condensation and its ramifications, both numerically by means of Monte Carlo simulations employing a previously introduced powerful logarithmic sampling of radial coordinates, and analytically, with special emphasis on the strong-coupling regime. We focus on the thin rod, or needle limit, that is naturally reached under strong coulombic couplings, where the typical inter-particle spacing $a'$ along the rod is much larger than its radius R. This regime is complementary and opposite to the simpler thick rod case where $a'\ll R$. We show that due account of counter-ion evaporation, a universal phenomenon in the sense that it occurs in the same clothing for both weakly and strongly coupled systems, allows to obtain excellent agreement between the numerical simulations and the strong-coupling calculations.

• 1 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2 : Departamento de Fisica

• ## De la frustration et du désordre dans les chaînes et les échelles de spins quantiques

### Arthur Lavarelo 1

#### Université Paris Sud - Paris XI (19/07/2013), Guillaume Roux (Dir.)

Dans les systèmes de spins quantiques, la frustration et la basse dimensionnalité génèrent des fluctuations quantiques et donnent lieu à des phases exotiques. Cette thèse étudie un modèle d'échelle de spins avec des couplages frustrants le long des montants, motivé par les expériences sur le cuprate BiCu$_2$PO$_6$. Dans un premier temps, on présente une méthode variationnelle originale pour décrire les excitations de basse énergie d'une seule chaîne frustrée. Le diagramme de phase de deux chaînes couplées est ensuite établi à l'aide de méthodes numériques. Le modèle exhibe une transition de phase quantique entre une phase dimérisée est une phase à liens de valence résonnants (RVB). La physique de la phase RVB et en particulier l'apparition de l'incommensurabilité sont étudiées numériquement et par un traitement en champ moyen. On étudie ensuite les effets d'impuretés non-magnétiques sur la courbe d'aimantation et la loi de Curie à basse température. Ces propriétés magnétiques sont tout d'abord discutées à température nulle à partir d'arguments probabilistes. Puis un modèle effectif de basse énergie est dérivé dans la théorie de la réponse linéaire et permet de rendre compte des propriétés magnétiques à température finie. Enfin, on étudie l'effet d'un désordre dans les liens, sur une seule chaîne frustrée. La méthode variationnelle, introduite dans le cas non-désordonné, donne une image à faible désordre de l'instabilité de la phase dimérisée, qui consiste en la formation de domaines d'Imry-Ma délimités par des spinons localisés. Ce résultat est finalement discuté à la lumière de la renormalisation dans l'espace réel à fort désordre.

• 1 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
CNRS : UMR8626 – Université Paris XI - Paris Sud

• ## Demonstration of Angle Dependent Casimir Force Between Corrugations

### A. A. Banishev 1, J. Wagner 1, T. Emig 2, R. Zandi 1, U. Mohideen 1

#### Physical Review Letters110 (2013) 250403

The normal Casimir force between a sinusoidally corrugated gold coated plate and a sphere was measured at various angles between the corrugations using an atomic force microscope. A strong dependence on the orientation angle of the corrugation is found. The measured forces were found to deviate from the proximity force approximation and are in agreement with the theory based on the gradient expansion including correlation effects of geometry and material properties. We analyze the role of temperature. The obtained results open new opportunities for control of the Casimir effect in micromechanical systems.

• 1 : Department of Physics and Astronomy
University of California, Riverside
• 2 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
CNRS : UMR8626 – Université Paris XI - Paris Sud

• ## Distribution of the ratio of consecutive level spacings in random matrix ensembles

### Y. Y. Atas 1, E. Bogomolny 1, O. Giraud 1, G. Roux 1

#### Physical Review Letters110 (2013) 084101

We derive expressions for the probability distribution of the ratio of two consecutive level spacings for the classical ensembles of random matrices. This ratio distribution was recently introduced to study spectral properties of many-body problems, as, contrary to the standard level spacing distributions, it does not depend on the local density of states. Our Wigner-like surmises are shown to be very accurate when compared to numerics and exact calculations in the large matrix size limit. Quantitative improvements are found through a polynomial expansion. Examples from a quantum many-body lattice model and from zeros of the Riemann zeta function are presented.

• 1 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
CNRS : UMR8626 – Université Paris XI - Paris Sud

• ## Dynamical tunneling with ultracold atoms in magnetic microtraps

### Martin Lenz1,2, Sebastian Wüster1,3, Christopher J. Vale1,4, Norman R. Heckenberg1, Halina Rubinsztein-Dunlop1, C. A. Holmes1, G. J. Milburn1, and Matthew J. Davis1

#### Phys. Rev. A 88, 013635 (2013)

The study of dynamical tunneling in a periodically driven anharmonic potential probes the quantum-classical transition via the experimental control of the effective Planck's constant for the system. In this paper we consider the prospects for observing dynamical tunneling with ultracold atoms in magnetic microtraps on atom chips. We outline the driven anharmonic potentials that are possible using standard magnetic traps and find the Floquet spectrum for one of these as a function of the potential strength, modulation, and effective Planck's constant. We develop an integrable approximation to the nonintegrable Hamiltonian and find that it can explain the behavior of the tunneling rate as a function of the effective Planck's constant in the regular region of parameter space. In the chaotic region we compare our results with the predictions of models that describe chaos-assisted tunneling. Finally, we examine the practicality of performing these experiments in the laboratory with Bose-Einstein condensates.

• 1 The University of Queensland, School of Mathematics and Physics, Brisbane, Queensland 4072, Australia
• 2 University Paris Sud, CNRS, LPTMS, UMR 8626, Orsay 91405, France
• 3 Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, 01187 Dresden, Germany
• 4 ARC Centre of Excellence for Quantum-Atom Optics and Centre for Atom Optics and Ultrafast Spectroscopy, Swinburne University of Technology, Melbourne, Victoria 3122, Australia

• ## Dynamics of a tagged monomer: Effects of elastic pinning and harmonic absorption

### Shamik Gupta 1, Alberto Rosso 1, Christophe Texier 1, 2

#### Physical Review Letters111 (2013) 210601

We study the dynamics of a tagged monomer of a Rouse polymer for different initial configurations. In the case of free evolution, the monomer displays subdiffusive behavior with strong memory of the initial state. In presence of either elastic pinning or harmonic absorption, we show that the steady state is independent of the initial condition which however strongly affects the transient regime, resulting in non-monotonous behavior and power-law relaxation with varying exponents.

• 1 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2 : Laboratoire de Physique des Solides (LPS)
CNRS : UMR8502 – Université Paris XI - Paris Sud

• ## Edge usage, motifs and regulatory logic for cell cycling genetic networks

### M. Zagorski 1, A. Krzywicki 2, O. C. Martin 3, 4

#### Physical Review E87 (2013) 012727

The cell cycle is a tightly controlled process, yet its underlying genetic network shows marked differences across species. Which of the associated structural features follow solely from the ability to impose the appropriate gene expression patterns? We tackle this question in silico by examining the ensemble of all regulatory networks which satisfy the constraint of producing a given sequence of gene expressions. We focus on three cell cycle profiles coming from baker's yeast, fission yeast and mammals. First, we show that the networks in each of the ensembles use just a few interactions that are repeatedly reused as building blocks. Second, we find an enrichment in network motifs that is similar in the two yeast cell cycle systems investigated. These motifs do not have autonomous functions, but nevertheless they reveal a regulatory logic for cell cycling based on a feed-forward cascade of activating interactions.

• 1 : Marian Smoluchowski Institute of Physics and Mark Kac Complex Systems Research Center
Jagellonian University
• 2 : Laboratoire de Physique Théorique d'Orsay (LPT)
CNRS : UMR8627 – Université Paris XI - Paris Sud
• 3 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 4 : Génétique Végétale (GV)
CNRS : UMR8120 – Institut national de la recherche agronomique (INRA) : UMR0320 – Université Paris XI - Paris Sud – AgroParisTech

• ## Effect of Partial Absorption on Diffusion with Resetting

### Justin Whitehouse 1, Martin R. Evans 1, Satya N. Majumdar 2

#### Physical Review E87 (2013) 022118

The effect of partial absorption on a diffusive particle which stochastically resets its position with a finite rate $r$ is considered. The particle is absorbed by a target at the origin with absorption 'velocity' $a$; as the velocity $a$ approaches $\infty$ the absorption property of the target approaches that of a perfectly-absorbing target. The effect of partial absorption on first-passage time problems is studied, in particular, it is shown that the mean time to absorption (MTA) is increased by an additive term proportional to $1/a$. The results are extended to multiparticle systems where independent searchers, initially uniformly distributed with a given density, look for a single immobile target. It is found that the average survival probability $P^{av}$ is modified by a multiplicative factor which is a function of $1/a$, whereas the decay rate of the typical survival probability $P^{typ}$ is decreased by an additive term proportional to $1/a$.

• 1 : SUPA, School of Physics, University of Edinburgh
SUPA
• 2 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
CNRS : UMR8626 – Université Paris XI - Paris Sud

• ## Effect of winding edge currents

### Stephane Ouvry 1, Leonid Pastur 2, Andrey Yanovsky 2

#### Physics Letters A377 (2013) 804-809

We discuss persistent currents for particles with internal degrees of freedom. The currents arise because of winding properties essential for the chaotic motion of the particles in a confined geometry. The currents do not change the particle concentrations or thermodynamics, similar to the skipping orbits in a magnetic field.

• 1 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2 : Low Temperature Physics Institute, Kharkiv
National Academy of Sciences of Ukraine

• ## Einstein relation in systems with anomalous diffusion

### G. Gradenigo a,b</sup , A. Sarracino a, D. Villamaina c, A. Vulpiani a

#### Acta Physica Polonica B 44 (2013) 899-912

We discuss the role of non-equilibrium conditions in the context of anomalous dynamics. We study in detail the response properties in different models, featuring subdiffusion and superdiffusion: in such models, the presence of currents induces a violation of the Einstein relation. We show how in some of them it is possible to find the correlation function proportional to the linear response, in other words, we have a generalized fluctuation-response relation.

• a. CNR-ISC and Dipartimento di Fisica, Università Sapienza
p.le A. Moro 2, 00185, Roma, Italy
• b. Institut Physique Théorique (IPhT), CEA Saclay and CNRS URA 2306
91191 Gif Sur Yvette, France
• c. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud

• ## Emergence of clones in sexual populations

### Richard A. Neher 1, Marija Vucelja 2, Marc Mézard 3, Boris I. Shraiman 4

#### Journal of Statistical Mechanics: Theory and Experiment (2013) P01008

In sexual population, recombination reshuffles genetic variation and produces novel combinations of existing alleles, while selection amplifies the fittest genotypes in the population. If recombination is more rapid than selection, populations consist of a diverse mixture of many genotypes, as is observed in many populations. In the opposite regime, which is realized for example in the facultatively sexual populations that outcross in only a fraction of reproductive cycles, selection can amplify individual genotypes into large clones. Such clones emerge when the fitness advantage of some of the genotypes is large enough that they grow to a significant fraction of the population despite being broken down by recombination. The occurrence of this "clonal condensation" depends, in addition to the outcrossing rate, on the heritability of fitness. Clonal condensation leads to a strong genetic heterogeneity of the population which is not adequately described by traditional population genetics measures, such as Linkage Disequilibrium. Here we point out the similarity between clonal condensation and the freezing transition in the Random Energy Model of spin glasses. Guided by this analogy we explicitly calculate the probability, Y, that two individuals are genetically identical as a function of the key parameters of the model. While Y is the analog of the spin-glass order parameter, it is also closely related to rate of coalescence in population genetics: Two individuals that are part of the same clone have a recent common ancestor.

