# LPTMS Publications

Archives :

• ## Anderson localization of elementary excitations in a one dimensional Bose-Einstein condensate

### Nicolas Bilas 1, Nicolas Pavloff 1

#### European Physical Journal D 40 (2006) 387-397

We study the elementary excitations of a transversely confined Bose-Einstein condensate in presence of a weak axial random potential. We determine the localization length (i) in the hydrodynamical low energy regime, for a domain of linear densities ranging from the Tonks-Girardeau to the transverse Thomas-Fermi regime, in the case of a white noise potential and (ii) for all the range of energies, in the one-dimensional mean field regime'', in the case where the randomness is induced by a series of randomly placed point-like impurities. We discuss our results in view of recent experiments in elongated BEC systems.

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

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• ## Application of a two-length scale field theory to the solvation of charged molecules: I. Hydrophobic effect revisited

### G. Sitnikov 1, 2, S. Nechaev 3, M. D. Taran 4, A. Muryshev 2

#### Journal of Chemical Physics 124 (2006) 094501

On a basis of a two-length scale description of hydrophobic interactions we develop a continuous self-consistent theory of solute-water interactions which allows to determine a hydrophobic layer of a solute molecules of any geometry with explicit account of solvent structure described by its correlation function. We compute the mean solvent density profile n(r) surrounding the spherical solute molecule as well as its solvation free energy. We compare the two-length scale theory to the numerical data of Monte-Carlo simulations found in the literature and discuss the possibility of a self-consistent adjustment of the free parameters of the theory. In the frameworks of the discussed approach we compute also the solvation free energies of alkane molecules and the free energy of interaction of two spheres separated by some distance. We describe the general setting of a self-consistent account of electrostatic interactions in the frameworks of the model where the water is considered not as a continuous media, but as a gas of dipoles. We analyze the limiting cases where the proposed theory coincides with the electrostatics of a continuous media.

• 1. Moscow Institute of Physics and Technology (MIPT), Moscow Institute of Physics and Technology
• 2. Algodign LLC, Algodign LLC
• 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 4. State Scientific Center TRINITI, State scientific Center TRINITI

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• ## Artificial square ice and related dipolar nanoarrays

### Gunnar Moller 1, R. Moessner 2

#### Physical Review Letters 96 (2006) 237202

We study a frustrated dipolar array recently manufactured lithographically by Wang {\em et al.} [Nature {\bf 439}, 303 (2006)] in order to realize the square ice model in an artificial structure. We discuss models for thermodynamics and dynamics of this system. We show that an ice regime can be stabilized by small changes in the array geometry; a different magnetic state, kagome ice, can similarly be constructed. At low temperatures, the square ice regime is terminated by a thermodynamic ordering transition, which can be chosen to be ferro- or antiferromagnetic. We show that the arrays do not fully equilibrate experimentally, and identify a likely dynamical bottleneck.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Laboratoire de Physique Théorique de l'ENS (LPTENS), CNRS : UMR8549 – Université Paris VI - Pierre et Marie Curie – Ecole Normale Supérieure de Paris - ENS Paris

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• ## Average ground-state energy of finite Fermi systems

### M. Centelles 1, P. Leboeuf 2, A. G. Monastra 3, J. Roccia 2, P. Schuck 4, X. Vinas 1

#### Physical Review C 74 (2006) 034332

Semiclassical theories like the Thomas-Fermi and Wigner-Kirkwood methods give a good description of the smooth average part of the total energy of a Fermi gas in some external potential when the chemical potential is varied. However, in systems with a fixed number of particles N, these methods overbind the actual average of the quantum energy as N is varied. We describe a theory that accounts for this effect. Numerical illustrations are discussed for fermions trapped in a harmonic oscillator potential and in a hard wall cavity, and for self-consistent calculations of atomic nuclei. In the latter case, the influence of deformations on the average behavior of the energy is also considered.

• 1. Departament d'Estructura i Constituents de la Matèria, Facultat de Fisica, Universitat de Barcelona
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 3. TU Dresden Institut für Theoretische Physik, Institut für Theoretische Physik
• 4. Institut de Physique Nucléaire d'Orsay (IPNO), CNRS : UMR8608 – IN2P3 – Université Paris XI - Paris Sud

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• ## Bosonization, Pairing, and Superconductivity of the Fermionic Tonks-Girardeau Gas

### M. D. Girardeau 1, A. Minguzzi 2, 3

#### Physical Review Letters 96 (2006) 080404

We determine some exact static and time-dependent properties of the fermionic Tonks-Girardeau (FTG) gas, a spin-aligned one-dimensional Fermi gas with infinitely strongly attractive zero-range odd-wave interactions. We show that the two-particle reduced density matrix exhibits maximal off-diagonal long-range order, and on a ring an FTG gas with an even number of atoms has a highly degenerate ground state with quantization of Coriolis rotational flux and high sensitivity to rotation and to external fields and accelerations. For a gas initially under harmonic confinement we show that during an expansion the momentum distribution undergoes a 'dynamical bosonization', approaching that of an ideal Bose gas without violating the Pauli exclusion principle.

• 1. College of Optical Sciences, University of Arizona
• 2. Laboratoire de physique et modélisation des milieux condensés (LPMMC), CNRS : UMR5493 – Université Joseph Fourier - Grenoble I
• 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• ## Canonical Analysis of Condensation in Factorised Steady State

### M. R. Evans 1, Satya N. Majumdar 2, R. K. P. Zia 3

#### Journal of Statistical Physics 123 (2006) 357

We study the phenomenon of real space condensation in the steady state of a class of mass transport models where the steady state factorises. The grand canonical ensemble may be used to derive the criterion for the occurrence of a condensation transition but does not shed light on the nature of the condensate. Here, within the canonical ensemble, we analyse the condensation transition and the structure of the condensate, determining the precise shape and the size of the condensate in the condensed phase. We find two distinct condensate regimes: one where the condensate is gaussian distributed and the particle number fluctuations scale normally as $L^{1/2}$ where $L$ is the system size, and a second regime where the particle number fluctuations become anomalously large and the condensate peak is non-gaussian. Our results are asymptotically exact and can also be interpreted within the framework of sums of random variables. We further analyse two additional cases: one where the condensation transition is somewhat different from the usual second order phase transition and one where there is no true condensation transition but instead a pseudocondensate appears at superextensive densities.

• 1. SUPA, School of Physics, University of Edinburgh
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 3. Department of Physics and Center for Stochastic Processes in Science and Engineering, Virginia Tech

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• ## Casimir interaction between a plate and a cylinder

### T. Emig 1, 2, R. L. Jaffe 3, 4, M. Kardar 4, A. Scardicchio 3, 4

#### Physical Review Letters 96 (2006) 080403

We find the exact Casimir force between a plate and a cylinder, a geometry intermediate between parallel plates, where the force is known exactly, and the plate--sphere, where it is known at large separations. The force has an unexpectedly weak decay \sim L/(H^3 \ln(H/R)) at large plate--cylinder separations H (L and R are the cylinder length and radius), due to transverse magnetic modes. Path integral quantization with a partial wave expansion additionally gives a qualitative difference for the density of states of electric and magnetic modes, and corrections at finite temperatures.

• 1. Institut für Theoretische Physik, Universität zu Köln
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 3. Center for Theoretical Physics and Laboratory for Nuclear Science, Center for Theoretical Physics and Laboratory for Nuclear Science
• 4. Department of Physics Massachusetts Institute of Technology, Massachusetts Institute of Technology

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• ## Classical dimers with aligning interactions on the square lattice

### Fabien Alet 1, 2, Yacine Ikhlef 2, 3, Jesper Lykke Jacobsen 2, 3, Gregoire Misguich 2, Vincent Pasquier 2

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 74 (2006) 041124

We present a detailed study of a model of close-packed dimers on the square lattice with an interaction between nearest-neighbor dimers. The interaction favors parallel alignment of dimers, resulting in a low-temperature crystalline phase. With large-scale Monte Carlo and Transfer Matrix calculations, we show that the crystal melts through a Kosterlitz-Thouless phase transition to give rise to a high-temperature critical phase, with algebraic decays of correlations functions with exponents that vary continuously with the temperature. We give a theoretical interpretation of these results by mapping the model to a Coulomb gas, whose coupling constant and associated exponents are calculated numerically with high precision. Introducing monomers is a marginal perturbation at the Kosterlitz-Thouless transition and gives rise to another critical line. We study this line numerically, showing that it is in the Ashkin-Teller universality class, and terminates in a tricritical point at finite temperature and monomer fugacity. In the course of this work, we also derive analytic results relevant to the non-interacting case of dimer coverings, including a Bethe Ansatz (at the free fermion point) analysis, a detailed discussion of the effective height model and a free field analysis of height fluctuations.

• 1. Laboratoire de Physique Théorique - IRSAMC (LPT), CNRS : UMR5152 – Université Paul Sabatier - Toulouse III
• 2. Service de Physique Théorique (SPhT), CNRS : URA2306 – CEA : DSM/SPHT
• 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• ## Composite fermion theory of rapidly rotating two-dimensional bosons

### N. Regnault 1, C. C. Chang 2, Th. Jolicoeur 1, 3, J. K. Jain 2

#### Journal of Physics B 39 (2006) S89-S99

Ultracold neutral bosons in a rapidly rotating atomic trap have been predicted to exhibit fractional quantum Hall-like states. We describe how the composite fermion theory, used in the description of the fractional quantum Hall effect for electrons, can be applied to interacting bosons. Numerical evidence supporting the formation of composite fermions, each being the bound state of a boson and one flux quantum, is shown for filling fractions of the type nu=p/(p+1), both by spectral analysis and by direct comparison with trial wave functions. The rapidly rotating system of two-dimensional bosons thus constitutes an interesting example of 'statistical transmutation,' with bosons behaving like composite fermions. We also describe the difference between the electronic and the bosonic cases when p approaches infinity. Residual interactions between composite fermions are attractive in this limit, resulting in a paired composite-fermion state described by the Moore-Read wave function.

• 1. Laboratoire Pierre Aigrain (LPA), CNRS : UMR8551 – Université Paris VI - Pierre et Marie Curie – Université Paris VII - Paris Diderot – Ecole Normale Supérieure de Paris - ENS Paris
• 2. Department of Physics, 104 Davey Laboratory, The Pennsylvania State University
• 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• ## Constraint Satisfaction by Survey Propagation

### A. Braunstein 1, M. Mezard 2, M. Weigt 3, R. Zecchina 1

#### Computational Complexity and Statistical Physics 107 (2006) part 2 : 4

Survey Propagation is an algorithm designed for solving typical instances of random constraint satisfiability problems. It has been successfully tested on random 3-SAT and random $G(n,\frac{c}{n})$ graph 3-coloring, in the hard region of the parameter space. Here we provide a generic formalism which applies to a wide class of discrete Constraint Satisfaction Problems.

• 1. ICTP, ICTP
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 3. Institute for Scientific Interchange, Institute for Scientific Interchange

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• ## Correlation-induced inhomogeneity in circular quantum dots

### Amit Ghosal 1, A. D. Guclu 2, C. J. Umrigar 2, Denis Ullmo 1, 3, Harold U. Baranger 1

#### Nature Physics 2 (2006) 336-340

Physical properties of the electron gas'' -- in which conduction electrons interact via Coulomb forces but the ionic potential is neglected -- change dramatically depending on the balance between the strength of the kinetic energy and the Coulomb repulsion. The limiting cases are well understood: For weak interactions (high density), the system behaves as a Fermi liquid, with delocalized electrons. In contrast, in the strongly interacting limit (low density), the electrons localize and become ordered in a Wigner crystal phase. The physics at intermediate densities is phenomenally rich and remains a subject of fundamental research. Here we study the intermediate density electron gas confined to a circular quantum dot. By using accurate quantum Monte Carlo techniques, we show that the correlation induced by increasing interaction strength smoothly causes, first, ring structure and, then, angular modulation, without any signature of a sharp transition or even a cross-over in this density regime.

• 1. Duke Physics, Duke University
• 2. Laboratory of Atomic and Solid State Physics (LASSP), Cornell University
• 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• ## Coulombian Disorder in Periodic Systems

### Edmond Orignac 1, Alberto Rosso 2, R. Chitra 3, T. Giamarchi 4

#### Physical Review B 73 (2006) 035112

We study the effect of unscreened charged impurities on periodic systems. We show that the long wavelength component of the disorder becomes long ranged and dominates static correlation functions. On the other hand, because of the statistical tilt symmetry, dynamical properties such as pinning remain unaffected. As a concrete example, we focus on the effect of Coulombian disorder generated by charged impurities, on 3D charge density waves with non local elasticity. We calculate the x-ray intensity and find that it is identical to the one produced by thermal fluctuations in a disorder-free smectic-A. We discuss the consequences of these results for experiments.

• 1. Laboratoire de Physique Théorique de l'ENS (LPTENS), CNRS : UMR8549 – Université Paris VI - Pierre et Marie Curie – Ecole Normale Supérieure de Paris - ENS Paris
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 3. Laboratoire de Physique Théorique des Liquides (LPTL), CNRS : UMR7600 – Université Paris VI - Pierre et Marie Curie
• 4. Departement de Physique de la Matiere Condensee (DPMC), University of Geneva

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• ## Dimensional reduction on a sphere

### Gunnar Moller 1, Sergey I. Matveenko 2, Stephane Ouvry 1

#### International Journal of Modern Physics B 20 (2006) 3533-3546

The question of the dimensional reduction of two-dimensional (2d) quantum models on a sphere to one-dimensional (1d) models on a circle is adressed. A possible application is to look at a relation between the 2d anyon model and the 1d Calogero-Sutherland model, which would allow for a better understanding of the connection between 2d anyon exchange statistics and Haldane exclusion statistics. The latter is realized microscopically in the 2d LLL anyon model and in the 1d Calogero model. In a harmonic well of strength \omega or on a circle of radius R - both parameters \omega and R have to be viewed as long distance regulators - the Calogero spectrum is discrete. It is well known that by confining the anyon model in a 2d harmonic well and projecting it on a particular basis of the harmonic well eigenstates, one obtains the Calogero-Moser model. It is then natural to consider the anyon model on a sphere of radius R and look for a possible dimensional reduction to the Calogero-Sutherland model on a circle of the same radius. First, the free one-body case is considered, where a mapping from the 2d sphere to the 1d chiral circle is established by projection on a special class of spherical harmonics. Second, the N-body interacting anyon model is considered : it happens that the standard anyon model on the sphere is not adequate for dimensional reduction. One is thus lead to define a new spherical anyon-like model deduced from the Aharonov-Bohm problem on the sphere where each flux line pierces the sphere at one point and exits it at its antipode.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Landau Institute for Theoretical Physics, Landau Institute for Theoretical Physics

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• ## Dynamics below the depinning threshold

### Alejandro B. Kolton 1, Alberto Rosso 2, Thierry Giamarchi 1, Werner Krauth 3

#### Physical Review Letters 97 (2006) 057001

We study the steady-state low-temperature dynamics of an elastic line in a disordered medium below the depinning threshold. Analogously to the equilibrium dynamics, in the limit T->0, the steady state is dominated by a single configuration which is occupied with probability one. We develop an exact algorithm to target this dominant configuration and to analyze its geometrical properties as a function of the driving force. The roughness exponent of the line at large scales is identical to the one at depinning. No length scale diverges in the steady state regime as the depinning threshold is approached from below. We do find, a divergent length, but it is associated only with the transient relaxation between metastable states.

• 1. DPMC-MaNEP, University of Geneva
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 3. Laboratoire de Physique Statistique de l'ENS (LPS), CNRS : UMR8550 – Université Paris VI - Pierre et Marie Curie – Université Paris VII - Paris Diderot – Ecole Normale Supérieure de Paris - ENS Paris

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• ## Dynamics of a tracer granular particle as a non-equilibrium Markov process

### Andrea Puglisi 1, Paolo Visco 1, 2, Emmanuel Trizac 2, Frederic van Wijland 1, 3

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 73 (2006) 021301

The dynamics of a tracer particle in a stationary driven granular gas is investigated. We show how to transform the linear Boltzmann equation describing the dynamics of the tracer into a master equation for a continuous Markov process. The transition rates depend upon the stationary velocity distribution of the gas. When the gas has a Gaussian velocity probability distribution function (pdf), the stationary velocity pdf of the tracer is Gaussian with a lower temperature and satisfies detailed balance for any value of the restitution coefficient $\\alpha$. As soon as the velocity pdf of the gas departs from the Gaussian form, detailed balance is violated. This non-equilibrium state can be characterized in terms of a Lebowitz-Spohn action functional $W(\\tau)$ defined over trajectories of time duration $\\tau$. We discuss the properties of this functional and of a similar functional $\\bar{W}(\\tau)$ which differs from the first for a term which is non-extensive in time. On the one hand we show that in numerical experiments, i.e. at finite times $\\tau$, the two functionals have different fluctuations and $\\bar{W}$ always satisfies an Evans-Searles-like symmetry. On the other hand we cannot observe the verification of the Lebowitz-Spohn-Gallavotti-Cohen (LS-GC) relation, which is expected for $W(\\tau)$ at very large times $\\tau$. We give an argument for the possible failure of the LS-GC relation in this situation. We also suggest practical recipes for measuring $W(\\tau)$ and $\\bar{W}(\\tau)$ in experiments.