• 1 : Max Planck Institute for Developmental Biology
Max Planck Institute for Developmental Biology
• 2 : Courant Institute for Mathematical Sciences
New York University
• 3 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 4 : Kavli Institute for Theoretical Physics and Department of Physics
University of California, Santa Barbara

• ## Entanglement production in non-ideal cavities and optimal opacity

### Dario Villamaina 1, Pierpaolo Vivo 1

#### Physical Review B (Condensed Matter)88 (2013) 041301

We compute analytically the distributions of concurrence $\bm{\mathcal{C}}$ and squared norm $\bm{\mathcal{N}}$ for the production of electronic entanglement in a chaotic quantum dot. The dot is connected to the external world via one ideal and one partially transparent lead, characterized by the opacity $\gamma$. The average concurrence increases with $\gamma$ while the average squared norm of the entangled state decreases, making it less likely to be detected. When a minimal detectable norm $\bm{\mathcal{N}}_0$ is required, the average concurrence is maximal for an optimal value of the opacity $\gamma^\star(\bm{\mathcal{N}}_0)$ which is explicitly computed as a function of $\bm{\mathcal{N}}_0$. If $\bm{\mathcal{N}}_0$ is larger than the critical value $\bm{\mathcal{N}}_0^\star\simeq 0.3693\dots$, the average entanglement production is maximal for the completely ideal case, a direct consequence of an interesting bifurcation effect.

• 1 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
CNRS : UMR8626 – Université Paris XI - Paris Sud

• ## Ergodic vs diffusive decoherence in mesoscopic devices

### Thibaut Capron 1, 2, Christophe Texier 3, 4, Gilles Montambaux 4, Dominique Mailly 5, Andreas D. Wieck 6, Christopher Bäuerle 1, Laurent Saminadayar 1

#### Physical Review B (Condensed Matter)87, 4 (2013) 041307

We report on the measurement of phase coherence length in a high mobility two-dimensional electron gas patterned in two different geometries, a wire and a ring. The phase coherence length is extracted both from the weak localization correction in long wires and from the amplitude of the Aharonov-Bohm oscillations in a single ring, in a low temperature regime when decoherence is dominated by electronic interactions. We show that these two measurements lead to different phase coherence lengths, namely $L_{\Phi}^\mathrm{wire}\propto T^{-1/3}$ and $L_{\Phi}^\mathrm{ring}\propto T^{-1/2}$. This difference reflects the fact that the electrons winding around the ring necessarily explore the whole sample (ergodic trajectories), while in a long wire the electrons lose their phase coherence before reaching the edges of the sample (diffusive regime).

• 1 : Institut Néel (NEEL)
CNRS : UPR2940 – Université Joseph Fourier - Grenoble I – Institut National Polytechnique de Grenoble (INPG)
• 2 : Université de Grenoble
Université Joseph Fourier - Grenoble I – Université Stendhal - Grenoble III – Université Pierre-Mendès-France - Grenoble II
• 3 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 4 : Laboratoire de Physique des Solides (LPS)
CNRS : UMR8502 – Université Paris XI - Paris Sud
• 5 : Laboratoire de photonique et de nanostructures (LPN)
CNRS : UPR20
• 6 : Lehrstuhl für Angewandte Festkörperphysik
Lehrstuhl für Angewandte Festkörperphysik

• ## Exact distributions of the number of distinct and common sites visited by N independent random walkers

### Anupam Kundu 1, Satya N. Majumdar 1, Gregory Schehr 1

#### Physical Review Letters110 (2013) 220602

We study the number of distinct sites S_N(t) and common sites W_N(t) visited by N independent one dimensional random walkers, all starting at the origin, after t time steps. We show that these two random variables can be mapped onto extreme value quantities associated to N independent random walkers. Using this mapping, we compute exactly their probability distributions P_N^d(S,t) and P_N^d(W,t) for any value of N in the limit of large time t, where the random walkers can be described by Brownian motions. In the large N limit one finds that S_N(t)/\sqrt{t} \propto 2 \sqrt{\log N} + \widetilde{s}/(2 \sqrt{\log N}) and W_N(t)/\sqrt{t} \propto \widetilde{w}/N where \widetilde{s} and \widetilde{w} are random variables whose probability density functions (pdfs) are computed exactly and are found to be non trivial. We verify our results through direct numerical simulations.

• 1 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
CNRS : UMR8626 – Université Paris XI - Paris Sud

• ## Exact results for the spectra of interacting bosons and fermions on the lowest Landau level

### Stefan Mashkevich 1, 2, Sergey Matveenko 3, Stéphane Ouvry 4

#### Journal of Statistical Mechanics (2013) P02013

A system of N interacting bosons or fermions in a two-dimensional harmonic potential (or, equivalently, magnetic field) whose states are projected onto the lowest Landau level is considered. Generic expressions are derived for matrix elements of any interaction, in the basis of angular momentum eigenstates. For the fermion "ground state" (N=1 Laughlin state), this makes it possible to exactly calculate its energy all the way up to the mesoscopic regime N ~ 1000. It is also shown that for N = 3 and Coulomb interaction, several rational low-lying values of energy exist, for bosons and fermions alike.

• 1 : Schrodinger
Schrodinger
• 2 : Bogolyubov Institute for Theoretical Physics
Bogolyobov Institute for Theoretical Physics
• 3 : Landau Institute for Theoretical Physics
Landau Institute for Theoretical Physics
• 4 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
CNRS : UMR8626 – Université Paris XI - Paris Sud

• ## Exact Statistics of the Gap and Time Interval Between the First Two Maxima of Random Walks

### Satya N. Majumdar 1, Philippe Mounaix 2, Gregory Schehr 1

#### Physical Review Letters111 (2013) 070601

We investigate the statistics of the gap, G_n, between the two rightmost positions of a Markovian one-dimensional random walker (RW) after n time steps and of the duration, L_n, which separates the occurrence of these two extremal positions. The distribution of the jumps \eta_i's of the RW, f(\eta), is symmetric and its Fourier transform has the small k behavior 1-\hat{f}(k)\sim| k|^\mu with 0 < \mu \leq 2. We compute the joint probability density function (pdf) P_n(g,l) of G_n and L_n and show that, when n \to \infty, it approaches a limiting pdf p(g,l). The corresponding marginal pdf of the gap, p_{\rm gap}(g), is found to behave like p_{\rm gap}(g) \sim g^{-1 - \mu} for g \gg 1 and 0<\mu < 2. We show that the limiting marginal distribution of L_n, p_{\rm time}(l), has an algebraic tail p_{\rm time}(l) \sim l^{-\gamma(\mu)} for l \gg 1 with \gamma(1<\mu \leq 2) = 1 + 1/\mu, and \gamma(0<\mu<1) = 2. For l, g \gg 1 with fixed l g^{-\mu}, p(g,l) takes the scaling form p(g,l) \sim g^{-1-2\mu} \tilde p_\mu(l g^{-\mu}) where \tilde p_\mu(y) is a (\mu-dependent) scaling function. We also present numerical simulations which verify our analytic results.

• 1 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2 : Centre de Physique Théorique (CPHT)
CNRS : UMR7644 – Polytechnique - X

• ## Exact theory of dense amorphous hard spheres in high dimension. II. The high density regime and the Gardner transition

### Jorge Kurchan 1, Giorgio Parisi 2, Pierfrancesco Urbani 3, Francesco Zamponi 4

#### The Journal of Physical Chemistry B117 (2013) 12979-12994

We consider the theory of the glass phase and jamming of hard spheres in the large space dimension limit. Building upon the exact expression for the free-energy functional obtained previously, we find that the Random First Order Transition (RFOT) scenario is realized here with two thermodynamic transitions: the usual Kauzmann point associated with entropy crisis, and a further transition at higher pressures in which a glassy structure of micro-states is developed within each amorphous state. This kind of glass-glass transition into a phase dominating the higher densities was described years ago by Elisabeth Gardner, and may well be a generic feature of RFOT. Micro states that are small excitations of an amorphous matrix -- separated by low entropic or energetic barriers -- thus emerge naturally, and modify the high pressure (or low temperature) limit of the thermodynamic functions.

• 1 : Physique et mécanique des milieux hétérogenes (PMMH)
CNRS : UMR7636 – Université Pierre et Marie Curie (UPMC) - Paris VI – Université Paris VII - Paris Diderot – ESPCI ParisTech
• 2 : Dipartimento di Fisica and INFM
Università degli studi di Roma I - La Sapienza
• 3 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 4 : Laboratoire de Physique Théorique de l'ENS (LPTENS)
CNRS : UMR8549 – Université Pierre et Marie Curie (UPMC) - Paris VI – École normale supérieure [ENS] - Paris

• ## Experimental Observation of Localized Modes in a Dielectric Square Resonator

### S. Bittner 1, E. Bogomolny 2, B. Dietz 3, M. Miski-Oglu 3, A. Richter 4

#### Physical Review E88 (2013) 062906

We investigated the frequency spectra and field distributions of a dielectric square resonator in a microwave experiment. Since such systems cannot be treated analytically, the experimental studies of their properties are indispensable. The momentum representation of the measured field distributions shows that all resonant modes are localized on specific classical tori of the square billiard. Based on these observations a semiclassical model was developed. It shows excellent agreement with all but a single class of measured field distributions that will be treated separately.

• 1 : Institut für Kernphysik
• 2 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 3 : Institut für Kernphysik
• 4 : Institute of Environmental Physics
University of Bremen

• ## Finite-size critical fluctuations in microscopic models of mode-coupling theory

### Silvio Franz 1, Mauro Sellitto 2

#### Journal of Statistical Mechanics (2013) P02025

Facilitated spin models on random graphs provide an ideal microscopic realization of the mode-coupling theory of supercooled liquids: they undergo a purely dynamic glass transition with no thermodynamic singularity. In this paper we study the fluctuations of dynamical heterogeneity and their finite-size scaling properties in the beta-relaxation regime of such microscopic spin models. We compare the critical fluctuations behavior for two distinct measures of correlations with the results of a recently proposed field theoretical description based on quasi-equilibrium ideas. We find that the theoretical predictions perfectly fit the numerical simulation data once the relevant order parameter is identified with the persistence function of the spins.

• 1 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2 : Laboratoire de Physique de l'ENS Lyon (Phys-ENS)
CNRS : UMR5672 – École Normale Supérieure (ENS) - Lyon

• ## Fluctuations quantiques et effets non-linéaires dans les condensats de Bose-Einstein : des ondes de choc dispersives au rayonnement de Hawking acoustique

### Pierre-Élie Larré 1

#### Université Paris Sud - Paris XI (20/09/2013), Nicolas Pavloff (Dir.)

Cette thèse est dédiée à l'étude de l'analogue du rayonnement de Hawking dans les condensats de Bose-Einstein. Le premier chapitre présente de nouvelles configurations d'intérêt expérimental permettant de réaliser l'équivalent acoustique d'un trou noir gravitationnel dans l'écoulement d'un condensat atomique unidimensionnel. Nous donnons dans chaque cas une description analytique du profil de l'écoulement, des fluctuations quantiques associées et du spectre du rayonnement de Hawking. L'analyse des corrélations à deux corps de la densité dans l'espace des positions et des impulsions met en évidence l'émergence de signaux révélant l'effet Hawking dans nos systèmes. En démontrant une règle de somme vérifiée par la matrice densité à deux corps connexe, on montre que les corrélations à longue portée de la densité doivent être associées aux modifications diagonales de la matrice densité à deux corps lorsque l'écoulement du condensat présente un horizon acoustique. Motivés par des études expérimentales récentes de profils d'onde générés dans des condensats de polaritons en microcavité semi-conductrice, nous analysons dans un second chapitre les caractéristiques superfluides et dissipatives de l'écoulement autour d'un obstacle localisé d'un condensat de polaritons unidimensionnel obtenu par pompage incohérent. Nous examinons la réponse du condensat dans la limite des faibles perturbations et au moyen de la théorie de Whitham dans le régime non-linéaire. On identifie un régime dépendant du temps séparant deux types d'écoulement stationnaire et dissipatif : un principalement visqueux à faible vitesse et un autre caractérisé par un rayonnement de Cherenkov d'ondes de densité à grande vitesse. Nous présentons enfin des effets de polarisation obtenus en incluant le spin des polaritons dans la description du condensat et montrons dans le troisième chapitre que des effets similaires en présence d'un horizon acoustique pourraient être utilisés pour démontrer expérimentalement le rayonnement de Hawking dans les condensats de polaritons.