• 1. Laboratoire de Physique Théorique d'Orsay (LPT), CNRS : UMR8627 – Université Paris XI - Paris Sud
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 3. Matière et Systèmes Complexes (MSC), CNRS : UMR7057 – Université Paris VII - Paris Diderot

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• ## Energy fluctuations in vibrated and driven granular gases

### P. Visco 1, 2, A. Puglisi 1, A. Barrat 1, F. van Wijland 1, 3, E. Trizac 2

#### European Physical Journal B 51 (2006) 377

We investigate the behavior of energy fluctuations in several models of granular gases maintained in a non-equilibrium steady state. In the case of a gas heated from a boundary, the inhomogeneities of the system play a predominant role. Interpreting the total kinetic energy as a sum of independent but not identically distributed random variables, it is possible to compute the probability density function (pdf) of the total energy. Neglecting correlations and using the analytical expression for the inhomogeneous temperature profile obtained from the granular hydrodynamic equations, we recover results which have been previously observed numerically and which had been attributed to the presence of correlations. In order to separate the effects of spatial inhomogeneities from those ascribable to velocity correlations, we have also considered two models of homogeneously thermostated gases: in this framework it is possible to reveal the presence of non-trivial effects due to velocity correlations between particles. Such correlations stem from the inelasticity of collisions. Moreover, the observation that the pdf of the total energy tends to a Gaussian in the large system limit, suggests that they are also due to the finite size of the system.

• 1. Laboratoire de Physique Théorique d'Orsay (LPT), CNRS : UMR8627 – Université Paris XI - Paris Sud
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 3. Matière et Systèmes Complexes (MSC), CNRS : UMR7057 – Université Paris VII - Paris Diderot

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• ## Exact asymptotic expansions for the cylindrical Poisson-Boltzmann equation

### G. Tellez 1, E. Trizac 2, 3

#### Journal of Statistical Mechanics: Theory and Experiment 1 (2006) P06018

The mathematical theory of integrable Painleve/Toda type systems sheds new light on the behavior of solutions to the Poisson-Boltzmann equation for the potential due to a long rod-like macroion. We investigate here the case of symmetric electrolytes together with that of 1:2 and 2:1 salts. Short and large scale features are analyzed, with a particular emphasis on the low salinity regime. Analytical expansions are derived for several quantities relevant for polyelectrolytes theory, such as the Manning radius. In addition, accurate and practical expressions are worked out for the electrostatic potential, which improve upon previous work and cover the full range of radial distances.

• 1. Departamento de Fisica, Universidad de Los Andes
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 3. Center for Theoretical Biological Physics (CTBP), University of San Diego

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• ## Exact solution of a model of time-dependent evolutionary dynamics in a rugged fitness landscape

### Satya N. Majumdar 2, David S. Dean 1

#### Journal of Statistical Mechanics: Theory and Experiment (2006) L07001

A simplified form of the quasispecies model of biological evolution is solved via a mapping onto a random flux model whose asymptotic behavior can be described in terms of a random walk. The statistics of the number of changes of the dominant species from a finite set of genotypes are exactly obtained confirming existing conjectures based on numerics.

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

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• ## Expansion dynamics of a dipolar Bose-Einstein condensate

### S. Giovanazzi 1, P. Pedri 2, L. M.N.B.F. Santos 3, A. Griesmaier 1, M. Fattori 1, T. Koch 1, J. Stuhler 1, T. Pfau 1

#### Physical Review A: Atomic, Molecular and Optical Physics 74 (2006) 013621

Our recent measurements on the expansion of a chromium dipolar condensate after release from an optical trapping potential are in good agreement with an exact solution of the hydrodynamic equations for dipolar Bose gases. We report here the theoretical method used to interpret the measurement data as well as more details of the experiment and its analysis. The theory reported here is a tool for the investigation of different dynamical situations in time-dependent harmonic traps.

• 1. Physikalisches Institut, Universität Stuttgart
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 3. Institut für Theoretische Physik III, Universität Stuttgart

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• ## Factorised Steady States in Mass Transport Models on an Arbitrary Graph

### M. R. Evans 1, 2, Satya N. Majumdar 3, R. K. P. Zia 4

#### Journal of Physics A 39 (2006) 4859-4873

We study a general mass transport model on an arbitrary graph consisting of $L$ nodes each carrying a continuous mass. The graph also has a set of directed links between pairs of nodes through which a stochastic portion of mass, chosen from a site-dependent distribution, is transported between the nodes at each time step. The dynamics conserves the total mass and the system eventually reaches a steady state. This general model includes as special cases various previously studied models such as the Zero-range process and the Asymmetric random average process. We derive a general condition on the stochastic mass transport rules, valid for arbitrary graph and for both parallel and random sequential dynamics, that is sufficient to guarantee that the steady state is factorisable. We demonstrate how this condition can be achieved in several examples. We show that our generalized result contains as a special case the recent results derived by Greenblatt and Lebowitz for $d$-dimensional hypercubic lattices with random sequential dynamics.

• 1. SUPA, School of Physics, University of Edinburgh
• 2. Isaac Newton Institute for Mathematical Sciences, Isaac Newton Institute for Mathematical Sciences
• 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 4. Department of Physics and Center for Stochastic Processes in Science and Engineering, Virginia Tech

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• ## Ferroelectricity and Charge Ordering in Quasi One-Dimensional Organic Conductors

### Serguei Brazovskii 1, 2

#### x, France (2006)

The family of molecular conductors TMTTF/TMTSF-X demonstrates almost all known electronic phases in parallel with a set of weak structural modifications of anion ordering and mysterious structureless transitions. Only in early 2000's their nature became elucidated by discoveries of a huge anomaly in the dielectric permittivity and by the NMR evidences for the charge ordering (disproportionation). These observations have been interpreted as the never expected ferroelectric transition. The phenomenon unifies a variety of different concepts and observations in quite unusual aspects or conjunctions: ferroelectricity of good conductors, structural instability towards the Mott-Hubbard state, Wigner crystallization in a dense electronic system, the ordered 4K_F density wave, richness of physics of solitons, interplay of structural and electronic symmetries. The corresponding theory of the 'combined Mott-Hubbard state' deals with orthogonal contributions to the Umklapp scattering of electrons coming from the two symmetry breaking effects: the build-in nonequivalence of bonds and the spontaneous nonequivalence of sites. The state gives rise to several types of solitons, all of them showing in experiments. On this basis we can interpret the complex of existing experiments, and suggest some future ones, such as optical absorption and photoconductivity, combined ferroelectric resonance and the phonon anti-resonance, plasma frequency reduction.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. L.D. Landau Institute for Theoretical Physics, Landau Institute for Theoretical Physics

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• ## Finite size scaling in Villain’s fully frustrated model and singular effects of plaquette disorder

### J. Lukic 1, E. Marinari 2, O. C. Martin 3

#### Europhysics Letters (EPL) 73 (2006) 779-785

The ground state and low T behavior of two-dimensional spin systems with discrete binary couplings are subtle but can be analyzed using exact computations of finite volume partition functions. We first apply this approach to Villain's fully frustrated model, unveiling an unexpected finite size scaling law. Then we show that the introduction of even a small amount of disorder on the plaquettes dramatically changes the scaling laws associated with the T=0 critical point.