• 1 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
CNRS : UMR8626 – Université Paris XI - Paris Sud

• ## Flux-based classification of reactions reveals a functional bow-tie organization of complex metabolic networks

### Shalini Singh 1, 2, Areejit Samal 1, 3, 4, Varun Giri 1, Sandeep Krishna 5, Nandula Raghuram 6, Sanjay Jain 1, 7, 8

#### Physical Review E87 (2013) 052708

Unraveling the structure of complex biological networks and relating it to their functional role is an important task in systems biology. Here we attempt to characterize the functional organization of the large-scale metabolic networks of three microorganisms. We apply flux balance analysis to study the optimal growth states of these organisms in different environments. By investigating the differential usage of reactions across flux patterns for different environments, we observe a striking bimodal distribution in the activity of reactions. Motivated by this, we propose a simple algorithm to decompose the metabolic network into three sub-networks. It turns out that our reaction classifier which is blind to the biochemical role of pathways leads to three functionally relevant sub-networks that correspond to input, output and intermediate parts of the metabolic network with distinct structural characteristics. Our decomposition method unveils a functional bow-tie organization of metabolic networks that is different from the bow-tie structure determined by graph-theoretic methods that do not incorporate functionality.

• 1 : Department of Physics and Astrophysics
University of Delhi
• 2 : Department of Genetics
University of Delhi
• 3 : Max Planck Institute for Mathematics in the Sciences (MPI-MIS)
Max-Planck-Institut
• 4 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 5 : National Centre for Biological Sciences
UAS-GKVK Campus
• 6 : School of Biotechnology
GGS Indraprastha University
• 7 : Jawaharlal Nehru Centre for Advanced Scientific Research
Jawaharlal Nehru Centre for Advanced Scientific Research
• 8 : Santa Fe Institute
Santa Fe Institute

• ## Fractal globule as an molecular machine

### V. A. Avetisov 1, 2, V. A. Ivanov 3, D. A. Meshkov 1, S. K. Nechaev 4, 5

#### JETP Letters98, 4 (2013) 242-246

The relaxation of an elastic network, constructed by a contact map of a fractal (crumpled) polymer globule is investigated. We found that: i) the slowest mode of the network is separated from the rest of the spectrum by a wide gap, and ii) the network quickly relaxes to a low--dimensional (one-dimensional, in our demonstration) manifold spanned by slowest degrees of freedom with a large basin of attraction, and then slowly approaches the equilibrium not escaping this manifold. By these dynamic properties, the fractal globule elastic network is similar to real biological molecular machines, like myosin. We have demonstrated that unfolding of a fractal globule can be described as a cascade of equilibrium phase transitions in a hierarchical system. Unfolding manifests itself in a sequential loss of stability of hierarchical levels with the temperature change.

• 1 : The Semenov Institute of Chemical Physics
• 2 : National Research University Higher School of Economics
National Research University Higher School of Economics
• 3 : Moscow State University
Moscow State University
• 4 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 5 : P. N. Lebedev Physical Institute

• ## Freezing Transitions in Liquids Characterized by a Favoured Local Structure

### Pierre Ronceray 1, 2, Peter Harrowell 3

#### Physical Review E87 (2013) 052313

The ordering transitions of a 2D lattice liquid characterized by a single favoured local structure (FLS) are studied using Monte Carlo simulations. All eight distinct geometries for the FLS are considered and we find a variety of ordering transitions - first order, continuous and multi-step transitions. Using a microcanonical representation of the freezing transition we resolve the dual influence of the local structure on the ordering transition, i.e. via the energy of the crystal and the entropy cost of structure in the liquid.

• 1 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2 : Ecole Normale Supérieure de Paris (ENS Paris)
École normale supérieure [ENS] - Paris
• 3 : Faculty of Sciences
University of Sydney

• ## From elongated spanning trees to vicious random walks

### A. Gorsky 1, S. Nechaev 2, 3, V. S. Poghosyan 4, V. B. Priezzhev 5

#### Nuclear Physics B870 (2013) 55-77

Given a spanning forest on a large square lattice, we consider by combinatorial methods a correlation function of $k$ paths ($k$ is odd) along branches of trees or, equivalently, $k$ loop--erased random walks. Starting and ending points of the paths are grouped in a fashion a $k$--leg watermelon. For large distance $r$ between groups of starting and ending points, the ratio of the number of watermelon configurations to the total number of spanning trees behaves as $r^{-\nu} \log r$ with $\nu = (k^2-1)/2$. Considering the spanning forest stretched along the meridian of this watermelon, we see that the two--dimensional $k$--leg loop--erased watermelon exponent $\nu$ is converting into the scaling exponent for the reunion probability (at a given point) of $k$ (1+1)--dimensional vicious walkers, $\tilde{\nu} = k^2/2$. Also, we express the conjectures about the possible relation to integrable systems.

• 1 : ITEP
ITEP
• 2 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 3 : P.N. Lebedev Physical Institute of the Russian Academy of Sciences
• 4 : Institute for Informatics and Automation Problems
NAS of Armenia,
• 5 : Bogolubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research

• ## Glassy Critical Points and Random Field Ising Model

### Silvio Franz 1, Giorgio Parisi 2, Federico Ricci-Tersenghi 2

#### Journal of Statistical Mechanics (2013) L02001

We consider the critical properties of points of continuous glass transition as one can find in liquids in presence of constraints or in liquids in porous media. Through a one loop analysis we show that the critical Replica Field Theory describing these points can be mapped in the $\phi^4$-Random Field Ising Model. We confirm our analysis studying the finite size scaling of the $p$-spin model defined on sparse random graph, where a fraction of variables is frozen such that the phase transition is of a continuous kind.

• 1 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2 : Dipartimento di Fisica and INFM
Università degli studi di Roma I - La Sapienza

• ## Hawking radiation in a two-component Bose-Einstein condensate

### P. -É. Larré 1, N. Pavloff 1

#### EPL103 (2013) 60001

We consider a simple realization of an event horizon in the flow of a one-dimensional two-component Bose-Einstein condensate. Such a condensate has two types of quasiparticles; In the system we study, one corresponds to density fluctuations and the other to polarization fluctuations. We treat the case where a horizon occurs only for one type of quasiparticles (the polarization ones). We study the one- and two-body signal associated to the analog of spontaneous Hawking radiation and demonstrate by explicit computation that it consists only in the emission of polarization waves. We discuss the experimental consequences of the present results in the domain of atomic Bose-Einstein condensates and also for the physics of exciton-polaritons in semiconductor microcavities.

• 1 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
CNRS : UMR8626 – Université Paris XI - Paris Sud

• ## Invariant $\beta$-Wishart ensembles, crossover densities and asymptotic corrections to the Marchenko-Pastur law

### Romain Allez 1, Jean-Philippe Bouchaud 2, Satya N. Majumdar 3, Pierpaolo Vivo 3

#### Journal of Physics A: Mathematical and Theoretical46 (2013) 015001

We construct a diffusive matrix model for the $\beta$-Wishart (or Laguerre) ensemble for general continuous $\beta\in [0,2]$, which preserves invariance under the orthogonal/unitary group transformation. Scaling the Dyson index $\beta$ with the largest size $M$ of the data matrix as $\beta=2c/M$ (with $c$ a fixed positive constant), we obtain a family of spectral densities parametrized by $c$. As $c$ is varied, this density interpolates continuously between the Mar\vcenko-Pastur ($c\to \infty$ limit) and the Gamma law ($c\to 0$ limit). Analyzing the full Stieltjes transform (resolvent) equation, we obtain as a byproduct the correction to the Mar\vcenko-Pastur density in the bulk up to order 1/M for all $\beta$ and up to order $1/M^2$ for the particular cases $\beta=1,2$.

• 1 : CEntre de REcherches en MAthématiques de la DEcision (CEREMADE)
CNRS : UMR7534 – Université Paris IX - Paris Dauphine
• 2 : Science et Finance
Science et Finance
• 3 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
CNRS : UMR8626 – Université Paris XI - Paris Sud

• ## Inverse inference in the asymmetric Ising model

### Jason Sakellariou 1

#### Université Paris Sud - Paris XI (22/02/2013), Marc Mézard (Dir.)

Recent experimental techniques in biology made possible the acquisition of overwhelming amounts of data concerning complex biological networks, such as neural networks, gene regulation networks and protein-protein interaction networks. These techniques are able to record states of individual components of such networks (neurons, genes, proteins) for a large number of configurations. However, the most biologically relevantinformation lies in their connectivity and in the way their components interact, information that these techniques aren't able to record directly. The aim of this thesis is to study statistical methods for inferring information about the connectivity of complex networks starting from experimental data. The subject is approached from a statistical physics point of view drawing from the arsenal of methods developed in the study of spin glasses. Spin-glasses are prototypes of networks of discrete variables interacting in a complex way and are widely used to model biological networks. After an introduction of the models used and a discussion on the biological motivation of the thesis, all known methods of network inference are introduced and analysed from the point of view of their performance. Then, in the third part of the thesis, a new method is proposed which relies in the remark that the interactions in biology are not necessarily symmetric (i.e. the interaction from node A to node B is not the same as the one from B to A). It is shown that this assumption leads to methods that are both exact and efficient. This means that the interactions can be computed exactly, given a sufficient amount of data, and in a reasonable amount of time. This is an important original contribution since no other method is known to be both exact and efficient.

• 1 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
CNRS : UMR8626 – Université Paris XI - Paris Sud

• ## Joint probability densities of level spacing ratios in random matrices

### Y. Y. Atas 1, E. Bogomolny 1, O. Giraud 1, P. Vivo 1, E. Vivo 2

#### Journal of Physics A: Mathematical and Theoretical46 (2013) 355204

We calculate analytically, for finite-size matrices, joint probability densities of ratios of level spacings in ensembles of random matrices characterized by their associated confining potential. We focus on the ratios of two spacings between three consecutive real eigenvalues, as well as certain generalizations such as the overlapping ratios. The resulting formulas are further analyzed in detail in two specific cases: the beta-Hermite and the beta-Laguerre cases, for which we offer explicit calculations for small N. The analytical results are in excellent agreement with numerical simulations of usual random matrix ensembles, and with the level statistics of a quantum many-body lattice model and zeros of the Riemann zeta function.

• 1 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2 : Departamento de Matemáticas and Grupo Interdisciplinar de Sistemas Complejos (GISC)

• ## Large deviations of the top eigenvalue of large Cauchy random matrices

### Satya N. Majumdar 1, Gregory Schehr 1, Dario Villamaina 1, Pierpaolo Vivo 1

#### Journal of Physics A: Mathematical and Theoretical46 (2013) 022001

We compute analytically the probability density function (pdf) of the largest eigenvalue $\lambda_{\max}$ in rotationally invariant Cauchy ensembles of $N\times N$ matrices. We consider unitary ($\beta = 2$), orthogonal ($\beta =1$) and symplectic ($\beta=4$) ensembles of such heavy-tailed random matrices. We show that a central non-Gaussian regime for $\lambda_{\max} \sim \mathcal{O}(N)$ is flanked by large deviation tails on both sides which we compute here exactly for any value of $\beta$. By matching these tails with the central regime, we obtain the exact leading asymptotic behaviors of the pdf in the central regime, which generalizes the Tracy-Widom distribution known for Gaussian ensembles, both at small and large arguments and for any $\beta$. Our analytical results are confirmed by numerical simulations.

• 1 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
CNRS : UMR8626 – Université Paris XI - Paris Sud

• ## Linear hydrodynamics for driven granular gases

### M. I. Garcia de Soria 1, P. Maynar 1, E. Trizac 2

#### Physical Review E87 (2013) 022201

We study the dynamics of a granular gas heated by the stochastic thermostat. From a Boltzmann description, we derive the hydrodynamic equations for small perturbations around the stationary state that is reached in the long time limit. Transport coefficients are identified as Green-Kubo formulas obtaining explicit expressions as a function of the inelasticity and the spacial dimension.

• 1 : Fisica Teorica, Universidad de Sevilla
• 2 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
CNRS : UMR8626 – Université Paris XI - Paris Sud

• ## Localization of spinons in random Majumdar-Ghosh chains

### Arthur Lavarélo 1, Guillaume Roux 1

#### Physical Review Letters110 (2013) 087204

We study the effect of disorder on frustrated dimerized spin-1/2 chains at the Majumdar-Ghosh point. Using variational methods and density-matrix renormalization group approaches, we identify two localization mechanisms for spinons which are the deconfined fractional elementary excitations of these chains. The first one belongs to the Anderson localization class and dominates at the random Majumdar-Ghosh (RMG) point. There, spinons are almost independent, remain gapped, and localize in Lifshitz states whose localization length is analytically obtained. The RMG point then displays a quantum phase transition to phase of localized spinons at large disorder. The other mechanism is a random confinement mechanism which induces an effective interaction between spinons and brings the chain into a gapless and partially polarized phase for arbitrarily small disorder.

• 1 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
CNRS : UMR8626 – Université Paris XI - Paris Sud

• ## Low-dimensional physics of ultracold gases with bound states and the sine-Gordon model

### Thierry Jolicoeur 1, Evgeni Burovski 2, Giuliano Orso 3

#### European Physical Journal - Special Topics217 (2013) 3-12

One-dimensional systems of interacting atoms are an ideal laboratory to study the Kosterlitz-Thouless phase transition. In the renormalization group picture there is essentially a two-parameter phase diagram to explore. We first present how detailed experiments have shown direct evidence for the theoretical treatment of this transition. Then generalization to the case of two-component systems with bound state formation is discussed. Trimer formation in the asymmetric attractive Hubbard model involve in a crucial way this kind of physics.

• 1 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2 : Department of Physics
Lancaster University
• 3 : Matériaux et Phénomènes Quantiques (MPQ)
CNRS : FR2437 – Université Paris VII - Paris Diderot

• ## Lyapunov exponents, one-dimensional Anderson localisation and products of random matrices

### Alain Comtet 1, 2, Christophe Texier 1, 3, Yves Tourigny 4

#### Journal of Physics A: Mathematical and Theoretical46 (2013) 254003

The concept of Lyapunov exponent has long occupied a central place in the theory of Anderson localisation; its interest in this particular context is that it provides a reasonable measure of the localisation length. The Lyapunov exponent also features prominently in the theory of products of random matrices pioneered by Furstenberg. After a brief historical survey, we describe some recent work that exploits the close connections between these topics. We review the known solvable cases of disordered quantum mechanics involving random point scatterers and discuss a new solvable case. Finally, we point out some limitations of the Lyapunov exponent as a means of studying localisation properties.

• 1 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2 : Unite mixte de service de l'institut Henri Poincaré (UMSIHP)
CNRS : UMS839 – Université Pierre et Marie Curie (UPMC) - Paris VI
• 3 : Laboratoire de Physique des Solides (LPS)
CNRS : UMR8502 – Université Paris XI - Paris Sud
• 4 : School of Mathematics [Bristol]
University of Bristol

• ## Magnetic responses of randomly depleted spin ladders

### Arthur Lavarélo 1, Guillaume Roux 1, Nicolas Laflorencie 2

#### Physical Review B (Condensed Matter)88, 13 (2013) 134420-134442

The magnetic responses of a spin-1/2 ladder doped with non-magnetic impurities are studied using various methods and including the regime where frustration induces incommensurability. Several improvements are made on the results of the seminal work of Sigrist and Furusaki [J. Phys. Soc. Jpn. 65, 2385 (1996)]. Deviations from the Brillouin magnetic curve due to interactions are also analyzed. First, the magnetic profile around a single impurity and effective interactions between impurities are analyzed within the bond-operator mean-field theory and compared to density-matrix renormalization group calculations. Then, the temperature behavior of the Curie constant is studied in details. At zero-temperature, we give doping-dependent corrections to the results of Sigrist and Furusaki on general bipartite lattice and compute exactly the distribution of ladder cluster due to chain breaking effects. Using exact diagonalization and quantum Monte-Carlo methods on the effective model, the temperature dependence of the Curie constant is compared to a random dimer model and a real-space renormalization group scenario. Next, the low-part of the magnetic curve corresponding to the contribution of impurities is computed using exact diagonalization. The random dimer model is shown to capture the bulk of the curve, accounting for the deviation from the Brillouin response. At zero-temperature, the effective model prediction agrees relatively well with density-matrix renormalization group calculations. Finite-temperature effects are displayed within the effective model and for large depleted ladder models using quantum Monte-Carlo simulations. In all, the effect of incommensurability does not display a strong qualitative effect on both the magnetic susceptibility and the magnetic curve. Consequences for experiments on the BiCu2PO6 compound and other spin-gapped materials are briefly discussed.

• 1 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2 : Laboratoire de Physique Théorique - IRSAMC (LPT)
CNRS : UMR5152 – Université Paul Sabatier (UPS) - Toulouse III

• ## Many-body study of a quantum point contact in the fractional quantum Hall regime at v=5/2

### Paul Soulé 1 Thierry Jolicoeur 1 Philippe Lecheminant 2

#### Physical Review B (Condensed Matter), American Physical Society, 2013, 88, pp.235107

We study a quantum point contact in the fractional quantum Hall regime at Landau level filling factors 1/3 and 5/2. By using exact diagonalizations in the cylinder geometry we identify the edge modes in the presence of a parabolic confining potential. By changing the sign of the potential we can access both the tunneling through the bulk of the fluid and the tunneling between spatially separated droplets. This geometry is realized in the quantum point contact geometry for two-dimensional electron gases. In the case of the model Moore-Read Pfaffian state at filling factor 5/2 we identify the conformal towers of many-body eigenstates including the non-Abelian sector. By a Monte-Carlo technique we compute the various scaling exponents that characterize the edge modes. In the case of hard-core interactions whose ground states are exact model wavefunction we find equality of neutral and charged velocities for the Pfaffian state both bosonic and fermionic.

• 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
• 2. LPTM - Laboratoire de Physique Théorique et Modélisation

• ## Material Dependence of the Wire-Particle Casimir Interaction

### E. Noruzifar 1, P. Rodriguez-Lopez 2, T. Emig 3, R. Zandi 1

#### Physical Review A87 (2013) 042504

We study the Casimir interaction between a metallic cylindrical wire and a metallic spherical particle by employing the scattering formalism. At large separations, we derive the asymptotic form of the interaction. In addition, we find the interaction between a metallic wire and an isotropic atom, both in the non-retarded and retarded limits. We identify the conditions under which the asymptotic Casimir interaction does not depend on the material properties of the metallic wire and the particle. Moreover, we compute the exact Casimir interaction between the particle and the wire numerically. We show that there is a complete agreement between the numerics and the asymptotic energies at large separations. For short separations, our numerical results show good agreement with the proximity force approximation.

• 1 : Department of Physics and Astronomy
University of California, Riverside
• 2 : Departamento de Fisica Aplicada
• 3 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
CNRS : UMR8626 – Université Paris XI - Paris Sud

• ## Mesoscopic fluctuations in the Fermi-liquid regime of the Kondo problem

### Denis Ullmo 1, * Dong E. Liu 2 Sébastien Burdin 3 Harold U. Baranger 2

#### European Physical Journal B: Condensed Matter and Complex Systems, Springer-Verlag, 2013, 86 (8), pp.353. 〈10.1140/epjb/e2013-40418-3〉

We consider the low temperature regime of the mesoscopic Kondo problem, and in particular the relevance of a Fermi-liquid description of this regime. Mesoscopic fluctuations of both the quasiparticle energy levels and the corresponding wavefunctions are large in this case. These mesoscopic fluctuations make the traditional approach to Fermi-liquids impracticable, as it assumes the existence of a limited number of relevant parameters. We show here how this difficulty can be overcome and discuss the relationship between the resulting Fermi-liquid description "à la Nozières" and the mean field slave fermion approximation.

• 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
• 2. Duke Physics
• 3. LOMA - Laboratoire Ondes et Matière d'Aquitaine

• ## Modeling of dynamics of field-induced transformations in charge density waves

### T. Yi 1,3 , N. Kirova 2,4 , and S. Brazovskii 1,4

#### Eur. Phys. J. Special Topics 222, 1035–1046 (2013)

We present a modeling of stationary states and their transient dynamic for charge density waves in restricted geometries of realistic junctions under the applied voltage or the passing current. The model takes into account multiple fields in mutual nonlinear interactions: the amplitude and the phase of the charge density wave complex order parameter, distributions of the electric field, the density and the current of normal carriers. The results show that stationary states with dislocations are formed after an initial turbulent multi-vortex process. Static dislocations multiply stepwise when the voltage across or the current through the junction exceed a threshold. The dislocation core forms a charge dipole which concentrates a steep drop of the voltage, thus working as a self-tuned microscopic tunnelling junction. That can gives rise to features observed in experiments on the inter-layer tunneling in mesa-junctions.

• 1 CNRS, LPTMS, URM 8502, Univerisit ́e Paris-sud, 91405 Orsay, France
• 2 CNRS, LPS, URM 8626, Univerisit ́e Paris-sud, 91405 Orsay, France
• 3 epartement of physics, South University of Science and Technology of China, Shenzhen, Guangdong 518055, China
• 4 International Institute of Physics, 59078-400 Natal, Rio Grande do Norte, Brazil

• ## Morphology transition at depinning in a solvable model of interface growth in a random medium

### Hiroki Ohta 1 Martin-Luc Rosinberg 2 Gilles Tarjus 2

#### Europhysics Letters, EDP Science, 2013, 104, pp.16003

We propose a simple, exactly solvable, model of interface growth in a random medium that is a variant of the zero-temperature random-field Ising model on the Cayley tree. This model is shown to have a phase diagram (critical depinning field versus disorder strength) qualitatively similar to that obtained numerically on the cubic lattice. We then introduce a specifically tailored random graph that allows an exact asymptotic analysis of the height and width of the interface. We characterize the change of morphology of the interface as a function of the disorder strength, a change that is found to take place at a multicritical point along the depinning-transition line.

• 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
• 2. LPTMC - Laboratoire de Physique Théorique de la Matière Condensée

• ## Near-extreme statistics of Brownian motion

### Anthony Perret 1, Alain Comtet 1, 2, Satya N. Majumdar 1, Gregory Schehr 1

#### Physical Review Letters111 (2013) 240601

We study the statistics of near-extreme events of Brownian motion (BM) on the time interval [0,t]. We focus on the density of states (DOS) near the maximum \rho(r,t) which is the amount of time spent by the process at a distance r from the maximum. We develop a path integral approach to study functionals of the maximum of BM, which allows us to study the full probability density function (PDF) of \rho(r,t) and obtain an explicit expression for the moments, \langle [\rho(r,t)]^k \rangle, for arbitrary integer k. We also study near-extremes of constrained BM, like the Brownian bridge. Finally we also present numerical simulations to check our analytical results.