• 1. Dipartimento di Fisica, SMC and UdR1 of INFM, Università degli studi di Roma I - La Sapienza
• 2. Dipartimento di Fisica, INFN, Università degli studi di Roma I - La Sapienza
• 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• ## First Experimental Observation of Superscars in a Pseudointegrable Barrier Billiard

### E. Bogomolny 1, B. Dietz 2, T. Friedrich 2, M. Miski-Oglu 2, A. Richter 2, F. Schaefer 2, C. Schmit 1

#### Physical Review Letters 97 (2006) 254102

With a perturbation body technique intensity distributions of the electric field strength in a flat microwave billiard with a barrier inside up to mode numbers as large as about 700 were measured. A method for the reconstruction of the amplitudes and phases of the electric field strength from those intensity distributions has been developed. Recently predicted superscars have been identified experimentally and - using the well known analogy between the electric field strength and the quantum mechanical wave function in a two-dimensional microwave billiard - their properties determined.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Institut für Kernphysik, Technische Universität Darmstadt

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• ## From simple to complex networks: inherent structures, barriers and valleys in the context of spin glasses

### Z. Burda, A. Krzywicki 1, O. C. Martin 2, Z. Tabor

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 73 (2006) 036110

Given discrete degrees of freedom (spins) on a graph interacting via an energy function, what can be said about the energy local minima and associated inherent structures? Using the lid algorithm in the context of a spin glass energy function, we investigate the properties of the energy landscape for a variety of graph topologies. First, we find that the multiplicity of the inherent structures generically has a lognormal distribution. Furthermore, the quenched and annealed values of the corresponding entropy are different except for the Sherrington-Kirkpatrick model. Second, we find simple scaling laws for the growth of the height of the energy barrier between the two degenerate ground states and the size of the associated valleys. For finite connectivity models, changing the topology of the underlying graph does not modify qualitatively the energy landscape, but at the quantitative level the models can differ substantially.

• 1. Laboratoire de Physique Théorique d'Orsay (LPT), CNRS : UMR8627 – Université Paris XI - Paris Sud
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• ## How long does it take to pull an ideal polymer into a small hole?

### A. Y. Grosberg 1, 2, S. Nechaev 1, 3, M. Tamm 1, 4, O. Vasilyev 3, 5

#### Physical Review Letters 96 (2006) 228105

We present scaling estimates for characteristic times $\tau_{\rm lin}$ and $\tau_{\rm br}$ of pulling ideal linear and randomly branched polymers of $N$ monomers into a small hole by a force $f$. We show that the absorbtion process develops as sequential straightening of folds of the initial polymer configuration. By estimating the typical size of the fold involved into the motion, we arrive at the following predictions: $\tau_{\rm lin}(N) \sim N^{3/2}/f$ and $\tau_{\rm br}(N) \sim N^{5/4}/f$, and we also confirm them by the molecular dynamics experiment.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Department of Physics, University of Minnesota-Crookston
• 3. L.D. Landau Institute for Theoretical Physics, Landau Institute for Theoretical Physics
• 4. Physics Department, Moscow State University
• 5. Centre de Recherche en Modélisation Moléculaire, Université de Mons-Hainaut

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• ## Inhomogenous model of crossing loops and multidegrees of some algebraic varieties

### P. Di Francesco 1, Paul Zinn-Justin 2

#### Communications in Mathematical Physics 262 (2006) 459-487

We consider a quantum integrable inhomogeneous model based on the Brauer algebra B(1) and discuss the properties of its ground state eigenvector. In particular we derive various sum rules, and show how some of its entries are related to multidegrees of algebraic varieties.

• 1. Service de Physique Théorique (SPhT), CNRS : URA2306 – CEA : DSM/SPHT
• 2. Laboratoire de Physique Théorique et Hautes Energies (LPTHE), CNRS : UMR7589 – Université Paris VI - Pierre et Marie Curie – Université Paris VII - Paris Diderot

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• ## Interaction driven real-space condensation

### M. R. Evans 1, 2, T. Hanney 1, 2, Satya N. Majumdar 2, 3

#### Physical Review Letters 97 (2006) 010602

We study real-space condensation in a broad class of stochastic mass transport models. We show that the steady state of such models has a pair-factorised form which generalizes the standard factorized steady states. The condensation in this class of models is driven by interactions which give rise to a spatially extended condensate that differs fundamentally from the previously studied examples. We present numerical results as well as a theoretical analysis of the condensation transition and show that the criterion for condensation is related to the binding-unbinding transition of solid-on-solid interfaces.

• 1. SUPA and School of Physics, University of Edinburgh
• 2. Isaac Newton Institute for Mathematical Sciences, Isaac Newton Institute for Mathematical Sciences
• 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• ## Large Deviations of Extreme Eigenvalues of Random Matrices

### David S. Dean 1, Satya N. Majumdar 2

#### Physical Review Letters 97 (2006) 160201

We calculate analytically the probability of large deviations from its mean of the largest (smallest) eigenvalue of random matrices belonging to the Gaussian orthogonal, unitary and symplectic ensembles. In particular, we show that the probability that all the eigenvalues of an (N\times N) random matrix are positive (negative) decreases for large N as \exp[-\beta \theta(0) N^2] where the parameter \beta characterizes the ensemble and the exponent \theta(0)=(\ln 3)/4=0.274653... is universal. We also calculate exactly the average density of states in matrices whose eigenvalues are restricted to be larger than a fixed number \zeta, thus generalizing the celebrated Wigner semi-circle law. The density of states generically exhibits an inverse square-root singularity at \zeta.

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

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• ## Level density of a Fermi gas: average growth and fluctuations

### Patricio Leboeuf 1, Jérôme Roccia 1

#### Physical Review Letters 97 (2006) 010401

We compute the level density of a two--component Fermi gas as a function of the number of particles, angular momentum and excitation energy. The result includes smooth low--energy corrections to the leading Bethe term (connected to a generalization of the partition problem and Hardy--Ramanujan formula) plus oscillatory corrections that describe shell effects. When applied to nuclear level densities, the theory provides a unified formulation valid from low--lying states up to levels entering the continuum. The comparison with experimental data from neutron resonances gives excellent results.

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

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• ## Message passing algorithms for non-linear nodes and data compression

### S. Ciliberti 1, M. Mezard 1, R. Zecchina 2

#### Complexus 3 (2006) 58

The use of parity-check gates in information theory has proved to be very efficient. In particular, error correcting codes based on parity checks over low-density graphs show excellent performances. Another basic issue of information theory, namely data compression, can be addressed in a similar way by a kind of dual approach. The theoretical performance of such a Parity Source Coder can attain the optimal limit predicted by the general rate-distortion theory. However, in order to turn this approach into an efficient compression code (with fast encoding/decoding algorithms) one must depart from parity checks and use some general random gates. By taking advantage of analytical approaches from the statistical physics of disordered systems and SP-like message passing algorithms, we construct a compressor based on low-density non-linear gates with a very good theoretical and practical performance.

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

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• ## Mott-insulator phase of coupled 1D atomic gases in a 2D optical lattice

### D. M. Gangardt 1, P. Pedri 2, 3, 4, L. M.N.B.F. Santos 2, 3, G. V. Shlyapnikov 1, 5

#### Physical Review Letters 96 (2006) 040403

We discuss the 2D Mott insulator (MI) state of a 2D array of coupled finite size 1D Bose gases. It is shown that the momentum distribution in the lattice plane is very sensitive to the interaction regime in the 1D tubes. In particular, we find that the disappearance of the interference pattern in time of flight experiments will not be a signature of the MI phase, but a clear consequence of the strongly interacting Tonks-Girardeau regime along the tubes.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Institut für Theoretische Physik III, Universität Stuttgart
• 3. Institut für Theoretische Physik, Universität Hannover
• 4. Dipartimento di Fisica, UNIVERSITÀ DEGLI STUDI DI TRENTO
• 5. Van der Waals-Zeeman Institute, University of Amsterdam

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• ## Off-diagonal correlations of lattice impenetrable bosons in one dimension

### D. M. Gangardt 1, G. V. Shlyapnikov 1, 2

#### New Journal of Physics 8 (2006) 167

We consider off-diagonal correlation functions of impenetrable bosons on a lattice. By using the Jordan-Wigner transformation the one-body density matrix is represented as (Toeplitz) determinant of a matrix of fermionic Green functions. Using the replica method we calculate exactly the full long-range asymptotic behaviour of the one-body density matrix. We discuss how subleading oscillating terms, originating from short-range correlations give rise to interesting features in the momentum distribution.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Van der Waals-Zeeman Institute, University of Amsterdam

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• ## Off-diagonal correlations of the Calogero-Sutherland model

### G. E. Astrakharchik 1, 2, D. M. Gangardt 3, Yu. E Lozovik 2, I. A. Sorokin 2

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 74 (2006) 021105

We study correlation functions of the Calogero-Sutherland model in the whole range of the interaction parameter. Using the replica method we obtain analytical expressions for the long-distance asymptotics of the one-body density matrix in addition to the previously derived asymptotics of the pair-distribution function [D.M. Gangardt and A. Kamenev, Nucl. Phys. B, 610, 578 (2001)]. The leading analytic and non-analytic terms in the short-distance expansion of the one-body density matrix are discussed. Exact numerical results for these correlation functions are obtained using Monte Carlo techniques for all distances. The momentum distribution and static structure factor are calculated. The potential and kinetic energies are obtained using the Hellmann-Feynman theorem. Perfect agreement is found between the analytical expressions and numerical data. These results allow for the description of physical regimes of the Calogero-Sutherland model. The zero temperature phase diagram is found to be of a crossover type and includes quasi-condensation, quasi-crystallization and quasi-supersolid regimes.