• 1 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2 : Unite mixte de service de l'institut Henri Poincaré (UMSIHP)
CNRS : UMS839 – Université Pierre et Marie Curie (UPMC) - Paris VI

• ## Network function shapes network structure: the case of the Arabidopsis flower organ specification genetic network

### Adrien Henry ab , Françoise Monéger c , Areejit Samal* ad and Olivier C. Martin* ab

#### Molecular Biosystems 9 (2013) 1726-1735

The reconstruction of many biological networks has allowed detailed studies of their structural properties. Several features exhibited by these networks have been interpreted to be the result of evolutionary dynamics. For instance the degree distributions may follow from a preferential attachment of new genes to older ones during evolution. Here we argue that even in the absence of any evolutionary dynamics, the presence of atypical features may follow from the fact that the network implements certain functions. To examine this network function shapes network structure scenario, we focus on the Arabidopsis genetic network controlling early flower organogenesis in which gene expression dynamics has been modelled using a Boolean framework. Specifically, for a system with 15 master genes, the phenotype consists of 10 experimentally determined steady-state expression patterns, considered here as the functional constraints on the network. The space of genetic networks satisfying these constraints is sometimes referred to as the neutral or genotype network. We sample this space using Markov Chain Monte Carlo which allows us to exhibit how the functional (phenotypic) constraints shape the gene network structure. We find that this shaping is strongest for the edge (interaction) usage, with effects that are functionally interpretable. In contrast, higher order features such as degree assortativity and network motifs are hardly shaped by the phenotypic constraints.

• a. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI - Paris Sud
• b. UMR de Génétique Végétale du Moulon, UMR 0320/UMR 8120, INRA / CNRS / Université Paris-Sud, 91190 Gif-sur-Yvette, France.
* E-mail: olivier.martin@u-psud.fr; Fax: +33 16933 2340
• c. Laboratoire Reproduction et Developpement des Plantes, UMR 5667, ENS / CNRS / INRA / Univ. Lyon I, 69364 Lyon cedex 07, France
• d. Max Planck Institute for Mathematics in the Sciences, Inselstr. 22, 04103 Leipzig, Germany.
* E-mail: samal@mis.mpg.de; Fax: +49 341 9959 658

• ## New phase transition in random planar diagrams and RNA-type matching

### Andrey Y. Lokhov 1, Olga V. Valba 1, 2, Mikhail V. Tamm 3, Sergei K. Nechaev 1, 4

#### Physical Review E88 (2013) 052117

We study the planar matching problem, defined by a symmetric random matrix with independent identically distributed entries, taking values 0 and 1. We show that the existence of a perfect planar matching structure is possible only above a certain critical density, $p_{c}$, of allowed contacts (i.e. of '1'). Using a formulation of the problem in terms of Dyck paths and a matrix model of planar contact structures, we provide an analytical estimation for the value of the transition point, $p_{c}$, in the thermodynamic limit. This estimation is close to the critical value, $p_{c} \approx 0.379$, obtained in numerical simulations based on an exact dynamical programming algorithm. We characterize the corresponding critical behavior of the model and discuss the relation of the perfect-imperfect matching transition to the known molten-glass transition in the context of random RNA secondary structure's formation. In particular, we provide strong evidence supporting the conjecture that the molten-glass transition at T=0 occurs at $p_{c}$.

• 1 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2 : Moscow Institute of Physics and Technology
Moscow Institute of Physics and Technology
• 3 : Department of Physics
Lomonosov State University
• 4 : P.N. Lebedev Physical Institute

• ## Non-Hermitian β-ensemble with real eigenvalues

### O. Bohigas 1 and M. P. Pato 2

#### AIP ADVANCES 3, 032130 (2013)

By removing the Hermitian condition of the so-called β-ensemble of tridiagonal matrices, an ensemble of non-Hermitian random matrices is constructed whose eigenvalues are all real. It is shown that they belong to the class of pseudo-Hermitian operators. Its statistical properties are investigated.

• 1 CNRS, Universite Paris-Sud, UMR8626, LPTMS, Orsay Cedex, F-91405, France
• 2 Instıtuto de F ́ısica, Universidade de S ̃ao Paulo, Caixa Postal 66318, 05314-970 Sao Paulo, S.P., Brazil

• ## Numerical approaches on driven elastic interfaces in random media

### Ezequiel E. Ferrero 1 Sebastian Bustingorry 1 Alejandro B. Kolton 1 Alberto Rosso 2

#### Comptes Rendus Physique, Elsevier Masson, 2013, 14 (8), pp.641 - 650. <10.1016/j.crhy.2013.08.002>

• 1. CONICET Centro Atomico Bariloche
• 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

• ## On the role of electron-nucleus contact and microwave saturation in Thermal Mixing DNP

### Sonia Colombo Serra 1, Alberto Rosso 2, Fabio Tedoldi 1

#### Physical Chemistry Chemical Physics15 (2013) 8416-8428

We have explored the manifold physical scenario emerging from a model of Dynamic Nuclear Polarization (DNP) via thermal mixing under the hypothesis of highly effective electron-electron interaction. When the electron and nuclear reservoirs are also assumed to be in strong thermal contact and the microwave irradiation saturates the target electron transition, the enhancement of the nuclear polarization is expected to be considerably high even if the irradiation frequency is set far away from the centre of the ESR line (as already observed by Borghini) and the typical polarization time is reduced on moving towards the boundaries of said line. More reasonable behaviours are obtained by reducing the level of microwave saturation or the contact between electrons and nuclei in presence of nuclear leakage. In both cases the function describing the dependency of the steady state nuclear polarization on the frequency of irradiation becomes sharper at the edges and the build up rate decreases on moving off-resonance. If qualitatively similar in terms of the effects produced on nuclear polarization, the degree of microwave saturation and of electron-nucleus contact has a totally different impact on electron polarization, which is of course strongly correlated to the effectiveness of saturation and almost insensitive, at the steady state, to the magnitude of the interactions between the two spin reservoirs. The likelihood of the different scenario is discussed in the light of the experimental data currently available in literature, to point out which aspects are suitably accounted and which are not by the declinations of thermal mixing DNP considered here.

• 1 : Centro Ricerche Bracco
Centro Ricerche Bracco
• 2 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
CNRS : UMR8626 – Université Paris XI - Paris Sud

• ## Optimal diffusive search: nonequilibrium resetting versus equilibrium dynamics

### Martin R. Evans 1, Satya N. Majumdar 2, Kirone Mallick 3

#### Journal of Physics A: Mathematical and Theoretical46 (2013) 185001

We study first-passage time problems for a diffusive particle with stochastic resetting with a finite rate $r$. The optimal search time is compared quantitatively with that of an effective equilibrium Langevin process with the same stationary distribution. It is shown that the intermittent, nonequilibrium strategy with non-vanishing resetting rate is more efficient than the equilibrium dynamics. Our results are extended to multiparticle systems where a team of independent searchers, initially uniformly distributed with a given density, looks for a single immobile target. Both the average and the typical survival probability of the target are smaller in the case of nonequilibrium dynamics.

• 1 : SUPA, School of Physics, University of Edinburgh
SUPA
• 2 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 3 : Institut de Physique Théorique (ex SPhT) (IPHT)
CNRS : URA2306 – CEA : DSM/IPHT

• ## Persistence and First-Passage Properties in Non-equilibrium Systems

### Alan J. Bray 1, Satya N. Majumdar 2, G. Schehr 2

#### Advances in Physics62, 3 (2013) 225-361

In this review we discuss the persistence and the related first-passage properties in extended many-body nonequilibrium systems. Starting with simple systems with one or few degrees of freedom, such as random walk and random acceleration problems, we progressively discuss the persistence properties in systems with many degrees of freedom. These systems include spins models undergoing phase ordering dynamics, diffusion equation, fluctuating interfaces etc. Persistence properties are nontrivial in these systems as the effective underlying stochastic process is non-Markovian. Several exact and approximate methods have been developed to compute the persistence of such non-Markov processes over the last two decades, as reviewed in this article. We also discuss various generalisations of the local site persistence probability. Persistence in systems with quenched disorder is discussed briefly. Although the main emphasis of this review is on the theoretical developments on persistence, we briefly touch upon various experimental systems as well.

• 1 : School of Physics and Astronomy
University of Manchester
• 2 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
CNRS : UMR8626 – Université Paris XI - Paris Sud

• ## Phase Diagram and Approximate Message Passing for Blind Calibration and Dictionary Learning

### Florent Krzakala 1 Marc Mézard 2 Lenka Zdeborová 3

#### IEExplore, 2013, Information Theory Proceedings (ISIT), 2013 IEEE International Symposium, pp.659 - 663 <10.1109/ISIT.2013.6620308 >

We consider dictionary learning and blind calibration for signals and matrices created from a random ensemble. We study the mean-squared error in the limit of large signal dimension using the replica method and unveil the appearance of phase transitions delimiting impossible, possible-but-hard and possible inference regions. We also introduce an approximate message passing algorithm that asymptotically matches the theoretical performance, and show through numerical tests that it performs very well, for the calibration problem, for tractable system sizes.

• 1. LPCT - Laboratoire de Physico-Chimie Théorique
• 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
• 3. IPHT - Institut de Physique Théorique - UMR CNRS 3681

• ## Planar diagrams from optimization for concave potentials

### S. K. Nechaev 1, 2, A. N. Sobolevski 3, 4, O. V. Valba 1, 5

#### Physical Review E87 (2013) 012102

We propose a new toy model of a heteropolymer chain capable of forming planar secondary structures typical for RNA molecules. In this model the sequential intervals between neighboring monomers along a chain are considered as quenched random variables. Using the optimization procedure for a special class of concave--type potentials, borrowed from optimal transport analysis, we derive the local difference equation for the ground state free energy of the chain with the planar (RNA--like) architecture of paired links. We consider various distribution functions of intervals between neighboring monomers (truncated Gaussian and scale--free) and demonstrate the existence of a topological crossover from sequential to essentially embedded (nested) configurations of paired links.

• 1 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2 : P. N. Lebedev Physical Institute
• 3 : Higher School of Economics
National Research University
• 4 : Kharkevich Institute for Information Transmission Problems
• 5 : Moscow Institute of Physics and Technology (MIPT)
Moscow Institute of Physics and Technology

• ## Polarization hydrodynamics in a one-dimensional polariton condensate

### P. -É Larré 1 N. Pavloff 1 A. M. Kamchatnov 2

#### Physical Review B (Condensed Matter), American Physical Society, 2013, 88, pp.224503

We study the hydrodynamics of a nonresonantly-pumped polariton condensate in a quasi-one-dimensional quantum wire taking into account the spin degree of freedom. We clarify the relevance of the Landau criterion for superfluidity in this dissipative two-component system. Two Cherenkov-like critical velocities are identified corresponding to the opening of different channels of radiation: one of (damped) density fluctuations and another of (weakly damped) polarization fluctuations. We determine the drag force exerted onto an external obstacle and propose experimentally measurable consequences of the specific features of the fluctuations of polarization.