• 1. Dipartimento di Fisica, UNIVERSITÀ DEGLI STUDI DI TRENTO
• 2. Institute of Spectroscopy, Institute of Spectroscopy
• 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• ## On the free energy within the mean-field approximation

### R. Agra 1, F. van Wijland 1, E. Trizac 2

#### European Journal of Physics 27 (2006) 407-412

We compare two widespread formulations of the mean-field approximation, based on minimizing an appropriately built mean-field free energy. We use the example of the antiferromagnetic Ising model to show that one of these formulations does not guarantee the existence of an underlying variational principle. This results in a severe failure where straightforward minimization of the corresponding mean-field free energy leads to incorrect results.

• 1. Laboratoire de Physique Théorique d'Orsay (LPT), CNRS : UMR8627 – Université Paris XI - Paris Sud
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• ## On the spacing distribution of the Riemann zeros: corrections to the asymptotic result

### E. Bogomolny 1, O. Bohigas 1, P. Leboeuf 1, A. G. Monastra 2

#### Journal of Physics A: Mathematical and General 39 (2006) 10743-10754

It has been conjectured that the statistical properties of zeros of the Riemann zeta function near $z = 1/2 + \ui E$ tend, as $E \to \infty$, to the distribution of eigenvalues of large random matrices from the Unitary Ensemble. At finite $E$ numerical results show that the nearest-neighbour spacing distribution presents deviations with respect to the conjectured asymptotic form. We give here arguments indicating that to leading order these deviations are the same as those of unitary random matrices of finite dimension $N_{\rm eff}=\log(E/2\pi)/\sqrt{12 \Lambda}$, where $\Lambda=1.57314 ...$ is a well defined constant.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. TU Dresden, Institut für Theoretische Physik

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• ## Onsager-Manning-Oosawa condensation phenomenon and the effect of salt

### Emmanuel Trizac 1, 2, Gabriel Tellez 3

#### Physical Review Letters 96 (2006) 038302

Making use of results pertaining to Painleve III type equations, we revisit the celebrated Onsager-Manning-Oosawa condensation phenomenon for charged stiff linear polymers, in the mean-field approximation with salt. We obtain analytically the associated critical line charge density, and show that it is severely affected by finite salt effects, whereas previous results focused on the no salt limit. In addition, we obtain explicit expressions for the condensate thickness and the electric potential. The case of asymmetric electrolytes is also briefly addressed.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Theoretical Biological Physics, University of California, San Diego
• 3. Departamento de Fisica, Universidad de Los Andes

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• ## Ordering of geometrically frustrated classical and quantum Ising magnets

### Ying Jiang 1, Thorsten Emig 1, 2

#### Physical Review B 73 (2006) 104452

A systematic study of both classical and quantum geometric frustrated Ising models with a competing ordering mechanism is reported in this paper. The ordering comes in the classical case from a coupling of 2D layers and in the quantum model from the quantum dynamics induced by a transverse field. By mapping the Ising models on a triangular lattice to elastic lattices of non-crossing strings, we derive an exact relation between the spin variables and the displacement field of the strings. Using this map both for the classical (2+1)D stacked model and the quantum frustrated 2D system, we obtain a microscopic derivation of an effective Hamiltonian which was proposed before on phenomenological grounds within a Landau-Ginzburg-Wilson approach. In contrast to the latter approach, our derivation provides the coupling constants and hence the entire transverse field--versus--temperature phase diagram can be deduced, including the universality classes of both the quantum and the finite--temperature transitions. The structure of the ordered phase is obtained from a detailed entropy argument. We compare our predictions to recent simulations of the quantum system and find good agreement. We also analyze the connections to a dimer model on the hexagonal lattice and its height profile representation, providing a simple derivation of the continuum free energy and a physical explanation for the universality of the stiffness of the height profile for anisotropic couplings.

• 1. Institut für Theoretische Physik, Universität zu Köln
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• ## Partial Survival and Crossing Statistics for a Diffusing Particle in a Transverse Shear Flow

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

#### Journal of Physics A: Mathematical and General 39 (2006) L625-L631

We consider a non-Gaussian stochastic process where a particle diffuses in the $y$-direction, $dy/dt=\eta(t)$, subject to a transverse shear flow in the $x$-direction, $dx/dt=f(y)$. Absorption with probability $p$ occurs at each crossing of the line $x=0$. We treat the class of models defined by $f(y) = \pm v_{\pm}(\pm y)^\alpha$ where the upper (lower) sign refers to $y>0$ ($y<0$). We show that the particle survives up to time $t$ with probability $Q(t) \sim t^{-\theta(p)}$ and we derive an explicit expression for $\theta(p)$ in terms of $\alpha$ and the ratio $v_+/v_-$. From $\theta(p)$ we deduce the mean and variance of the density of crossings of the line $x=0$ for this class of non-Gaussian processes.

• 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

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• ## Photon density of states for deformed surfaces

### Thorsten Emig 1, 2

#### Journal of Physics A 39 (2006) 6309

A new approach to the Helmholtz spectrum for arbitrarily shaped boundaries and a rather general class of boundary conditions is introduced. We derive the boundary induced change of the density of states in terms of the free Green's function from which we obtain both perturbative and non-perturbative results for the Casimir interaction between deformed surfaces. As an example, we compute the lateral electrodynamic Casimir force between two corrugated surfaces over a wide parameter range. Universal behavior, fixed only by the largest wavelength component of the surface shape, is identified at large surface separations. This complements known short distance expansions which are also reproduced.

• 1. Institut für Theoretische Physik, Universität zu Köln
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• ## Planar defects and the fate of the Bragg glass phase of type-II superconductors

### Thorsten Emig 1, 2, Thomas Nattermann 1

#### Physical Review Letters 97 (2006) 177002

It is shown that the Bragg glass phase can become unstable with respect to planar defects. A single defect plane that is oriented parallel to the magnetic field as well as to one of the main axis of the Abrikosov flux line lattice is always relevant, whereas we argue that a plane with higher Miller index is irrelevant, even at large defect potentials. A finite density of parallel defects with random separations can be relevant even for larger Miller indices. Defects that are aligned with the applied field restore locally the flux density oscillations which decay algebraically with distance from the defect. The current voltage relation is changed to ln V(J) -J^{-1}. The theory exhibits some similarities to the physics of Luttinger liquids with impurities.

• 1. Institut für Theoretische Physik, Universität zu Köln
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• ## Proof of Razumov-Stroganov conjecture for some infinite families of link patterns

### Paul Zinn-Justin 1

#### Electronic Journal of Combinatories 13 (2006) R110

We prove the Razumov--Stroganov conjecture relating ground state of the O(1) loop model and counting of Fully Packed Loops in the case of certain types of link patterns. The main focus is on link patterns with three series of nested arches, for which we use as key ingredient of the proof a generalization of the Mac Mahon formula for the number of plane partitions which includes three series of parameters.

• 1. Laboratoire de Physique Théorique et Hautes Energies (LPTHE), CNRS : UMR7589 – Université Paris VI - Pierre et Marie Curie – Université Paris VII - Paris Diderot

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• ## Quenched Averages for self-avoiding walks and polygons on deterministic fractals

### S. Sumedha 1, 2, Deepak Dhar 1

#### Journal of Statistical Physics 125 (2006) 55-76

We study rooted self avoiding polygons and self avoiding walks on deterministic fractal lattices of finite ramification index. Different sites on such lattices are not equivalent, and the number of rooted open walks W_n(S), and rooted self-avoiding polygons P_n(S) of n steps depend on the root S. We use exact recursion equations on the fractal to determine the generating functions for P_n(S), and W_n(S) for an arbitrary point S on the lattice. These are used to compute the averages $< P_n(S)>, ,$ and  over different positions of S. We find that the connectivity constant $\mu$, and the radius of gyration exponent $\nu$ are the same for the annealed and quenched averages. However, $~ n log \mu + (\alpha_q -2) log n$, and $~ n log \mu + (\gamma_q -1)log n$, where the exponents $\alpha_q$ and $\gamma_q$ take values different from the annealed case. These are expressed as the Lyapunov exponents of random product of finite-dimensional matrices. For the 3-simplex lattice, our numerical estimation gives $\alpha_q \simeq 0.72837 \pm 0.00001$; and $\gamma_q \simeq 1.37501 \pm 0.00003$, to be compared with the annealed values $\alpha_a = 0.73421$ and $\gamma_a = 1.37522$.