• 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
• 2. Institute of Spectroscopy

• ## Quasi-equilibrium in glassy dynamics: an algebraic view

### Silvio Franz 1, Giorgio Parisi 2

#### Journal of Statistical Mechanics (2013) P02003

We study a chain of identical glassy systems in a constrained equilibrium where each bond of the chain is forced to remain at a preassigned distance to the previous one. We apply this description to Mean Field Glassy systems in the limit of long chain where each bond is close to the previous one. We show that in specific conditions this pseudo-dynamic process can formally describe real relaxational dynamics the long time. In particular, in mean field spin glass models we can recover in this way the equations of Langevin dynamics in the long time limit at the dynamical transition temperature and below. We interpret the formal identity as an evidence that in these situations the configuration space is explored in a quasi-equilibrium fashion. Our general formalism, that relates dynamics to equilibrium puts slow dynamics in a new perspective and opens the way to the computation of new dynamical quantities in glassy systems.

• 1 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2 : Dipartimento di Fisica and INFM
Università degli studi di Roma I - La Sapienza

• ## Quasistationarity in a long-range interacting model of particles moving on a sphere

### Shamik Gupta 1, David Mukamel 2

#### Physical Review E88 (2013) 052137

We consider a long-range interacting system of $N$ particles moving on a spherical surface under an attractive Heisenberg-like interaction of infinite range, and evolving under deterministic Hamilton dynamics. The system may also be viewed as one of globally coupled Heisenberg spins. In equilibrium, the system has a continuous phase transition from a low-energy magnetized phase, in which the particles are clustered on the spherical surface, to a high-energy homogeneous phase. The dynamical behavior of the model is studied analytically by analyzing the Vlasov equation for the evolution of the single-particle distribution, and numerically by direct simulations. The model is found to exhibit long lived non-magnetized quasistationary states (QSSs) which in the thermodynamic limit are dynamically stable within an energy range where the equilibrium state is magnetized. For finite $N$, these states relax to equilibrium over a time that increases algebraically with $N$. In the dynamically unstable regime, non-magnetized states relax fast to equilibrium over a time that scales as $\log N$. These features are retained in presence of a global anisotropy in the magnetization.

• 1 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2 : Weizmann Institute
Weizmann Institut

• ## Random Aharonov-Bohm vortices and some exact families of integrals: Part III

### Stephane Ouvry 1

#### Journal of Statistical Mechanics: Theory and Experiment, Institute of Physics: Hybrid Open Access, 2013, pp.P02002

As a sequel to [1] and [2], I present some recent progress on Bessel integrals $\int_0^{\infty}{\rmd u}\; uK_0(u)^{n}$, $\int_0^{\infty}{\rmd u}\; u^{3}K_0(u)^{n}$, ... where the power of the integration variable is odd and where $n$, the Bessel weight, is a positive integer. Some of these integrals for weights n=3 and n=4 are known to be intimately related to the zeta numbers zeta(2) and zeta(3). Starting from a Feynman diagram inspired representation in terms of n dimensional multiple integrals on an infinite domain, one shows how to partially integrate to n-2 dimensional multiple integrals on a finite domain. In this process the Bessel integrals are shown to be periods. Interestingly enough, these "reduced" multiple integrals can be considered in parallel with some simple integral representations of zeta numbers. One also generalizes the construction of [2] on a particular sum of double nested Bessel integrals to a whole family of double nested integrals. Finally a strong PSLQ numerical evidence is shown to support a surprisingly simple expression of zeta(5) as a linear combination with rational coefficients of Bessel integrals of weight n= 8.

• 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

• ## Record-breaking statistics for random walks in the presence of measurement error and noise

### Yaniv Edery 1, Alexander B. Kostinski 2, Satya N. Majumdar 3, Brian Berkowitz 1

#### Physical Review Letters110 (2013) 180602

We address the question of distance record-setting by a random walker in the presence of measurement error, $\delta$, and additive noise, $\gamma$ and show that the mean number of (upper) records up to $n$ steps still grows universally as $< R_n> \sim n^{1/2}$ for large $n$ for all jump distributions, including Lévy flights, and for all $\delta$ and $\gamma$. In contrast to the universal growth exponent of 1/2, the pace of record setting, measured by the pre-factor of $n^{1/2}$, depends on $\delta$ and $\gamma$. In the absence of noise ($\gamma=0$), the pre-factor $S(\delta)$ is evaluated explicitly for arbitrary jump distributions and it decreases monotonically with increasing $\delta$ whereas, in case of perfect measurement $(\delta=0)$, the corresponding pre-factor $T(\gamma)$ increases with $\gamma$. Our analytical results are supported by extensive numerical simulations and qualitatively similar results are found in two and three dimensions.

• 1 : Department of Environmental Sciences and Energy Research
Weizmann Institute of Science,
• 2 : Department of Physics
Michigan Technological University
• 3 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
CNRS : UMR8626 – Université Paris XI - Paris Sud

• ## Relaxation dynamics of the Kuramoto model with uniformly distributed natural frequencies

### Anandamohan Ghosh 1, Shamik Gupta 2

#### Physica A: Statistical Mechanics and its Applications392 (2013) 3812-3818

The Kuramoto model describes a system of globally coupled phase-only oscillators with distributed natural frequencies. The model in the steady state exhibits a phase transition as a function of the coupling strength, between a low-coupling incoherent phase in which the oscillators oscillate independently and a high-coupling synchronized phase. Here, we consider a uniform distribution for the natural frequencies, for which the phase transition is known to be of first order. We study how the system close to the phase transition in the supercritical regime relaxes in time to the steady state while starting from an initial incoherent state. In this case, numerical simulations of finite systems have demonstrated that the relaxation occurs as a step-like jump in the order parameter from the initial to the final steady state value, hinting at the existence of metastable states. We provide numerical evidence to suggest that the observed metastability is a finite-size effect, becoming an increasingly rare event with increasing system size.

• 1 : Indian Institute of Science Education and Research
Indian Institute of Science Education and Research
• 2 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
CNRS : UMR8626 – Université Paris XI - Paris Sud

• ## Reunion probability of N vicious walkers: typical and large fluctuations for large N

### Gregory Schehr 1, Satya N. Majumdar 1, Alain Comtet 1, 2, Peter J. Forrester 3

#### Journal of Statistical Physics150 (2013) 491-530

We consider three different models of N non-intersecting Brownian motions on a line segment [0,L] with absorbing (model A), periodic (model B) and reflecting (model C) boundary conditions. In these three cases we study a properly normalized reunion probability, which, in model A, can also be interpreted as the maximal height of N non-intersecting Brownian excursions on the unit time interval. We provide a detailed derivation of the exact formula for these reunion probabilities for finite N using a Fermionic path integral technique. We then analyse the asymptotic behavior of this reunion probability for large N using two complementary techniques: (i) a saddle point analysis of the underlying Coulomb gas and (ii) orthogonal polynomial method. These two methods are complementary in the sense that they work in two different regimes, respectively for L\ll O(\sqrt{N}) and L\geq O(\sqrt{N}). A striking feature of the large N limit of the reunion probability in the three models is that it exhibits a third-order phase transition when the system size L crosses a critical value L=L_c(N)\sim \sqrt{N}. This transition is akin to the Douglas-Kazakov transition in two-dimensional continuum Yang-Mills theory. While the central part of the reunion probability, for L \sim L_c(N), is described in terms of the Tracy-Widom distributions (associated to GOE and GUE depending on the model), the emphasis of the present study is on the large deviations of these reunion probabilities, both in the right [L \gg L_c(N)] and the left [L \ll L_c(N)] tails. In particular, for model B, we find that the matching between the different regimes corresponding to typical L \sim L_c(N) and atypical fluctuations in the right tail L \gg L_c(N) is rather unconventional, compared to the usual behavior found for the distribution of the largest eigenvalue of GUE random matrices.

• 1 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2 : Unite mixte de service de l'institut Henri Poincaré (UMSIHP)
CNRS : UMS839 – Université Pierre et Marie Curie (UPMC) - Paris VI
• 3 : Department of Mathematics and Statistics [Melbourne]
University of Melbourne

• ## Sampling fractional Brownian motion in presence of absorption: a Markov chain method

### Alexander K. Hartmann 1, Satya N. Majumdar 2, Alberto Rosso 2

#### Physical Review E88 (2013) 022119

We study fractional Brownian motion (fBm) characterized by the Hurst exponent H. Using a Monte Carlo sampling technique, we are able to numerically generate fBm processes with an absorbing boundary at the origin at discrete times for a large number of 10^7 time steps even for small values like H=1/4. The results are compatible with previous analytical results that the distribution of (rescaled) endpoints y follow a power law P(y) y^\phi with \phi=(1-H)/H, even for small values of H. Furthermore, for the case H=0.5 we also study analytically the finite-length corrections to the first order, namely a plateau of P(y) for y->0 which decreases with increasing process length. These corrections are compatible with the numerical results.

• 1 : Institute of Physics
University of Oldenburg
• 2 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
CNRS : UMR8626 – Université Paris XI - Paris Sud

• ## Spatial extent of an outbreak in animal epidemics

### Eric Dumonteil 1, Satya N. Majumdar 2, Alberto Rosso 2, Andrea Zoia 1

#### Proceedings of the National Academy of Sciences110 (2013) 4239-4244

Characterizing the spatial extent of epidemics at the outbreak stage is key to controlling the evolution of the disease. At the outbreak, the number of infected individuals is typically small, so that fluctuations around their average are important: then, it is commonly assumed that the susceptible-infected-recovered (SIR) mechanism can be described by a stochastic birth-death process of Galton-Watson type. The displacements of the infected individuals can be modelled by resorting to Brownian motion, which is applicable when long-range movements and complex network interactions can be safely neglected, as in case of animal epidemics. In this context, the spatial extent of an epidemic can be assessed by computing the convex hull enclosing the infected individuals at a given time. We derive the exact evolution equations for the mean perimeter and the mean area of the convex hull, and compare them with Monte Carlo simulations.

• 1 : CEA/Saclay
CEA
• 2 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
CNRS : UMR8626 – Université Paris XI - Paris Sud

• ## Spin clusters and conformal field theory

### Gesualdo Delfino 1 Marco Picco 2 Raoul Santachiara 3 Jacopo Viti 4

#### Journal of Statistical Mechanics: Theory and Experiment, IOP Science, 2013, pp.P11011. <10.1088/1742-5468/2013/11/P11011>

We study numerically the fractal dimensions and the bulk three-point connectivity for the spin clusters of the Q-state Potts model in two dimensions with $1\leq Q\leq 4$. We check that the usually invoked correspondence between FK clusters and spin clusters works at the level of fractal dimensions. However, the fine structure of the conformal field theories describing critical clusters first manifests at the level of the three-point connectivities. Contrary to what recently found for FK clusters, no obvious relation emerges for generic Q between the spin cluster connectivity and the structure constants obtained from analytic continuation of the minimal model ones. The numerical results strongly suggest then that spin and FK clusters are described by conformal field theories with different realizations of the color symmetry of the Potts model.

• 1. SISSA / ISAS - Scuola Internazionale Superiore di Studi Avanzati / International School for Advanced Studies
• 2. LPTHE - Laboratoire de Physique Théorique et Hautes Energies
• 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
• 4. LPTENS - Laboratoire de Physique Théorique de l'ENS

• ## Static replica approach to critical correlations in glassy systems

### Silvio Franz 1, Hugo Jacquin 2, Giorgio Parisi 3, Pierfrancesco Urbani 1, Francesco Zamponi 4

#### Journal of Chemical Physics138 (2013) 12A540

We discuss the slow relaxation phenomenon in glassy systems by means of replicas by constructing a static field theory approach to the problem. At the mean field level we study how criticality in the four point correlation functions arises because of the presence of soft modes and we derive an effective replica field theory for these critical fluctuations. By using this at the Gaussian level we obtain many physical quantities: the correlation length, the exponent parameter that controls the Mode-Coupling dynamical exponents for the two-point correlation functions, and the prefactor of the critical part of the four point correlation functions. Moreover we perform a one-loop computation in order to identify the region in which the mean field Gaussian approximation is valid. The result is a Ginzburg criterion for the glass transition. We define and compute in this way a proper Ginzburg number. Finally, we present numerical values of all these quantities obtained from the Hypernetted Chain approximation for the replicated liquid theory.