• 1. Department of Theoretical Physics, Tata institute of Fundamental Research
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• ## Randomly incomplete spectra and intermediate statistics

### O. Bohigas 1, M. P. Pato 1, 2

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 74 (2006) 036212

By randomly removing a fraction of levels from a given spectrum a model is constructed that describes a crossover from this spectrum to a Poisson spectrum. The formalism is applied to the transitions towards Poisson from random matrix theory (RMT) spectra and picket fence spectra. It is shown that the Fredholm determinant formalism of RMT extends naturally to describe incomplete RMT spectra.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Instituto de Fisica, Universidade de São Paulo

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• ## Reconstruction on trees and spin glass transition

### Marc Mezard 1, Andrea Montanari 2

#### Journal of Statistical Physics 124 (2006) 1317-1350

Consider an information source generating a symbol at the root of a tree network whose links correspond to noisy communication channels, and broadcasting it through the network. We study the problem of reconstructing the transmitted symbol from the information received at the leaves. In the large system limit, reconstruction is possible when the channel noise is smaller than a threshold. We show that this threshold coincides with the dynamical (replica symmetry breaking) glass transition for an associated statistical physics problem. Motivated by this correspondence, we derive a variational principle which implies new rigorous bounds on the reconstruction threshold. Finally, we apply a standard numerical procedure used in statistical physics, to predict the reconstruction thresholds in various channels. In particular, we prove a bound on the reconstruction problem for the antiferromagnetic Potts'' channels, which implies, in the noiseless limit, new results on random proper colorings of infinite regular trees. This relation to the reconstruction problem also offers interesting perspective for putting on a clean mathematical basis the theory of glasses on random graphs.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Laboratoire de Physique Théorique de l'ENS (LPTENS), CNRS : UMR8549 – Université Paris VI - Pierre et Marie Curie – Ecole Normale Supérieure de Paris - ENS Paris

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• ## Secondary Structures in Long Compact Polymers

### Richard Oberdorf 1, Allison Ferguson 1, Jesper L. Jacobsen 2, 3, Jane' Kondev 1

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 74 (2006) 051801

Compact polymers are self-avoiding random walks which visit every site on a lattice. This polymer model is used widely for studying statistical problems inspired by protein folding. One difficulty with using compact polymers to perform numerical calculations is generating a sufficiently large number of randomly sampled configurations. We present a Monte-Carlo algorithm which uniformly samples compact polymer configurations in an efficient manner allowing investigations of chains much longer than previously studied. Chain configurations generated by the algorithm are used to compute statistics of secondary structures in compact polymers. We determine the fraction of monomers participating in secondary structures, and show that it is self averaging in the long chain limit and strictly less than one. Comparison with results for lattice models of open polymer chains shows that compact chains are significantly more likely to form secondary structure.

• 1. Department of Physics, Brandeis University
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 3. Service de Physique Théorique (SPhT), CNRS : URA2306 – CEA : DSM/SPHT

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• ## Short time relaxation of a driven elastic string in a random medium

### Alejandro B. Kolton 1, Alberto Rosso 2, Ezequiel V. Albano 3, Thierry Giamarchi 1

#### Physical Review B 74 (2006) 140201

We study numerically the relaxation of a driven elastic string in a two dimensional pinning landscape. The relaxation of the string, initially flat, is governed by a growing length $L(t)$ separating the short steady-state equilibrated lengthscales, from the large lengthscales that keep memory of the initial condition. We find a macroscopic short time regime where relaxation is universal, both above and below the depinning threshold, different from the one expected for standard critical phenomena. Below the threshold, the zero temperature relaxation towards the first pinned configuration provides a novel, experimentally convenient way to access all the critical exponents of the depinning transition independently.

• 1. DPMC-MaNEP, University of Geneva
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 3. INIFTA, Facultad C. Exactas, Universidad Nacional de la Plata

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• ## Spatial survival probability for one-dimensional fluctuating interfaces in the steady state

### Satya N. Majumdar 1, Chandan Dasgupta 2

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 73 (2006) 011602

We report numerical and analytic results for the spatial survival probability for fluctuating one-dimensional interfaces with Edwards-Wilkinson or Kardar-Parisi-Zhang dynamics in the steady state. Our numerical results are obtained from analysis of steady-state profiles generated by integrating a spatially discretized form of the Edwards-Wilkinson equation to long times. We show that the survival probability exhibits scaling behavior in its dependence on the system size and the sampling interval\' used in the measurement for both steady-state\' and finite\' initial conditions. Analytic results for the scaling functions are obtained from a path-integral treatment of a formulation of the problem in terms of one-dimensional Brownian motion. A deterministic approximation\' is used to obtain closed-form expressions for survival probabilities from the formally exact analytic treatment. The resulting approximate analytic results provide a fairly good description of the numerical data.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science

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• ## Spectral statistics in an open parametric billiard system

### B. Dietz 1, A. Heine 1, A. Richter 1, O. Bohigas 2, P. Leboeuf 2

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 73 (2006) 035201

We present experimental results on the eigenfrequency statistics of a superconducting, chaotic microwave billiard containing a rotatable obstacle. Deviations of the spectral fluctuations from predictions based on Gaussian orthogonal ensembles of random matrices are found. They are explained by treating the billiard as an open scattering system in which microwave power is coupled in and out via antennas. To study the interaction of the quantum (or wave) system with its environment a highly sensitive parametric correlator is used.

• 1. Institut für Kernphysik, Technische Universitat Darmstadt
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• ## Spectroscopy of the Kondo Problem in a Box

### Ribhu K. Kaul 1, 2, Gergely Zaránd 3, 4, Shailesh Chandrasekharan 1, Denis Ullmo 1, 5, Harold U. Baranger 1

#### Physical Review Letters 96 (2006) 176802

Motivated by experiments on double quantum dots, we study the problem of a single magnetic impurity confined in a finite metallic host. We prove an exact theorem for the ground state spin, and use analytic and numerical arguments to map out the spin structure of the excitation spectrum of the many-body Kondo-correlated state, throughout the weak to strong coupling crossover. These excitations can be probed in a simple tunneling-spectroscopy transport experiment; for that situation we solve rate equations for the conductance.

• 1. Duke Physics, Duke University
• 2. Institut fur Theorie der Kondensierten Materie, Universität Karlsruhe
• 3. Research Institute of Physics, Technical University Budapest
• 4. Institut fur Theoretische Feskorperphysik, Universitat Karlsruhe
• 5. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• ## Stationary state of a heated granular gas: fate of the usual H-functional

### Ioana Bena 1, Francois Coppex 1, Michel Droz 1, Paolo Visco 2, 3, Emmanuel Trizac 2, Frederic van Wijland 4

#### Physica A 370 (2006) 179-189

We consider the characterization of the nonequilibrium stationary state of a randomly-driven granular gas in terms of an entropy-production based variational formulation. Enforcing spatial homogeneity, we first consider the temporal stability of the stationary state reached after a transient. In connection, two heuristic albeit physically motivated candidates for the non-equilibrium entropy production are put forward. It turns out that none of them displays an extremum for the stationary velocity distribution selected by the dynamics. Finally, the relevance of the relative Kullbach entropy is discussed.