• 1 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2 : Matière et Systèmes Complexes (MSC)
CNRS : UMR7057 – Université Paris VII - Paris Diderot
• 3 : Dipartimento di Fisica and INFM
Università degli studi di Roma I - La Sapienza
• 4 : Laboratoire de Physique Théorique de l'ENS (LPTENS)
CNRS : UMR8549 – Université Pierre et Marie Curie (UPMC) - Paris VI – École normale supérieure [ENS] - Paris

• ## Statistical analysis of networks and biophysical systems of complex architecture

### Olga Valba 1

#### Université Paris Sud - Paris XI (15/10/2013), Sergeï Nechaev (Dir.)

Complex organization is found in many biological systems. For example, biopolymers could possess very hierarchic structure, which provides their functional peculiarity. Understating such, complex organization allows describing biological phenomena and predicting molecule functions. Besides, we can try to characterize the specific phenomenon by some probabilistic quantities (variances, means, etc), assuming the primary biopolymer structure to be randomly formed according to some statistical distribution. Such a formulation is oriented toward evolutionary problems.Artificially constructed biological network is another common object of statistical physics with rich functional properties. A behavior of cells is a consequence of complex interactions between its numerous components, such as DNA, RNA, proteins and small molecules. Cells use signaling pathways and regulatory mechanisms to coordinate multiple processes, allowing them to respond and to adapt to changing environment. Recent theoretical advances allow us to describe cellular network structure using graph concepts to reveal the principal organizational features shared with numerous non-biological networks.The aim of this thesis is to develop bunch of methods for studying statistical and dynamic objects of complex architecture and, in particular, scale-free structures, which have no characteristic spatial and/or time scale. For such systems, the use of standard mathematical methods, relying on the average behavior of the whole system, is often incorrect or useless, while a detailed many-body description is almost hopeless because of the combinatorial complexity of the problem. Here we focus on two problems.The first part addresses to statistical analysis of random biopolymers. Apart from the evolutionary context, our studies cover more general problems of planar topology appeared in description of various systems, ranging from gauge theory to biophysics. We investigate analytically and numerically a phase transition of a generic planar matching problem, from the regime, where almost all the vertices are paired, to the situation, where a finite fraction of them remains unmatched.The second part of this work focus on statistical properties of networks. We demonstrate the possibility to define co-expression gene clusters within a network context from their specific motif distribution signatures. We also show how a method based on the shortest path function (SPF) can be applied to gene interactions sub-networks of co-expression gene clusters, to efficiently predict novel regulatory transcription factors (TFs). The biological significance of this method by applying it on groups of genes with a shared regulatory locus, found by genetic genomics, is presented. Finally, we discuss formation of stable patters of motifs in networks under selective evolution in context of creation of islands of "superfamilies".

• 1 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
CNRS : UMR8626 – Université Paris XI - Paris Sud

• ## Statistics of quantum transport in weakly non-ideal chaotic cavities

### Sergio Rodriguez-Perez 1, Ricardo Marino 2, Marcel Novaes 1, Pierpaolo Vivo 2

#### Physical Review E88 (2013) 052912

We consider statistics of electronic transport in chaotic cavities where time-reversal symmetry is broken and one of the leads is weakly non-ideal, i.e. it contains tunnel barriers characterized by tunneling probabilities $\Gamma_i$. Using symmetric function expansions and a generalized Selberg integral, we develop a systematic perturbation theory in $1-\Gamma_i$ valid for arbitrary number of channels, and obtain explicit formulas up to second order for the average and variance of the conductance, and for the average shot-noise. Higher moments of the conductance are considered to leading order.

• 1 : Departamento de fisica
Universidade Federal de Sao Carlos - UFSCar (BRAZIL)
• 2 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
CNRS : UMR8626 – Université Paris XI - Paris Sud

• ## The Lyapunov exponent of products of random $2\times2$ matrices close to the identity

### A. Comtet 1, 2, J. M. Luck 3, C. Texier 1, 4, Y. Tourigny 5

#### Journal of Statistical Physics150 (2013) 13-65

We study products of arbitrary random real $2 \times 2$ matrices that are close to the identity matrix. Using the Iwasawa decomposition of $\text{SL}(2,{\mathbb R})$, we identify a continuum regime where the mean values and the covariances of the three Iwasawa parameters are simultaneously small. In this regime, the Lyapunov exponent of the product is shown to assume a scaling form. In the general case, the corresponding scaling function is expressed in terms of Gauss' hypergeometric function. A number of particular cases are also considered, where the scaling function of the Lyapunov exponent involves other special functions (Airy, Bessel, Whittaker, elliptic). The general solution thus obtained allows us, among other things, to recover in a unified framework many results known previously from exactly solvable models of one-dimensional disordered systems.

• 1 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2 : Unite mixte de service de l'institut Henri Poincaré (UMSIHP)
CNRS : UMS839 – Université Pierre et Marie Curie (UPMC) - Paris VI
• 3 : Institut de Physique Théorique (ex SPhT) (IPHT)
CNRS : URA2306 – CEA : DSM/IPHT
• 4 : Laboratoire de Physique des Solides (LPS)
CNRS : UMR8502 – Université Paris XI - Paris Sud
• 5 : Department of Mathematics [Bristol]
University of Bristol – University Walk

• ## Thick Filament Length and Isoform Composition Determine Self-Organized Contractile Units in Actomyosin Bundles

### Todd Thoresen 1 Martin Lenz 2, 1, 3 Margaret Gardel 1, 3

#### Biophysical Journal, Biophysical Society, 2013, 104, pp.655-665. <10.1016/j.bpj.2012.12.042>

Diverse myosin II isoforms regulate contractility of actomyosin bundles in disparate physiological processes by variations in both motor mechanochemistry and the extent to which motors are clustered into thick filaments. Although the role of mechanochemistry is well appreciated, the extent to which thick filament length regulates actomyosin contractility is unknown. Here, we study the contractility of minimal actomyosin bundles formed in vitro by mixtures of F-actin and thick filaments of nonmuscle, smooth, and skeletal muscle myosin isoforms with varied length. Diverse myosin II isoforms guide the self-organization of distinct contractile units within in vitro bundles with shortening rates similar to those of in vivo myofibrils and stress fibers. The tendency to form contractile units increases with the thick filament length, resulting in a bundle shortening rate proportional to the length of constituent myosin thick filament. We develop a model that describes our data, providing a framework in which to understand how diverse myosin II isoforms regulate the contractile behaviors of disordered actomyosin bundles found in muscle and nonmuscle cells. These experiments provide insight into physiological processes that use dynamic regulation of thick filament length, such as smooth muscle contraction.

• 1. The James Franck Institute, Institute Biophysical Dynamics
• 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
• 3. Department of Physics - Department of Physics
• ## Tradeoffs for number-squeezing in collisions of Bose-Einstein condensates

### P. Deuar 1, T. Wasak 2, P. Zin 3, 4, J. Chwedenczuk 2, M. Trippenbach 2, 3

#### Physical Review A88 (2013) 013617

We investigate the factors that influence the usefulness of supersonic collisions of Bose-Einstein condensates as a potential source of entangled atomic pairs by analyzing the reduction of the number difference fluctuations between regions of opposite momenta. We show that non-monochromaticity of the mother clouds is typically the leading limitation on number squeezing, and that the squeezing becomes less robust to this effect as the density of pairs grows. We develop a simple model that explains the relationship between density correlations and the number squeezing, allows one to estimate the squeezing from properties of the correlation peaks, and shows how the multi-mode nature of the scattering must be taken into account to understand the behavior of the pairing. We analyze the impact of the Bose enhancement on the number squeezing, by introducing a simplified low-gain model. We conclude that as far as squeezing is concerned the preferable configuration occurs when atoms are scattered not uniformly but rather into two well separated regions.

• 1 : Institut of Physics
• 2 : Institute of Theoretical Physics
Warsaw University
• 3 : Andrzej Soltan Institute for Nuclear Studies
Warsaw University
• 4 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
CNRS : UMR8626 – Université Paris XI - Paris Sud

• ## Transition between Hermitian and non-Hermitian Gaussian ensembles

### O. Bohigas 1 and M. P. Pato 2

#### J. Phys. A: Math. Theor. 46 (2013) 115001 (11pp)

The transition between Hermitian and non-Hermitian matrices of the Gaussian unitary ensemble is revisited. An expression for the kernel of the rescaled Hermite polynomials is derived which expresses the sum in terms of the highest order polynomials. From this Christoffel–Darboux-like formula some results are derived including an extension to the complex plane of the Airy kernel.

• 1 CNRS, Universite Paris-Sud, UMR8626, LPTMS, Orsay Cedex, F-91405, France
• 2 Instıtuto de F ́ısica, Universidade de Sao Paulo, Caixa Postal 66318, 05314-970 Sao Paulo, S.P., Brazil

• ## Two-dimensional dipolar Bose gas with the roton-maxon excitation spectrum

### Abdelâali Boudjemaâ 1, G. V. Shlyapnikov 2

#### Physical Review A87 (2013) 025601

We discuss fluctuations in a dilute two-dimensional Bose-condensed dipolar gas, which has a roton-maxon character of the excitation spectrum. We calculate the density-density correlation function, fluctuation corrections to the chemical potential, compressibility, and the normal (superfluid) fraction. It is shown that the presence of the roton strongly enhances fluctuations of the density, and we establish the validity criterion of the Bogoliubov approach. At T=0 the condensate depletion becomes significant if the roton minimum is sufficiently close to zero. At finite temperatures exceeding the roton energy, the effect of thermal fluctuations is stronger and it may lead to a large normal fraction of the gas and compressibility.

• 1 : Department of Physics
Hassiba Benbouali University of Chlef
• 2 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
CNRS : UMR8626 – Université Paris XI - Paris Sud

• ## Two-point correlation function for Dirichlet L-functions

### E Bogomolny 1,2 and J P Keating 3

#### J. Phys. A: Math. Theor. 46 (2013) 095202 (10pp)

The two-point correlation function for the zeros of Dirichlet L-functions at a height E on the critical line is calculated heuristically using a generalization of the Hardy–Littlewood conjecture for pairs of primes in arithmetic progression. The result matches the conjectured random-matrix form in the limit as E → ∞ and, importantly, includes finite-E corrections. These finite-E corrections differ from those in the case of the Riemann zeta-function, obtained in Bogomolny and Keating (1996 Phys. Rev. Lett. 77 1472), by certain finite products of primes which divide the modulus of the primitive character used to construct the L-function in question.
PACS numbers: 02.10.De, 03.65.Sq, 02.10.Yn

• 1. Laboratoire de Physique Th ́eorique et Mod`eles Statistiques, Universite Paris-Sud, Orsay, F-91405, France
• 2 CNRS, UMR8626, Orsay, F-91405, France
• 3 School of Mathematics, University of Bristol, Bristol BS8 1TW, UK

• ## Uniqueness of the thermodynamic limit for driven disordered elastic interfaces

### A Kolton 1 S Bustingorry 1 E E Ferrero 1 A Rosso 2

#### Journal of Statistical Mechanics: Theory and Experiment, IOP Science, 2013, 2013 (12), <10.1088/1742-5468/2013/12/P12004>

• 1. CONICET Centro Atomico Bariloche
• 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

• ## Universality Classes of Critical Points in Constrained Glasses

### Silvio Franz 1, Giorgio Parisi 2

#### Journal of Statistical Mechanics (2013) P11012

We analyze critical points that can be induced in glassy systems by the presence of constraints. These critical points are predicted by the Mean Field Thermodynamic approach and they are precursors of the standard glass transition in absence of constraints. Through a deep analysis of the soft modes appearing in the replica field theory we can establish the universality class of these points. In the case of the "annealed potential" of a symmetric coupling between two copies of the system, the critical point is in the Ising universality class. More interestingly, is the case of the "quenched potential" where the a single copy is coupled with an equilibrium reference configuration, or the "pinned particle" case where a fraction of particles is frozen in fixed positions. In these cases we find the Random Field Ising Model (RFIM) universality class. The effective random field is a "self-generated" disorder that reflects the random choice of the reference configuration. The RFIM representation of the critical theory predicts non-trivial relations governing the leading singular behavior of relevant correlation functions, that can be tested in numerical simulations.