• 1. department of theoretical physics, University of Geneva
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 3. Laboratoire de Physique Théorique d'Orsay (LPT), CNRS : UMR8627 – Université Paris XI - Paris Sud
• 4. Matière et Systèmes Complexes (MSC), CNRS : UMR7057 – Université Paris VII - Paris Diderot

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• ## Statistical mechanics of error exponents for error-correcting codes

### Thierry Mora 1, Olivier Rivoire 2

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 74 (2006) 056110

Error exponents characterize the exponential decay, when increasing message length, of the probability of error of many error-correcting codes. To tackle the long standing problem of computing them exactly, we introduce a general, thermodynamic, formalism that we illustrate with maximum-likelihood decoding of low-density parity-check (LDPC) codes on the binary erasure channel (BEC) and the binary symmetric channel (BSC). In this formalism, we apply the cavity method for large deviations to derive expressions for both the average and typical error exponents, which differ by the procedure used to select the codes from specified ensembles. When decreasing the noise intensity, we find that two phase transitions take place, at two different levels: a glass to ferromagnetic transition in the space of codewords, and a paramagnetic to glass transition in the space of codes.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Laboratory of Living Matter, The Rockefeller University

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• ## Statistical Properties of Functionals of the Paths of a Particle Diffusing in a One-Dimensional Random Potential

### Sanjib Sabhapandit 1, 2, Satya N. Majumdar 1, Alain Comtet 1, 2

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 73 (2006) 051102

We present a formalism for obtaining the statistical properties of functionals and inverse functionals of the paths of a particle diffusing in a one-dimensional quenched random potential. We demonstrate the implementation of the formalism in two specific examples: (1) where the functional corresponds to the local time spent by the particle around the origin and (2) where the functional corresponds to the occupation time spent by the particle on the positive side of the origin, within an observation time window of size $t$. We compute the disorder average distributions of the local time, the inverse local time, the occupation time and the inverse occupation time, and show that in many cases disorder modifies the behavior drastically.

• 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 Paris VI - Pierre et Marie Curie

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• ## Strong clustering of non-interacting, sliding passive scalars driven by fluctuating surfaces

### Apoorva Nagar 1, Satya N. Majumdar 2, Mustansir Barma 1

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 74 (2006) 021124

We study the clustering of passive, non-interacting particles moving under the influence of a fluctuating field and random noise, in one dimension. The fluctuating field in our case is provided by a surface governed by the Kardar-Parisi-Zhang (KPZ) equation and the sliding particles follow the local surface slope. As the KPZ equation can be mapped to the noisy Burgers equation, the problem translates to that of passive scalars in a Burgers fluid. We study the case of particles moving in the same direction as the surface, equivalent to advection in fluid language. Monte-Carlo simulations on a discrete lattice model reveal extreme clustering of the passive particles. The resulting Strong Clustering State is defined using the scaling properties of the two point density-density correlation function. Our simulations show that the state is robust against changing the ratio of update speeds of the surface and particles. In the equilibrium limit of a stationary surface and finite noise, one obtains the Sinai model for random walkers on a random landscape. In this limit, we obtain analytic results which allow closed form expressions to be found for the quantities of interest. Surprisingly, these results for the equilibrium problem show good agreement with the results in the non-equilibrium regime.

• 1. Department of Theoretical Physics, Tata institute of Fundamental Research
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• ## Strong universality and algebraic scaling in two-dimensional Ising spin glasses

### T. Joerg 1, J. Lukic 1, E. Marinari 2, O. C. Martin 3

#### Physical Review Letters 96 (2006) 237205

At zero temperature, two-dimensional Ising spin glasses are known to fall into several universality classes. Here we consider the scaling at low but non-zero temperature and provide numerical evidence that $\eta \approx 0$ and $\nu \approx 3.5$ in all cases, suggesting a unique universality class. This algebraic (as opposed to exponential) scaling holds in particular for the $\pm J$ model, with or without dilutions and for the plaquette diluted model. Such a picture, associated with an exceptional behavior at T=0, is consistent with a real space renormalization group approach. We also explain how the scaling of the specific heat is compatible with the hyperscaling prediction.

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

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• ## Temperature Chaos in Two-Dimensional Ising Spin Glasses with Binary Couplings: a Further Case for Universality

### Jovanka Lukic 1, Enzo Marinari 2, Olivier C. Martin 3, Silvia Sabatini 4

#### Journal of Statistical Mechanics (2006) L10001

We study temperature chaos in a two-dimensional Ising spin glass with random quenched bimodal couplings, by an exact computation of the partition functions on large systems. We study two temperature correlators from the total free energy and from the domain wall free energy: in the second case we detect a chaotic behavior. We determine and discuss the chaos exponent and the fractal dimension of the domain walls.

• 1. Dipartimento di Fisica, Universita` di Roma Tor Vergata, Università degli studi di Roma II
• 2. Dipartimento di Fisica, INFM-CNR and INFN, 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. Dipartimento di Fisica, Università degli studi di Roma I - La Sapienza

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• ## Testing the relevance of effective interaction potentials between highly charged colloids in suspension

### J. Dobnikar 1, 2, R. Castañeda-Priego 3, H. H. von Grünberg 2, E. Trizac 4, 5

#### New Journal of Physics 8 (2006) 277

Combining cell and Jellium model mean-field approaches, Monte Carlo together with integral equation techniques, and finally more demanding many-colloid mean-field computations, we investigate the thermodynamic behavior, pressure and compressibility of highly charged colloidal dispersions, and at a more microscopic level, the force distribution acting on the colloids. The Kirkwood-Buff identity provides a useful probe to challenge the self-consistency of an approximate effective screened Coulomb (Yukawa) potential between colloids. Two effective parameter models are put to the test: cell against renormalized Jellium models.

• 1. Jozef Stefan Institute, Jozef Stefan Institute
• 2. Institut für Chemie, Karl-Franzens-Universität
• 3. Instituto de Fisica, Universidad de Guanajuato
• 4. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 5. Center for Theoretical Biological Physics (CTBP), University of San Diego

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• ## The Boltzmann equation for driven systems of inelastic soft spheres

### M. H. Ernst, E. Trizac 1, A. Barrat 2

#### Journal of Statistical Physics 124 (2006) 549

We study a generic class of inelastic soft sphere models with a binary collision rate $g^\nu$ that depends on the relative velocity $g$. This includes previously studied inelastic hard spheres ($\nu=1$) and inelastic Maxwell molecules ($\nu=0$). We develop a new asymptotic method for analyzing large deviations from Gaussian behavior for the velocity distribution function $f(c)$. The framework is that of the spatially uniform nonlinear Boltzmann equation and special emphasis is put on the situation where the system is driven by white noise. Depending on the value of exponent $\nu$, three different situations are reported. For $\nu<-2$, the non-equilibrium steady state is a repelling fixed point of the dynamics. For $\nu>-2$, it becomes an attractive fixed point, with velocity distributions $f(c)$ having stretched exponential behavior at large $c$. The corresponding dominant behavior of $f(c)$ is computed together with sub-leading corrections. In the marginally stable case $\nu=-2$, the high energy tail of $f(c)$ is of power law type and the associated exponents are calculated. Our analytical predictions are confronted with Monte Carlo simulations, with a remarkably good agreement.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Laboratoire de Physique Théorique d'Orsay (LPT), CNRS : UMR8627 – Université Paris XI - Paris Sud

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• ## The Glass-like Structure of Globular Proteins and the Boson Peak

### Stefano Ciliberti 1, Paolo De Los Rios 2, Francesco Piazza 2

#### Physical Review Letters 96 (2006) 198103

Vibrational spectra of proteins and topologically disordered solids display a common anomaly at low frequencies, known as Boson peak. We show that such feature in globular proteins can be deciphered in terms of an energy landscape picture, as it is for glassy systems. Exploiting the tools of Euclidean random matrix theory, we clarify the physical origin of such anomaly in terms of a mechanical instability of the system. As a natural explanation, we argue that such instability is relevant for proteins in order for their molecular functions to be optimally rooted in their structures.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Laboratoire de Biophysique Statistique-ITP, EPFL

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• ## The number of matchings in random graphs

### Lenka Zdeborová 1, Marc Mézard 1

#### Journal of Statistical Mechanics: Theory and Experiment 1 (2006) P05003

We study matchings on sparse random graphs by means of the cavity method. We first show how the method reproduces several known results about maximum and perfect matchings in regular and Erdos-Renyi random graphs. Our main new result is the computation of the entropy, i.e. the leading order of the logarithm of the number of solutions, of matchings with a given size. We derive both an algorithm to compute this entropy for an arbitrary graph with a girth that diverges in the large size limit, and an analytic result for the entropy in regular and Erdos-Renyi random graph ensembles.