• 1 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2 : Dipartimento di Fisica and INFM
Università degli studi di Roma I - La Sapienza

• ## Wigner time-delay distribution in chaotic cavities and freezing transition

### Christophe Texier 1, 2, Satya N. Majumdar 1

#### Physical Review Letters110 (2013) 250602

Using the joint distribution for proper time-delays of a chaotic cavity derived by Brouwer, Frahm & Beenakker [Phys. Rev. Lett. {\bf 78}, 4737 (1997)], we obtain, in the limit of large number of channels $N$, the large deviation function for the distribution of the Wigner time-delay (the sum of proper times) by a Coulomb gas method. We show that the existence of a power law tail originates from narrow resonance contributions, related to a (second order) freezing transition in the Coulomb gas.

• 1 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2 : Laboratoire de Physique des Solides (LPS)
CNRS : UMR8502 – Université Paris XI - Paris Sud

• ## Zero sound in a two-dimensional dipolar Fermi gas

### Zhen-Kai Lu 1, S. I. Matveenko 2, 3, G. V. Shlyapnikov 2, 4, 5

#### Physical Review A88 (2013) 033625

We study zero sound in a weakly interacting 2D gas of single-component fermionic dipoles (polar molecules or atoms with a large magnetic moment) tilted with respect to the plane of their translational motion. It is shown that the propagation of zero sound is provided by both mean field and many-body (beyond mean field) effects, and the anisotropy of the sound velocity is the same as the one of the Fermi velocity. The damping of zero sound modes can be much slower than that of quasiparticle excitations of the same energy. One thus has wide possibilities for the observation of zero sound modes in experiments with 2D fermionic dipoles, although the zero sound peak in the structure function is very close to the particle-hole continuum.

• 1 : Max-Planck-Institut für Quantenoptik
Max-Planck-Institut für Quantenoptik
• 2 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
CNRS : UMR8626 – Université Paris XI - Paris Sud
• 3 : L. D. Landau Institute for Theoretical Physics
L. D. Landau Institute for Theoretical Physics
• 4 : Van der Waals-Zeeman Institute
University of Amsterdam
• 5 : Kavli Institute for Theoretical Physics
University of California, Santa Barbara

• ## A one-year comprehensive chemical characterisation of fine aerosol (PM<sub>2.5</sub>) at urban, suburban and rural background sites in the region of Paris (France) – Archive ouverte HAL

### M. Bressi 1, 2 J. Sciare 1 V. GhersiN. Bonnaire 1 J. B. Nicolas 1, 2 J.-E. Petit 1 S. Moukhtar 3 A. Rosso 4 N. Mihalopoulos 5 A. Féron 1

#### M. Bressi, J. Sciare, V. Ghersi, N. Bonnaire, J. B. Nicolas, et al.. A one-year comprehensive chemical characterisation of fine aerosol (PM<sub>2.5</sub>) at urban, suburban and rural background sites in the region of Paris (France). Atmospheric Chemistry and Physics, European Geosciences Union, 2013, 13 (15), pp.7825-7844. ⟨10.5194/acp-13-7825-2013⟩. ⟨hal-02923974⟩

Studies describing the chemical composition of fine aerosol (PM2.5) in urban areas are often conducted for a few weeks only and at one sole site, giving thus a narrow view of their temporal and spatial characteristics. This paper presents a one-year (11 September 2009–10 September 2010) survey of the daily chemical composition of PM2.5 in the region of Paris, which is the second most populated "Larger Urban Zone" in Europe. Five sampling sites representative of suburban (SUB), urban (URB), northeast (NER), northwest (NWR) and south (SOR) rural backgrounds were implemented. The major chemical components of PM2.5 were determined including elemental carbon (EC), organic carbon (OC), and the major ions. OC was converted to organic matter (OM) using the chemical mass closure methodology, which leads to conversion factors of 1.95 for the SUB and URB sites, and 2.05 for the three rural ones. On average, gravimetrically determined PM2.5 annual mass concentrations are 15.2, 14.8, 12.6, 11.7 and 10.8 μg m−3 for SUB, URB, NER, NWR and SOR sites, respectively. The chemical composition of fine aerosol is very homogeneous at the five sites and is composed of OM (38–47%), nitrate (17–22%), non-sea-salt sulfate (13–16%), ammonium (10–12%), EC (4–10%), mineral dust (2–5%) and sea salt (3–4%). This chemical composition is in agreement with those reported in the literature for most European environments. On an annual scale, Paris (URB and SUB sites) exhibits its highest PM2.5 concentrations during late autumn, winter and early spring (higher than 15 μg m−3 on average, from December to April), intermediates during late spring and early autumn (between 10 and 15 μg m−3 during May, June, September, October, and November) and the lowest during summer (below 10 μg m−3 during July and August). PM levels are mostly homogeneous on a regional scale, during the whole project (e.g. for URB plotted against NER sites: slope = 1.06, r2=0.84, n=330), suggesting the importance of mid- or long-range transport, and regional instead of local scale phenomena. During this one-year project, two thirds of the days exceeding the PM2.5 2015 EU annual limit value of 25 μg m−3 were due to continental import from countries located northeast, east of France. This result questions the efficiency of local, regional and even national abatement strategies during pollution episodes, pointing to the need for a wider collaborative work with the neighbouring countries on these topics. Nevertheless, emissions of local anthropogenic sources lead to higher levels at the URB and SUB sites compared to the others (e.g. 26% higher on average at the URB than at the NWR site for PM2.5, during the whole campaign), which can even be emphasised by specific meteorological conditions such as low boundary layer heights. OM and secondary inorganic species (nitrate, non-sea-salt sulfate and ammonium, noted SIA) are mainly imported by mid- or long-range transport (e.g. for NWR plotted against URB sites: slope = 0.79, r2=0.72, n=335 for OM, and slope = 0.91, r2=0.89, n=335 for SIA) whereas EC is primarily locally emitted (e.g. for SOR plotted against URB sites: slope = 0.27; r2=0.03; n=335). This database will serve as a basis for investigating carbonaceous aerosols, metals as well as the main sources and geographical origins of PM in the region of Paris.

• 1. LSCE - Laboratoire des Sciences du Climat et de l'Environnement [Gif-sur-Yvette]
• 2. ADEME - Agence de l'Environnement et de la Maîtrise de l'Energie
• 3. Centre for Atmospheric Chemistry [Toronto]
• 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
• 5. ECPL - Environmental Chemical Processes Laboratory [Heraklion]
• ## Archive ouverte HAL – Optimal diffusive search: nonequilibrium resetting versus equilibrium dynamics

### Martin R. Evans 1 Satya N. Majumdar 2 Kirone Mallick 3

#### Martin R. Evans, Satya N. Majumdar, Kirone Mallick. Optimal diffusive search: nonequilibrium resetting versus equilibrium dynamics. Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 2013, 46, pp.185001. ⟨10.1088/1751-8113/46/18/185001⟩. ⟨hal-00825684⟩

We study first-passage time problems for a diffusive particle with stochastic resetting with a finite rate $r$. The optimal search time is compared quantitatively with that of an effective equilibrium Langevin process with the same stationary distribution. It is shown that the intermittent, nonequilibrium strategy with non-vanishing resetting rate is more efficient than the equilibrium dynamics. Our results are extended to multiparticle systems where a team of independent searchers, initially uniformly distributed with a given density, looks for a single immobile target. Both the average and the typical survival probability of the target are smaller in the case of nonequilibrium dynamics.

• 1. SUPA School of Physics and Astronomy [Edinburgh]
• 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
• 3. IPHT - Institut de Physique Théorique - UMR CNRS 3681

• ## Optimal diffusive search: nonequilibrium resetting versus equilibrium dynamics – Archive ouverte HAL

### Martin R. Evans 1 Satya N. Majumdar 2 Kirone Mallick 3

#### Martin R. Evans, Satya N. Majumdar, Kirone Mallick. Optimal diffusive search: nonequilibrium resetting versus equilibrium dynamics. Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 2013, 46, pp.185001. ⟨10.1088/1751-8113/46/18/185001⟩. ⟨hal-00825684⟩

We study first-passage time problems for a diffusive particle with stochastic resetting with a finite rate $r$. The optimal search time is compared quantitatively with that of an effective equilibrium Langevin process with the same stationary distribution. It is shown that the intermittent, nonequilibrium strategy with non-vanishing resetting rate is more efficient than the equilibrium dynamics. Our results are extended to multiparticle systems where a team of independent searchers, initially uniformly distributed with a given density, looks for a single immobile target. Both the average and the typical survival probability of the target are smaller in the case of nonequilibrium dynamics.

• 1. SUPA School of Physics and Astronomy [Edinburgh]
• 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
• 3. IPHT - Institut de Physique Théorique - UMR CNRS 3681

• ## Archive ouverte HAL – On the origin of the halo stabilization

### Martin Trulsson 1 Bo Jönsson 2 Christophe Labbez 3

#### Martin Trulsson, Bo Jönsson, Christophe Labbez. On the origin of the halo stabilization. Physical Chemistry Chemical Physics, Royal Society of Chemistry, 2013, 15 (2), pp.541-545. ⟨10.1039/c2cp42404e⟩. ⟨hal-02376063⟩

• 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
• 2. THEORETICAL CHEMISTRY - Theoretical Chemistry
• 3. LICB - Laboratoire Interdisciplinaire Carnot de Bourgogne
• ## Archive ouverte HAL – A one-year comprehensive chemical characterisation of fine aerosol (PM<sub>2.5</sub>) at urban, suburban and rural background sites in the region of Paris (France)

### M. Bressi 1 J. Sciare 2 V. GhersiN. Bonnaire 2 J. NicolasJ.-E. Petit 2 S. Moukhtar 3 A. Rosso 4 N. Mihalopoulos 5 A. Féron 6

#### M. Bressi, J. Sciare, V. Ghersi, N. Bonnaire, J. Nicolas, et al.. A one-year comprehensive chemical characterisation of fine aerosol (PM<sub>2.5</sub>) at urban, suburban and rural background sites in the region of Paris (France). Atmospheric Chemistry and Physics, European Geosciences Union, 2013, 13 (15), pp.7825-7844. ⟨10.5194/acp-13-7825-2013⟩. ⟨hal-02923974⟩

• 1. IES - JRC Institute for Environment and Sustainability
• 2. LSCE - Laboratoire des Sciences du Climat et de l'Environnement [Gif-sur-Yvette]
• 3. Centre for Atmospheric Chemistry [Toronto]
• 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
• 5. ECPL - Environmental Chemical Processes Laboratory [Heraklion]
• 6. LISA (UMR_7583) - Laboratoire Interuniversitaire des Systèmes Atmosphériques
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