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

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• ## The rich behavior of the Boltzmann equation for dissipative gases

### M. H. Ernst, E. Trizac 1, A. Barrat 2

#### Europhysics Letters (EPL) 76 (2006) 56

Within the framework of the homogeneous non-linear Boltzmann equation, we present a new analytic method, without the intrinsic limitations of existing methods, for obtaining asymptotic solutions. This method permits extension of existing results for Maxwell molecules and hard spheres to large classes of particle interactions, from very hard spheres to softer than Maxwell molecules, as well as to more general forcing mechanisms, beyond free cooling and white noise driving. By combining this method with numerical solutions, obtained from the Direct Simulation Monte Carlo (DSMC) method, we study a broad class of models relevant for the dynamics of dissipative fluids, including granular gases. We establish a criterion connecting the stability of the non-equilibrium steady state to an exponentially bound form for the velocity distribution $F$, which varies depending on the forcing mechanism. Power laws arise in marginal stability cases, of which several new cases are reported. Our results provide a minimal framework for interpreting large classes of experiments on driven granular gases.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Laboratoire de Physique Théorique d'Orsay (LPT), CNRS : UMR8627 – Université Paris XI - Paris Sud

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• ## The Statistics of the Number of Minima in a Random Energy Landscape

### Satya N. Majumdar 1, Olivier C. Martin 1

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 74 (2006) 061112

We consider random energy landscapes constructed from d-dimensional lattices or trees. The distribution of the number of local minima in such landscapes follows a large deviation principle and we derive the associated law exactly for dimension 1. Also of interest is the probability of the maximum possible number of minima; this probability scales exponentially with the number of sites. We calculate analytically the corresponding exponent for the Cayley tree and the two-leg ladder; for 2 to 5 dimensional hypercubic lattices, we compute the exponent numerically and compare to the Cayley tree case.

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

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• ## Threshold values of Random K-SAT from the cavity method

### Stephan Mertens 1, Marc Mezard 2, Riccardo Zecchina 3

#### Random Structures and Algorithms 28 (2006) 340-373

Using the cavity equations of \cite{mezard:parisi:zecchina:02,mezard:zecchina:02}, we derive the various threshold values for the number of clauses per variable of the random $K$-satisfiability problem, generalizing the previous results to $K \ge 4$. We also give an analytic solution of the equations, and some closed expressions for these thresholds, in an expansion around large $K$. The stability of the solution is also computed. For any $K$, the satisfiability threshold is found to be in the stable region of the solution, which adds further credit to the conjecture that this computation gives the exact satisfiability threshold.

• 1. Institut für Theoretische Physik, Otto-von-Guericke Universitat
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 3. ICTP, the Abdus Salam International Centre for Theoretical Physics

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• ## Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models. IV. Chromatic polynomial with cyclic boundary conditions

### Jesper Lykke Jacobsen, Jesus Salas 1

#### Journal of Statistical Physics 122 (2006) 705-760

We study the chromatic polynomial P_G(q) for m \times n square- and triangular-lattice strips of widths 2\leq m \leq 8 with cyclic boundary conditions. This polynomial gives the zero-temperature limit of the partition function for the antiferromagnetic q-state Potts model defined on the lattice G. We show how to construct the transfer matrix in the Fortuin--Kasteleyn representation for such lattices and obtain the accumulation sets of chromatic zeros in the complex q-plane in the limit n\to\infty. We find that the different phases that appear in this model can be characterized by a topological parameter. We also compute the bulk and surface free energies and the central charge.

• 1. Grupo de Modelizacion, Simulacion Numerica y Matematica Industrial, Universidad Carlos III de Madrid

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• ## Unconventional continuous phase transition in a three dimensional dimer model

### Fabien Alet 1, Gregoire Misguich 2, Vincent Pasquier 2, Roderich Moessner 3, Jesper Lykke Jacobsen 2, 4

#### Physical Review Letters 97 (2006) 030403

Phase transitions occupy a central role in physics, due both to their experimental ubiquity and their fundamental conceptual importance. The explanation of universality at phase transitions was the great success of the theory formulated by Ginzburg and Landau, and extended through the renormalization group by Wilson. However, recent theoretical suggestions have challenged this point of view in certain situations. In this Letter we report the first large-scale simulations of a three-dimensional model proposed to be a candidate for requiring a description beyond the Landau-Ginzburg-Wilson framework: we study the phase transition from the dimer crystal to the Coulomb phase in the cubic dimer model. Our numerical results strongly indicate that the transition is continuous and are compatible with a tricritical universality class, at variance with previous proposals.

• 1. Laboratoire de Physique Théorique - IRSAMC (LPT), CNRS : UMR5152 – Université Paul Sabatier - Toulouse III
• 2. Service de Physique Théorique (SPhT), CNRS : URA2306 – CEA : DSM/SPHT
• 3. Laboratoire de Physique Théorique de l'ENS (LPTENS), CNRS : UMR8549 – Université Paris VI - Pierre et Marie Curie – Ecole Normale Supérieure de Paris - ENS Paris
• 4. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• ## Unified Solution of the Expected Maximum of a Random Walk and the Discrete Flux to a Spherical Trap

### Satya N. Majumdar 1, Alain Comtet 1, 2, Robert M. Ziff 3

#### Journal of Statistical Physics 122 (2006) 833-856

Two random-walk related problems which have been studied independently in the past, the expected maximum of a random walker in one dimension and the flux to a spherical trap of particles undergoing discrete jumps in three dimensions, are shown to be closely related to each other and are studied using a unified approach as a solution to a Wiener-Hopf problem. For the flux problem, this work shows that a constant c = 0.29795219 which appeared in the context of the boundary extrapolation length, and was previously found only numerically, can be derived explicitly. The same constant enters in higher-order corrections to the expected-maximum asymptotics. As a byproduct, we also prove a new universal result in the context of the flux problem which is an analogue of the Sparre Andersen theorem proved in the context of the random walker's maximum.

• 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 Paris VI - Pierre et Marie Curie
• 3. Michigan Center for Theoretical Physics and Department of chemical Engineering, University of Michigan-Ann Arbor

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• ## Universal Asymptotic Statistics of Maximal Relative Height in One-dimensional Solid-on-solid Models

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

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 73 (2006) 056103

We study the probability density function $P(h_m,L)$ of the maximum relative height $h_m$ in a wide class of one-dimensional solid-on-solid models of finite size $L$. For all these lattice models, in the large $L$ limit, a central limit argument shows that, for periodic boundary conditions, $P(h_m,L)$ takes a universal scaling form $P(h_m,L) \sim (\sqrt{12}w_L)^{-1}f(h_m/(\sqrt{12} w_L))$, with $w_L$ the width of the fluctuating interface and $f(x)$ the Airy distribution function. For one instance of these models, corresponding to the extremely anisotropic Ising model in two dimensions, this result is obtained by an exact computation using transfer matrix technique, valid for any $L>0$. These arguments and exact analytical calculations are supported by numerical simulations, which show in addition that the subleading scaling function is also universal, up to a non universal amplitude, and simply given by the derivative of the Airy distribution function $f'(x)$.

• 1. Theoretische Physik, Universität des Saarlandes
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• ## Work fluctuations for a Brownian particle between two thermostats

### Paolo Visco 1

#### Journal of Statistical Mechanics: Theory and Experiment 1 (2006) P06006

We explicitly determine the large deviation function of the energy flow of a Brownian particle coupled to two heat baths at different temperatures. This toy model, initially introduced by Derrida and Brunet [B. Derrida and E. Brunet, in 'Einstein aujourd'hui', EDP Sciences, 2005], allows not only to sort out the influence of initial conditions on large deviation functions but also to pinpoint various restrictions bearing upon the range of validity of the Fluctuation Relation.

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

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• ## Liquid friction on charged surfaces: From hydrodynamic slippage to electrokinetics

### Laurent Joly 1 Christophe Ybert 2 Emmanuel Trizac 3 Lydéric Bocquet 2

#### Journal of Chemical Physics, American Institute of Physics, 2006, 125 (20), 〈10.1063/1.2397677〉

• 1. DAEP - Département Aérodynamique Energétique et Propulsion
• 2. LPMCN - Laboratoire de Physique de la Matière Condensée et Nanostructures
• 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
• ## Electrokinetic Effects on Slipping Surfaces

### Laurent Joly 1 Christophe Ybert 2 Lydéric Bocquet 2 Emmanuel Trizac 3

#### La Houille Blanche - Revue internationale de l'eau, EDP Sciences, 2006, pp.53 - 58. 〈10.1051/lhb:200601006〉

• 1. DAEP - Département Aérodynamique Energétique et Propulsion
• 2. LPMCN - Laboratoire de Physique de la Matière Condensée et Nanostructures
• 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques