# LPTMS Publications

Archives :

• ## Airy Distribution Function: From the Area Under a Brownian Excursion to the Maximal Height of Fluctuating Interfaces

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

#### Journal of Statistical Physics 119 (2005) 777-826

The Airy distribution function describes the probability distribution of the area under a Brownian excursion over a unit interval. Surprisingly, this function has appeared in a number of seemingly unrelated problems, mostly in computer science and graph theory. In this paper, we show that this distribution also appears in a rather well studied physical system, namely the fluctuating interfaces. We present an exact solution for the distribution P(h_m,L) of the maximal height h_m (measured with respect to the average spatial height) in the steady state of a fluctuating interface in a one dimensional system of size L with both periodic and free boundary conditions. For the periodic case, we show that P(h_m,L)=L^{-1/2}f(h_m L^{-1/2}) for all L where the function f(x) is the Airy distribution function. This result is valid for both the Edwards-Wilkinson and the Kardar-Parisi-Zhang interfaces. For the free boundary case, the same scaling holds P(h_m,L)=L^{-1/2}F(h_m L^{-1/2}), but the scaling function F(x) is different from that of the periodic case. We compute this scaling function explicitly for the Edwards-Wilkinson interface and call it the F-Airy distribution function. Numerical simulations are in excellent agreement with our analytical results. Our results provide a rather rare exactly solvable case for the distribution of extremum of a set of strongly correlated random variables. Some of these results were announced in a recent Letter [ S.N. Majumdar and A. Comtet, Phys. Rev. Lett., 92, 225501 (2004)].

• 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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• ## Around the Razumov-Stroganov conjecture: proof of a multi-parameter sum rule

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

#### Electronic Journal of Combinatories 12 (2005) R6

We prove that the sum of entries of the suitably normalized groundstate vector of the O(1) loop model with periodic boundary conditions on a periodic strip of size 2n is equal to the total number of n x n alternating sign matrices. This is done by identifying the state sum of a multi-parameter inhomogeneous version of the O(1) model with the partition function of the inhomogeneous six-vertex model on a n x n square grid with domain wall boundary conditions.

• 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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• ## Brownian Functionals in Physics and Computer Science

### Satya N. Majumdar 1

#### Current Science 89 (2005) 2076

This is a brief review on Brownian functionals in one dimension and their various applications, a contribution to the special issue The Legacy of Albert Einstein' of Current Science. After a brief description of Einstein's original derivation of the diffusion equation, this article provides a pedagogical introduction to the path integral methods leading to the derivation of the celebrated Feynman-Kac formula. The usefulness of this technique in calculating the statistical properties of Brownian functionals is illustrated with several examples in physics and probability theory, with particular emphasis on applications in computer science. The statistical properties of 'first-passage Brownian functionals' and their applications are also discussed.

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

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• ## Cavity Approach to the Random Solid State

### Xiaoming Mao 1, Paul M. Goldbart 1, Marc Mezard 2, Martin Weigt 3

#### Physical Review Letters 95 (2005) 148302

The cavity approach is used to address the physical properties of random solids in equilibrium. Particular attention is paid to the fraction of localized particles and the distribution of localization lengths characterizing their thermal motion. This approach is of relevance to a wide class of random solids, including rubbery media (formed via the vulcanization of polymer fluids) and chemical gels (formed by the random covalent bonding of fluids of atoms or small molecules). The cavity approach confirms results that have been obtained previously via replica mean-field theory, doing so in a way that sheds new light on their physical origin.

• 1. Physics Department (UIUC), University of Illinois at Urbana Champaign
• 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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• ## Cluster Algorithms for Quantum Impurity Models and Mesoscopic Kondo Physics

### Jaebeom Yoo 1, Shailesh Chandrasekharan 1, Ribhu K. Kaul 1, Denis Ullmo 1, 2, Harold U. Baranger 1

#### Physical Review B 71 (2005) 201309

Nanoscale physics and dynamical mean field theory have both generated increased interest in complex quantum impurity problems and so have focused attention on the need for flexible quantum impurity solvers. Here we demonstrate that the mapping of single quantum impurity problems onto spin-chains can be exploited to yield a powerful and extremely flexible impurity solver. We implement this cluster algorithm explicitly for the Anderson and Kondo Hamiltonians, and illustrate its use in the mesoscopic Kondo problem\'\'. To study universal Kondo physics, a large ratio between the effective bandwidth $D_\\mathrm{eff}$ and the temperature $T$ is required; our cluster algorithm treats the mesoscopic fluctuations exactly while being able to approach the large $D_\\mathrm{eff}/T$ limit with ease. We emphasize that the flexibility of our method allows it to tackle a wide variety of quantum impurity problems; thus, it may also be relevant to the dynamical mean field theory of lattice problems.

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

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• ## Clustering of solutions in the random satisfiability problem

### M. Mezard 1, T. Mora 1, R. Zecchina 2

#### Physical Review Letters 94 (2005) 197205

Using elementary rigorous methods we prove the existence of a clustered phase in the random $K$-SAT problem, for $K\\geq 8$. In this phase the solutions are grouped into clusters which are far away from each other. The results are in agreement with previous predictions of the cavity method and give a rigorous confirmation to one of its main building blocks. It can be generalized to other systems of both physical and computational interest.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. The Abdus Salam International Centre for Theoretical Physics, ICTP Trieste

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• ## Composite Fermions in Negative Effective Magnetic Field: A Monte-Carlo Study

### Gunnar Moller 1, 2, Steven H. Simon 1

#### Physical Review B 72 (2005) 045344

The method of Jain and Kamilla [PRB {\\bf 55}, R4895 (1997)] allows numerical generation of composite fermion trial wavefunctions for large numbers of electrons in high magnetic fields at filling fractions of the form nu=p/(2mp+1) with m and p positive integers. In the current paper we generalize this method to the case where the composite fermions are in an effective (mean) field with opposite sign from the actual physical field, i.e. when p is negative. We examine both the ground state energies and the low energy neutral excitation spectra of these states. Using particle-hole symmetry we can confirm the correctness of our method by comparing results for the series m=1 with p>0 (previously calculated by others) to our results for the conjugate series m=1 with p <0. Finally, we present similar results for ground state energies and low energy neutral excitations for the states with m=2 and p <0 which were not previously addressable, comparing our results to the m=1 case and the p > 0, m=2 cases.

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

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• ## Conformal Geometry and Invariants of 3-strand Brownian Braids

### Sergei K. Nechaev 1, Raphael Voituriez 2

#### Nuclear Physics B 714 (2005) 336-356

We propose a simple geometrical construction of topological invariants of 3-strand Brownian braids viewed as world lines of 3 particles performing independent Brownian motions in the complex plane z. Our construction is based on the properties of conformal maps of doubly-punctured plane z to the universal covering surface. The special attention is paid to the case of indistinguishable particles. Our method of conformal maps allows us to investigate the statistical properties of the topological complexity of a bunch of 3-strand Brownian braids and to compute the expectation value of the irreducible braid length in the non-Abelian case.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Laboratoire de Physique Théorique des Liquides (LPTL), CNRS : UMR7600 – Université Paris VI - Pierre et Marie Curie

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• ## Dephasing due to electron-electron interaction in a diffusive ring

### Christophe Texier 1, 2, Gilles Montambaux 2

#### Physical Review B 72 (2005) 115327

We study the effect of the electron-electron interaction on the weak localization correction of a ring pierced by a magnetic flux. We compute exactly the path integral giving the magnetoconductivity for an isolated ring. The results are interpreted in a time representation. This allows to characterize the nature of the phase coherence relaxation in the ring. The nature of the relaxation depends on the time regime (diffusive or ergodic) but also on the harmonics $n$ of the magnetoconductivity. Whereas phase coherence relaxation is non exponential for the harmonic $n=0$, it is always exponential for harmonics $n\\neq0$. Then we consider the case of a ring connected to reservoirs and discuss the effect of connecting wires. We recover the behaviour of the harmonics predicted recently by Ludwig & Mirlin for a large perimeter (compared to the Nyquist length). We also predict a new behaviour when the Nyquist length exceeds the perimeter.

• 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

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• ## Diatomic molecules in ultracold Fermi gases – Novel composite bosons

### D. S. Petrov 1, C. Salomon 2, G. V. Shlyapnikov 3, 4

#### Journal of Physics B 38 (2005) S645-S660

We give a brief overview of recent studies of weakly bound homonuclear molecules in ultracold two-component Fermi gases. It is emphasized that they represent novel composite bosons, which exhibit features of Fermi statistics at short intermolecular distances. In particular, Pauli exclusion principle for identical fermionic atoms provides a strong suppression of collisional relaxation of such molecules into deep bound states. We then analyze heteronuclear molecules which are expected to be formed in mixtures of different fermionic atoms. It is found how an increase in the mass ratio for the constituent atoms changes the physics of collisional stability of such molecules compared to the case of homonuclear ones. We discuss Bose-Einstein condensation of these composite bosons and draw prospects for future studies.

• 1. ITAMP, Harvard-Smithsonian Center for Astrophysics, and Harvard-MIT Center for Ultracold Atoms, Department of Physics, University of Harvard
• 2. Laboratoire Kastler Brossel (LKB (Lhomond)), CNRS : UMR8552 – Université Paris VI - Pierre et Marie Curie – Ecole Normale Supérieure de Paris - ENS Paris
• 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 4. Van der Waals-Zeeman Institute, University of Amsterdam

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• ## Equilibrium statistics of a slave estimator in Langevin processes

### David S. Dean 1, 2, Ian T. Drummond 1, Ron R. Horgan 1, Satya Majumdar 3

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 71 (2005) 031103

We analyze the statistics of an estimator, denoted by xi_t and referred to as the slave, for the equilibrium susceptibility of a one dimensional Langevin process x_t in a potential phi(x). The susceptibility can be measured by evolving the slave equation in conjunction with the original Langevin process. This procedure yields a direct estimate of the susceptibility and avoids the need, when performing numerical simulations, to include applied external fields explicitly. The success of the method however depends on the statistical properties of the slave estimator. The joint probability density function for x_t and xi_t is analyzed. In the case where the potential of the system has a concave component the probability density function of the slave acquires a power law tail characterized by a temperature dependent exponent. Thus we show that while the average value of the slave, in the equilibrium state, is always finite and given by the fluctuation dissipation relation, higher moments and indeed the variance may show divergences. The behavior of the power law exponent is analyzed in a general context and it is calculated explicitly in some specific examples. Our results are confirmed by numerical simulations and we discuss possible measurement discrepancies in the fluctuation dissipation relation which could arise due to this behavior.

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

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• ## Exact Asymptotic Results for a Model of Sequence Alignment

### Satya Majumdar 1, Sergei K. Nechaev 1, 2

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 72 (2005) 020901

Finding analytically the statistics of the longest common subsequence (LCS) of a pair of random sequences drawn from c alphabets is a challenging problem in computational evolutionary biology. We present exact asymptotic results for the distribution of the LCS in a simpler, yet nontrivial, variant of the original model called the Bernoulli matching (BM) model which reduces to the original model in the large c limit. We show that in the BM model, for all c, the distribution of the asymptotic length of the LCS, suitably scaled, is identical to the Tracy-Widom distribution of the largest eigenvalue of a random matrix whose entries are drawn from a Gaussian unitary ensemble. In particular, in the large c limit, this provides an exact expression for the asymptotic length distribution in the original LCS problem.

• 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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• ## Exact coherent states of a harmonically confined Tonks-Girardeau gas

### A. Minguzzi 1, D. M. Gangardt 1

#### Physical Review Letters 94 (2005) 240404

Using a scaling transformation we exactly determine the dynamics of an harmonically confined Tonks-Girardeau gas under arbitrary time variations of the trap frequency. We show how during a one-dimensional expansion a dynamical fermionization\'\' occurs as the momentum distribution rapidly approaches an ideal Fermi gas distribution, and that under a sudden change of the trap frequency the gas undergoes undamped breathing oscillations displaying alternating bosonic and fermionic character in momentum space. The absence of damping in the oscillations is a peculiarity of the truly Tonks regime.

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

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• ## Fermi Edge Singularities in the Mesoscopic Regime: I. Anderson Orthogonality Catastrophe

### Martina Hentschel 1, 2, Denis Ullmo 1, 3, Harold U. Baranger 1

#### Physical Review B 72 (2005) 035310

For generic mesoscopic systems like quantum dots or nanoparticles, we study the Anderson orthogonality catastrophe (AOC) and Fermi edge singularities in photoabsorption spectra in a series of two papers. In the present paper we focus on AOC for a finite number of particles in discrete energy levels where, in contrast to the bulk situation, AOC is not complete. Moreover, fluctuations characteristic for mesoscopic systems lead to a broad distribution of AOC ground state overlaps. The fluctuations originate dominantly in the levels around the Fermi energy, and we derive an analytic expression for the probability distribution of AOC overlaps in the limit of strong perturbations. We address the formation of a bound state and its importance for symmetries between the overlap distributions for attractive and repulsive potentials. Our results are based on a random matrix model for the chaotic conduction electrons that are subject to a rank one perturbation corresponding, e.g., to the localized core hole generated in the photoabsorption process.

• 1. Duke Physics, Duke University
• 2. Institut für Theoretische Physik, Universitat Regensburg
• 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• ## Finite temperature correlations and density profiles of an inhomogeneous interacting 1D Bose gas

### K. V. Kheruntsyan 1, D. M. Gangardt 2, 3, P. D. Drummond 1, G. V. Shlyapnikov 2, 4

#### Physical Review A: Atomic, Molecular and Optical Physics 71 (2005) 053615

We calculate the density profiles and density correlation functions of the one-dimensional Bose gas in a harmonic trap, using the exact finite-temperature solutions for the uniform case, and applying a local density approximation. The results are valid for a trapping potential which is slowly varying relative to a correlation length. They allow a direct experimental test of the transition from the weak coupling Gross-Pitaevskii regime to the strong coupling, \'fermionic\' Tonks-Girardeau regime. We also calculate the average two-particle correlation which characterizes the bulk properties of the sample, and find that it can be well approximated by the value of the local pair correlation in the trap center.

• 1. ARC Centre of Excellence for Quantum-Atom Optics, Department of Physics, University of Queensland
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 3. Laboratoire Kastler Brossel (LKB (Lhomond)), CNRS : UMR8552 – Université Paris VI - Pierre et Marie Curie – Ecole Normale Supérieure de Paris - ENS Paris
• 4. Van der Waals–Zeeman Institute, University of Amsterdam

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• ## Fluctuations in the level density of a Fermi gas

### P. Leboeuf 1, A. G. Monastra 2, A. Relano 3

#### Physical Review Letters 94 (2005) 102502

We present a theory that accurately describes the counting of excited states of a noninteracting fermionic gas. At high excitation energies the results reproduce Bethe\'s theory. At low energies oscillatory corrections to the many--body density of states, related to shell effects, are obtained. The fluctuations depend non-trivially on energy and particle number. Universality and connections with Poisson statistics and random matrix theory are established for regular and chaotic single--particle motion.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Institut fur Theoretische Physik, Technische Universitat Dresden
• 3. Departamento de Fisica Atomica, Molecular y Nuclear, Universidad Complutense de Madrid

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• ## Fluctuations of internal energy flow in a vibrated granular gas

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

#### Physical Review Letters 95 (2005) 110202

The non-equilibrium fluctuations of power flux in a fluidized granular media have been recently measured in an experiment [Phys. Rev. Lett. 92, 164301, 2004], which was announced to be a verification of the Fluctuation Relation (FR) by Gallavotti and Cohen. An effective temperature was also identified and proposed to be a useful probe for such non equilibrium systems. We explain these results in terms of a two temperature Poisson process. Within this model, supported by independent Molecular Dynamics simulations, power flux fluctuations do not satisfy the FR and the nature of the effective temperature is clarified. In the pursue of a hypothetical global quantity fulfilling the FR, this points to the need of considering other candidates than the power flux.

• 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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• ## Functionals of the Brownian motion, localization and metric graphs

### Alain Comtet 1, 2, Jean Desbois 1, Christophe Texier 1, 3

#### Journal of Physics A 38 (2005) R341-R383

We review several results related to the problem of a quantum particle in a random environment. In an introductory part, we recall how several functionals of the Brownian motion arise in the study of electronic transport in weakly disordered metals (weak localization). Two aspects of the physics of the one-dimensional strong localization are reviewed : some properties of the scattering by a random potential (time delay distribution) and a study of the spectrum of a random potential on a bounded domain (the extreme value statistics of the eigenvalues). Then we mention several results concerning the diffusion on graphs, and more generally the spectral properties of the Schr\\ödinger operator on graphs. The interest of spectral determinants as generating functions characterizing the diffusion on graphs is illustrated. Finally, we consider a two-dimensional model of a charged particle coupled to the random magnetic field due to magnetic vortices. We recall the connection between spectral properties of this model and winding functionals of the planar Brownian motion.

• 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. Laboratoire de Physique des Solides (LPS), CNRS : UMR8502 – Université Paris XI - Paris Sud

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• ## Geometry of Gaussian signals

### Alberto Rosso 1, Raoul Santachiara 2, Werner Krauth 3

#### Journal of Statistical Mechanics: Theory and Experiment 1 (2005) L08001

We consider Gaussian signals, i.e. random functions $u(t)$ ($t/L \\in [0,1]$) with independent Gaussian Fourier modes of variance $\\sim 1/q^{\\alpha}$, and compute their statistical properties in small windows $[x, x+\\delta]$. We determine moments of the probability distribution of the mean square width of $u(t)$ in powers of the window size $\\delta$. We show that the moments, in the small-window limit $\\delta \\ll 1$, become universal, whereas they strongly depend on the boundary conditions of $u(t)$ for larger $\\delta$. For $\\alpha > 3$, the probability distribution is computed in the small-window limit and shown to be independent of $\\alpha$.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Instituut voor Theoretische Fysica, Instituut voor Theoretische Fysica
• 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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• ## Granular gases: dynamics and collective effects

### Alain Barrat 1, Emmanuel Trizac 2, Matthieu H. Ernst 3

#### Journal of Physics: Condensed Matter 17 (2005) S2429-S2437

We present a biased review of some of the most \'spectacular\' effects appearing in the dynamics of granular gases where the dissipative nature of the collisions leads to a rich phenomenology, exhibiting striking differences with equilibrium gases. Among these differences, the focus here is on the illustrative examples of Maxwell Demon\'\'-like experiment, modification of Fourier\'s law, non-equipartition of energy and non-Gaussianity of the velocity distributions. The presentation remains as non technical as possible.

• 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. Instituut voor Theoretische Fysica, Universiteit Utrecht

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• ## Injected power and entropy flow in a heated granular gas

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

#### Europhysics Letters (EPL) 72 (2005) 55-61

Our interest goes to the power injected in a heated granular gas and to the possibility to interpret it in terms of entropy flow. We numerically determine the distribution of the injected power by means of Monte-Carlo simulations. Then, we provide a kinetic theory approach to the computation of such a distribution function. Finally, after showing why the injected power does not satisfy a Fluctuation Relation a la Gallavotti-Cohen, we put forward a new quantity which does fulfill such a relation, and is not only applicable in a variety of frameworks outside the granular world, but also experimentally accessible.

• 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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• ## Interacting classical dimers on the square lattice

### Fabien Alet 1, Jesper Lykke Jacobsen 1, 2, Gregoire Misguich 1, Vincent Pasquier 1, Frederic Mila 3, Matthias Troyer 4

#### Physical Review Letters 94 (2005) 235702

We study a model of close-packed dimers on the square lattice with a nearest neighbor interaction between parallel dimers. This model corresponds to the classical limit of quantum dimer models [D.S. Rokhsar and S.A. Kivelson, Phys. Rev. Lett.{\\bf 61}, 2376 (1988)]. By means of Monte Carlo and Transfer Matrix calculations, we show that this system undergoes a Kosterlitz-Thouless transition separating a low temperature ordered phase where dimers are aligned in columns from a high temperature critical phase with continuously varying exponents. This is understood by constructing the corresponding Coulomb gas, whose coupling constant is computed numerically. We also discuss doped models and implications on the finite-temperature phase diagram of quantum dimer models.

• 1. Service de Physique Théorique (SPhT), CNRS : URA2306 – CEA : DSM/SPHT
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 3. Institute of Theoretical Physics, École Polytechnique Fédérale de Lausanne
• 4. Theoretische Physik, ETH Zurich

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• ## Interaction Effects in the Mesoscopic Regime: A Quantum Monte Carlo Study of Irregular Quantum Dots

### Amit Ghosal 1, C. J. Umrigar 2, Hong Jiang 1, 3, Denis Ullmo 1, 4, Harold U. Baranger 1

#### Physical Review B 71 (2005) 241306

We address the issue of accurately treating interaction effects in the mesoscopic regime by investigating the ground state properties of isolated irregular quantum dots. Quantum Monte Carlo techniques are used to calculate the distributions of ground state spin and addition energy. We find a reduced probability of high spin and a somewhat larger even/odd alternation in the addition energy from quantum Monte Carlo than in local spin density functional theory. In both approaches, the even/odd effect gets smaller with increasing number of electrons, contrary to the theoretical understanding of large dots. We argue that the local spin density approximation over predicts the effects of interactions in quantum dots.

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

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• ## Interactions and Broken Time-Reversal Symmetry in Chaotic Quantum Dots

### Denis Ullmo 1, 2, Hong Jiang 1, 3, Weitao Yang 3, Harold U. Baranger 1

#### Physical Review B 71 (2005) 201310

When treating interactions in quantum dots within a RPA-like approach, time-reversal symmetry plays an important role as higher-order terms -- the Cooper series -- need to be included when this symmetry is present. Here we consider model quantum dots in a magnetic field weak enough to leave the dynamics of the dot chaotic, but strong enough to break time-reversal symmetry. The ground state spin and addition energy for dots containing 120 to 200 electrons are found using local spin density functional theory, and we compare the corresponding distributions with those derived from an RPA-like treatment of the interactions. The agreement between the two approaches is very good, significantly better than for analogous calculations in the presence of time-reversal symmetry. This demonstrates that the discrepancies between the two approaches in the time-reversal symmetric case indeed originate from the Cooper channel, indicating that these higher-order terms might not be properly taken into account in the spin density functional calculations.

• 1. Duke Physics, Duke University
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 3. Department of Chemistry, Duke University

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• ## Landscape of solutions in constraint satisfaction problems

### Marc Mezard 1, Matteo Palassini 1, 2, Olivier Rivoire 1

#### Physical Review Letters 95 (2005) 200202

We present a theoretical framework for characterizing the geometrical properties of the space of solutions in constraint satisfaction problems, together with practical algorithms for studying this structure on particular instances. We apply our method to the coloring problem, for which we obtain the total number of solutions and analyze in detail the distribution of distances between solutions.

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

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• ## Level density of a Fermion gas: average growth, fluctuations, universality

### Patricio Leboeuf 1

#### Nuclei and Mesoscopic Physics at the National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing : États-Unis (2005)

It has been shown by H. Bethe more than 70 years ago that the number of excited states of a Fermi gas grows, at high excitation energies $Q$, like the exponential of the square root of $Q$. This result takes into account only the average density of single particle (SP) levels near the Fermi energy. It ignores two important effects, namely the discreteness of the SP spectrum, and its fluctuations. We show that the discreteness of the SP spectrum gives rise to smooth finite--$Q$ corrections. Mathematically, these corrections are associated to the problem of partitions of an integer. On top of the smooth growth of the many--body density of states there are, generically, oscillations. An explicit expression of these oscillations is given. Their properties strongly depend on the regular or chaotic nature of the SP motion. In particular, we analyze their typical size, temperature dependence and probability distribution, with emphasis on their universal aspects.

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

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• ## Lossy data compression with random gates

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

#### Physical Review Letters 95 (2005) 038701

We introduce a new protocol for a lossy data compression algorithm which is based on constraint satisfaction gates. We show that the theoretical capacity of algorithms built from standard parity-check gates converges exponentially fast to the Shannon\'s bound when the number of variables seen by each gate increases. We then generalize this approach by introducing random gates. They have theoretical performances nearly as good as parity checks, but they offer the great advantage that the encoding can be done in linear time using the Survey Inspired Decimation algorithm, a powerful algorithm for constraint satisfaction problems derived from statistical physics.

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

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• ## Maxwell and very hard particle models for probabilistic ballistic annihilation: hydrodynamic description

### Francois Coppex 1, Michel Droz 1, Emmanuel Trizac 2

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 72 (2005) 021105

The hydrodynamic description of probabilistic ballistic annihilation, for which no conservation laws hold, is an intricate problem with hard sphere-like dynamics for which no exact solution exists. We consequently focus on simplified approaches, the Maxwell and very hard particles (VHP) models, which allows us to compute analytically upper and lower bounds for several quantities. The purpose is to test the possibility of describing such a far from equilibrium dynamics with simplified kinetic models. The motivation is also in turn to assess the relevance of some singular features appearing within the original model and the approximations invoked to study it. The scaling exponents are first obtained from the (simplified) Boltzmann equation, and are confronted against Monte Carlo simulation (DSMC technique). Then, the Chapman-Enskog method is used to obtain constitutive relations and transport coefficients. The corresponding Navier-Stokes equations for the hydrodynamic fields are derived for both Maxwell and VHP models. We finally perform a linear stability analysis around the homogeneous solution, which illustrates the importance of dissipation in the possible development of spatial inhomogeneities.

• 1. department of theoretical physics, University of Geneva
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• ## Mesoscopic Kondo Problem

### Ribhu K. Kaul 1, Denis Ullmo 1, 2, Shailesh Chandrasekharan 1, Harold U. Baranger 1

#### Europhysics Letters (EPL) 71 (2005) 973-979

We study the effect of mesoscopic fluctuations on a magnetic impurity coupled to a spatially confined electron gas with a temperature in the mesoscopic range (i.e. between the mean level spacing $\\Delta$ and the Thouless energy $E_{\\rm Th}$). Comparing poor-man\'s scaling\'\' with exact Quantum Monte Carlo, we find that for temperatures larger than the Kondo temperature, many aspects of the fluctuations can be captured by the perturbative technique. Using this technique in conjunction with semi-classical approximations, we are able to calculate the mesoscopic fluctuations for a wide variety of systems. For temperatures smaller than the Kondo temperature, we find large fluctuations and deviations from the universal behavior.

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

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• ## Non-equilibrium relaxation of an elastic string in a random potential

### Alejandro Kolton 1, Alberto Rosso 2, Thierry Giamarchi 1

#### Physical Review Letters 95 (2005) 180604

We study the non--equilibrium motion of an elastic string in a two dimensional pinning landscape using Langevin dynamics simulations. The relaxation of a line, initially flat, is characterized by a growing length, $L(t)$, separating the equilibrated short length scales from the flat long distance geometry that keep memory of the initial condition. We show that, in the long time limit, $L(t)$ has a non--algebraic growth with a universal distribution function. The distribution function of waiting times is also calculated, and related to the previous distribution. The barrier distribution is narrow enough to justify arguments based on scaling of the typical barrier.

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

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• ## Nonlinear Transport of Bose-Einstein Condensates Through Waveguides with Disorder

### Tobias Paul 1, Patricio Leboeuf 2, Nicolas Pavloff 2, Klaus Richter 1, Peter Schlagheck 1

#### Physical Review A: Atomic, Molecular and Optical Physics 72 (2005) 063621

We study the coherent flow of a guided Bose-Einstein condensate incident over a disordered region of length L. We introduce a model of disordered potential that originates from magnetic fluctuations inherent to microfabricated guides. This model allows for analytical and numerical studies of realistic transport experiments. The repulsive interaction among the condensate atoms in the beam induces different transport regimes. Below some critical interaction (or for sufficiently small L) a stationary flow is observed. In this regime, the transmission decreases exponentially with L. For strong interaction (or large L), the system displays a transition towards a time dependent flow with an algebraic decay of the time averaged transmission.

• 1. Institut für Theoretische Physik, Universität Regensburg, 93040 Regensburg, Germany, Universität Regensburg
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• ## Observation of dipole-dipole interaction in a degenerate quantum gas

### J. Stuhler 1, A. Griesmaier 1, T. Koch 1, M. Fattori 1, T. Pfau 1, S. Giovanazzi 2, P. Pedri 3, 4, L. M.N.B.F. Santos 3

#### Physical Review Letters 95 (2005) 150406

We have investigated the expansion of a Bose-Einstein condensate (BEC) of strongly magnetic chromium atoms. The long-range and anisotropic magnetic dipole-dipole interaction leads to an anisotropic deformation of the expanding Cr-BEC which depends on the orientation of the atomic dipole moments. Our measurements are consistent with the theory of dipolar quantum gases and show that a Cr-BEC is an excellent model system to study dipolar interactions in such gases.

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

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• ## On the area under a continuous time Brownian motion till its first-passage time

### Michael J. Kearney 1, Satya N. Majumdar 2

#### Journal of Physics A 38 (2005) 4097

The area swept out under a one-dimensional Brownian motion till its first-passage time is analysed using a backward Fokker-Planck technique. We obtain an exact expression of the area distribution for the zero drift case, and provide various asymptotic results for the non-zero drift case, emphasising the critical nature of the behaviour in the limit of vanishing drift. The results offer important insights into the asymptotic behaviour of the area-perimeter generating functions in a class of discrete polygons. We also provide a succinct derivation for the distribution of the maximum displacement observed till the first-passage time.

• 1. Advanced Technology Institute, School of Electronics and Physical Sciences, University of Surrey
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• ## On the Sign Problem in the Hirsch-Fye Algorithm for Impurity Problems

### Jaebeom Yoo 1, Shailesh Chandrasekharan 1, Ribhu K. Kaul 1, Denis Ullmo 1, 2, Harold U. Baranger 1

#### Journal of Physics A 38 (2005) 10307-10310

We show that there is no fermion sign problem in the Hirsch and Fye algorithm for the single-impurity Anderson model. Beyond the particle-hole symmetric case for which a simple proof exists, this has been known only empirically. Here we prove the nonexistence of a sign problem for the general case by showing that each spin trace for a given Ising configuration is separately positive. We further use this insight to analyze under what conditions orbitally degenerate Anderson models or the two-impurity Anderson model develop a sign.

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

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• ## Passive Sliders on Fluctuating Surfaces: Strong-Clustering States

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

#### Physical Review Letters 94 (2005) 240601

We study the clustering properties of particles sliding downwards on a fluctuating surface evolving through the Kardar-Parisi-Zhang equation, a problem equivalent to passive scalars driven by a Burgers fluid. Monte Carlo simulations on a discrete version of the problem in one dimension reveal that particles cluster very strongly: the two point density correlation function scales with the system size with a scaling function which diverges at small argument. Analytic results are obtained for the Sinai problem of random walkers in a quenched random landscape. This equilibrium system too has a singular scaling function which agrees remarkably with that for advected particles.

• 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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• ## Persistence of Randomly Coupled Fluctuating Interfaces

### Satya N. Majumdar 1, Dibyendu Das 2

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 71 (2005) 036129

We study the persistence properties in a simple model of two coupled interfaces characterized by heights h_1 and h_2 respectively, each growing over a d-dimensional substrate. The first interface evolves independently of the second and can correspond to any generic growing interface, e.g., of the Edwards-Wilkinson or of the Kardar-Parisi-Zhang variety. The evolution of h_2, however, is coupled to h_1 via a quenched random velocity field. In the limit d\\to 0, our model reduces to the Matheron-de Marsily model in two dimensions. For d=1, our model describes a Rouse polymer chain in two dimensions advected by a transverse velocity field. We show analytically that after a long waiting time t_0\\to \\infty, the stochastic process h_2, at a fixed point in space but as a function of time, becomes a fractional Brownian motion with a Hurst exponent, H_2=1-\\beta_1/2, where \\beta_1 is the growth exponent characterizing the first interface. The associated persistence exponent is shown to be \\theta_s^2=1-H_2=\\beta_1/2. These analytical results are verified by numerical simulations.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Department of Physics, Indian Institute of Technology Bombay

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• ## Precise Asymptotics for a Random Walker’s Maximum

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

#### Journal of Statistical Mechanics: Theory and Experiment 06 (2005) P06013

We consider a discrete time random walk in one dimension. At each time step the walker jumps by a random distance, independent from step to step, drawn from an arbitrary symmetric density function. We show that the expected positive maximum E[M_n] of the walk up to n steps behaves asymptotically for large n as, E[M_n]/\\sigma=\\sqrt{2n/\\pi}+ \\gamma +O(n^{-1/2}), where \\sigma^2 is the variance of the step lengths. While the leading \\sqrt{n} behavior is universal and easy to derive, the leading correction term turns out to be a nontrivial constant \\gamma. For the special case of uniform distribution over [-1,1], Coffmann et. al. recently computed \\gamma=-0.516068...by exactly enumerating a lengthy double series. Here we present a closed exact formula for \\gamma valid for arbitrary symmetric distributions. We also demonstrate how \\gamma appears in the thermodynamic limit as the leading behavior of the difference variable E[M_n]-E[|x_n|] where x_n is the position of the walker after n steps. An application of these results to the equilibrium thermodynamics of a Rouse polymer chain is pointed out. We also generalize our results to L\\évy walks.

• 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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• ## Propagation of a Dark Soliton in a Disordered Bose-Einstein Condensate

### N. Bilas 1, N. Pavloff 1

#### Physical Review Letters 95 (2005) 130403

We consider the propagation of a dark soliton in a quasi 1D Bose-Einstein condensate in presence of a random potential. This configuration involves nonlinear effects and disorder, and we argue that, contrarily to the study of stationary transmission coefficients through a nonlinear disordered slab, it is a well defined problem. It is found that a dark soliton decays algebraically, over a characteristic length which is independent of its initial velocity, and much larger than both the healing length and the 1D scattering length of the system. We also determine the characteristic decay time.

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

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• ## Quantum Knizhnik-Zamolodchikov equation, generalized Razumov-Stroganov sum rules and extended Joseph polynomials

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

#### Journal of Physics A 38 (2005) L815-L822

We prove higher rank analogues of the Razumov--Stroganov sum rule for the groundstate of the O(1) loop model on a semi-infinite cylinder: we show that a weighted sum of components of the groundstate of the A_{k-1} IRF model yields integers that generalize the numbers of alternating sign matrices. This is done by constructing minimal polynomial solutions of the level 1 U_q(\\hat{sl(k)}) quantum Knizhnik--Zamolodchikov equations, which may also be interpreted as quantum incompressible q-deformations of fractional quantum Hall effect wave functions at filling fraction nu=1/k. In addition to the generalized Razumov--Stroganov point q=-e^{i pi/k+1}, another combinatorially interesting point is reached in the rational limit q -> -1, where we identify the solution with extended Joseph polynomials associated to the geometry of upper triangular matrices with vanishing k-th power.

• 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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• ## Quantum oscillations in mesoscopic rings and anomalous diffusion

### Christophe Texier 1, 2, Gilles Montambaux 2

#### Journal of Physics A 38 (2005) 3455-3471

We consider the weak localization correction to the conductance of a ring connected to a network. We analyze the harmonics content of the Al\'tshuler-Aronov-Spivak (AAS) oscillations and we show that the presence of wires connected to the ring is responsible for a behaviour different from the one predicted by AAS. The physical origin of this behaviour is the anomalous diffusion of Brownian trajectories around the ring, due to the diffusion in the wires. We show that this problem is related to the anomalous diffusion along the skeleton of a comb. We study in detail the winding properties of Brownian curves around a ring connected to an arbitrary network. Our analysis is based on the spectral determinant and on the introduction of an effective perimeter probing the different time scales. A general expression of this length is derived for arbitrary networks. More specifically we consider the case of a ring connected to wires, to a square network, and to a Bethe lattice.

• 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

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• ## Random Aharonov-Bohm vortices and some exactly solvable families of integrals

### Stephane Ouvry 1

#### Journal of Statistical Mechanics: Theory and Experiment 1 (2005) P09004

A review of the random magnetic impurity model, introduced in the context of the integer Quantum Hall effect, is presented. It models an electron moving in a plane and coupled to random Aharonov-Bohm vortices carrying a fraction of the quantum of flux. Recent results on its perturbative expansion are given. In particular, some funny families of integrals show up to be related to the Riemann $\\zeta(3)$ and $\\zeta(2)$.

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

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• ## Random multi-index matching problems

### O. C. Martin 1, M. Mezard 1, O. Rivoire 1

#### Journal of Statistical Mechanics: Theory and Experiment 1 (2005) P09006

The multi-index matching problem (MIMP) generalizes the well known matching problem by going from pairs to d-uplets. We use the cavity method from statistical physics to analyze its properties when the costs of the d-uplets are random. At low temperatures we find for d>2 a frozen glassy phase with vanishing entropy. We also investigate some properties of small samples by enumerating the lowest cost matchings to compare with our theoretical predictions.

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

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• ## Regularity and chaos in the nuclear masses

### P. Leboeuf 1

#### Lecture Notes in Physics 652 (2005) 245

Shell effects in atomic nuclei are a quantum mechanical manifestation of the single--particle motion of the nucleons. They are directly related to the structure and fluctuations of the single--particle spectrum. Our understanding of these fluctuations and of their connections with the regular or chaotic nature of the nucleonic motion has greatly increased in the last decades. In the first part of these lectures these advances, based on random matrix theories and semiclassical methods, are briefly reviewed. Their consequences on the thermodynamic properties of Fermi gases and, in particular, on the masses of atomic nuclei are then presented. The structure and importance of shell effects in the nuclear masses with regular and chaotic nucleonic motion are analyzed theoretically, and the results are compared to experimental data. We clearly display experimental evidence of both types of motion

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

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• ## Scattering properties of weakly bound dimers of fermionic atoms

### D. S. Petrov 1, 2, 3, C. Salomon 4, G. V. Shlyapnikov 2, 3, 5, 6

#### Physical Review A: Atomic, Molecular and Optical Physics 71 (2005) 012708

We consider weakly bound diatomic molecules (dimers) formed in a two-component atomic Fermi gas with a large positive scattering length for the interspecies interaction. We develop a theoretical approach for calculating atom-dimer and dimer-dimer elastic scattering and for analyzing the inelastic collisional relaxation of the molecules into deep bound states. This approach is based on the single-channel zero range approximation, and we find that it is applicable in the vicinity of a wide two-body Feshbach resonance. Our results draw prospects for various interesting manipulations of weakly bound dimers of fermionic atoms.

• 1. ITAMP, Department of Physics, University of Harvard
• 2. Kavli Institute for Theoretical Physics, University of California, Santa Barbara
• 3. National Research Centre "Kurchatov Institute" (NRC KI), University of Moscow
• 4. Laboratoire Kastler Brossel (LKB (Lhomond)), CNRS : UMR8552 – Université Paris VI - Pierre et Marie Curie – Ecole Normale Supérieure de Paris - ENS Paris
• 5. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 6. Van der Waals-Zeeman Institute, University of Amsterdam

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• ## Scrambling and Gate Effects in Realistic Quantum Dots

### Hong Jiang 1, Denis Ullmo 2, 3, Weitao Yang 1, Harold U. Baranger 2

#### Physical Review B 71 (2005) 085313

We evaluate the magnitude of two important mesoscopic effects using a realistic model of typical quantum dots. Scrambling\'\' and gate effect\'\' are defined as the change in the single-particle spectrum due to added electrons or gate-induced shape deformation, respectively. These two effects are investigated systematically in both the self-consistent Kohn-Sham (KS) theory and a Fermi liquid-like Strutinsky approach. We find that the genuine scrambling effect is small because the potential here is smooth. In the KS theory, a key point is the implicit inclusion of residual interactions in the spectrum; these dominate and make scrambling appear larger. Finally, the gate effect is comparable in the two cases and, while small, is able to cause gate-induced spin transitions.

• 1. Department of Chemistry, Duke University
• 2. Duke Physics, Duke University
• 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• ## Spanning forests and the q-state Potts model in the limit q \\to 0

### Jesper Lykke Jacobsen 1, Jesus Salas 2, Alan D. Sokal 3

#### Journal of Statistical Physics 119 (2005) 1153-1281

We study the q-state Potts model with nearest-neighbor coupling v=e^{\\beta J}-1 in the limit q,v \\to 0 with the ratio w = v/q held fixed. Combinatorially, this limit gives rise to the generating polynomial of spanning forests; physically, it provides information about the Potts-model phase diagram in the neighborhood of (q,v) = (0,0). We have studied this model on the square and triangular lattices, using a transfer-matrix approach at both real and complex values of w. For both lattices, we have computed the symbolic transfer matrices for cylindrical strips of widths 2 \\le L \\le 10, as well as the limiting curves of partition-function zeros in the complex w-plane. For real w, we find two distinct phases separated by a transition point w=w_0, where w_0 = -1/4 (resp. w_0 = -0.1753 \\pm 0.0002) for the square (resp. triangular) lattice. For w > w_0 we find a non-critical disordered phase, while for w < w_0 our results are compatible with a massless Berker-Kadanoff phase with conformal charge c = -2 and leading thermal scaling dimension x_{T,1} = 2 (marginal operator). At w = w_0 we find a \'first-order critical point\': the first derivative of the free energy is discontinuous at w_0, while the correlation length diverges as w \\downarrow w_0 (and is infinite at w = w_0). The critical behavior at w = w_0 seems to be the same for both lattices and it differs from that of the Berker-Kadanoff phase: our results suggest that the conformal charge is c = -1, the leading thermal scaling dimension is x_{T,1} = 0, and the critical exponents are \\nu = 1/d = 1/2 and \\alpha = 1.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 3. Dept. of Physics, New York University

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• ## Spatial correlation functions in 3-d Ising spin glasses

### Cirano De Dominicis 1, Irene Giardina 2, Enzo Marinari 3, Olivier C. Martin 4, Francesco Zuliani 4

#### Physical Review B 72 (2005) 014443

We investigate spin-spin correlation functions in the low temperature phase of spin-glasses. With the replica field theory formalism, we examine in detail their infrared (long distance) behavior. In particular we identify a longitudinal mode that remains massive in the infinite volume limit. These issues are then addressed by numerical simulation; the analysis of our data is compatible with the prediction that the longitudinal mode remains massive, i.e., that it undergoes an exponential decay, a feature unexpected in the droplet/scaling framework.

• 1. Service de Physique Théorique (SPhT), CNRS : URA2306 – CEA : DSM/SPHT
• 2. CNR ISC, Via dei Taurini 19, 00185 Roma, Italy and Dipartimento di Fisica, Università degli studi di Roma I - La Sapienza
• 3. Dipartimento di Fisica and INFN, Università degli studi di Roma I - La Sapienza
• 4. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• ## Spin waves in a one-dimensional spinor Bose gas

### J. N. Fuchs 1, D. M. Gangardt 2, T. Keilmann 3, G. V. Shlyapnikov 2, 4

#### Physical Review Letters 95 (2005) 150402

We study a one-dimensional (iso)spin 1/2 Bose gas with repulsive delta-function interaction by the Bethe Ansatz method and discuss the excitations above the polarized ground state. In addition to phonons the system features spin waves with a quadratic dispersion. We compute analytically and numerically the effective mass of the spin wave and show that the spin transport is greatly suppressed in the strong coupling regime, where the isospin-density (or spin-charge\'\') separation is maximal. Using a hydrodynamic approach, we study spin excitations in a harmonically trapped system and discuss prospects for future studies of two-component ultracold atomic gases.

• 1. Laboratoire de Physique des Solides (LPS), CNRS : UMR8502 – Université Paris XI - Paris Sud
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 3. Max-Planck-Institut für Quantenoptik, Max-Planck-Institut
• 4. Van der Waals-Zeeman Institute, University of Amsterdam

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• ## Statistical mechanics of combinatorial optimization problems with site disorder

### David S. Dean 1, David Lancaster 2, Satya. N. Majumdar 3

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 72 (2005) 026125

We study the statistical mechanics of a class of problems whose phase space is the set of permutations of an ensemble of quenched random positions. Specific examples analyzed are the finite temperature traveling salesman problem on several different domains and various problems in one dimension such as the so called descent problem. We first motivate our method by analyzing these problems using the annealed approximation, then the limit of a large number of points we develop a formalism to carry out the quenched calculation. This formalism does not require the replica method and its predictions are found to agree with Monte Carlo simulations. In addition our method reproduces an exact mathematical result for the Maximum traveling salesman problem in two dimensions and suggests its generalization to higher dimensions. The general approach may provide an alternative method to study certain systems with quenched disorder.

• 1. Laboratoire de Physique Théorique - IRSAMC (LPT), CNRS : UMR5152 – Université Paul Sabatier - Toulouse III
• 2. Harrow School of Computer Science - University of Westminster, University of Westminster
• 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• ## Statistics of randomly branched polymers in a semi-space

### M. V. Tamm 1, 2, S. K. Nechaev 2, 3, I. Ya. Erukhimovich 1, 4

#### European Physical Journal E 17 (2005) 209-219

We investigate the statistical properties of a randomly branched 3--functional $N$--link polymer chain without excluded volume, whose one point is fixed at the distance $d$ from the impenetrable surface in a 3--dimensional space. Exactly solving the Dyson-type equation for the partition function $Z(N,d)=N^{-\\theta} e^{\\gamma N}$ in 3D, we find the \'surface\' critical exponent $\\theta={5/2}$, as well as the density profiles of 3--functional units and of dead ends. Our approach enables to compute also the pairwise correlation function of a randomly branched polymer in a 3D semi-space.

• 1. Physics Department, Moscow State University
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 3. Landau Institute for Theoretical Physics, Landau Institute for Theoretical Physics
• 4. A.N. Nesmeyanov Institute of Organoelement Coumpounds RAS, A.N. newmeyanov Institute of Organoelement Coumpounds RAS

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• ## Statistics of Wave Functions in Disordered Systems with Applications to Coulomb Blockade Peak Spacing

### Mike Miller 1, Denis Ullmo 1, 2, Harold U. Baranger 1

#### Physical Review B 72 (2005) 045305

Despite considerable work on the energy-level and wavefunction statistics of disordered quantum systems, numerical studies of those statistics relevant for electron-electron interactions in mesoscopic systems have been lacking. We plug this gap by using a tight-binding model to study a wide variety of statistics for the two-dimensional, disordered quantum system in the diffusive regime. Our results are in good agreement with random matrix theory (or its extensions) for simple statistics such as the probability distribution of energy levels or spatial correlation of a wavefunction. However, we see substantial disagreement in several statistics which involve both integrating over space and different energy levels, indicating that disordered systems are more complex than previously thought. These are exactly the quantities relevant to electron-electron interaction effects in quantum dots; in fact, we apply these results to the Coulomb blockade, where we find altered spacings between conductance peaks and wider spin distributions than traditionally expected.

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

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• ## Superfluid Fermi gas in a 1D optical lattice

### G. Orso 1, G. V. Shlyapnikov 2, 3

#### Physical Review Letters 95 (2005) 260402

We calculate the superfluid transition temperature for a two-component 3D Fermi gas in a 1D tight optical lattice and discuss a dimensional crossover from the 3D to quasi-2D regime. For the geometry of finite size discs in the 1D lattice, we find that even for a large number of atoms per disc, the critical effective tunneling rate for a quantum transition to the Mott insulator state can be large compared to the loss rate caused by three-body recombination. This allows the observation of the Mott transition, in contrast to the case of Bose-condensed gases in the same geometry.

• 1. BEC-INFM and Dipartimento di Fisica, UNIVERSITÀ DEGLI STUDI DI TRENTO
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 3. Van der Waals-Zeeman Institute, University of Amsterdam

Details Citations to the Article (20)

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• ## Survey propagation: an algorithm for satisfiability

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

#### Random Structures and Algorithms 27 (2005) 201-226

We study the satisfiability of randomly generated formulas formed by $M$ clauses of exactly $K$ literals over $N$ Boolean variables. For a given value of $N$ the problem is known to be most difficult with $\\alpha=M/N$ close to the experimental threshold $\\alpha_c$ separating the region where almost all formulas are SAT from the region where all formulas are UNSAT. Recent results from a statistical physics analysis suggest that the difficulty is related to the existence of a clustering phenomenon of the solutions when $\\alpha$ is close to (but smaller than) $\\alpha_c$. We introduce a new type of message passing algorithm which allows to find efficiently a satisfiable assignment of the variables in the difficult region. This algorithm is iterative and composed of two main parts. The first is a message-passing procedure which generalizes the usual methods like Sum-Product or Belief Propagation: it passes messages that are surveys over clusters of the ordinary messages. The second part uses the detailed probabilistic information obtained from the surveys in order to fix variables and simplify the problem. Eventually, the simplified problem that remains is solved by a conventional heuristic.

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

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• ## Survey-propagation decimation through distributed local computations

### Joel Chavas 1, Cyril Furtlehner 2, Marc Mezard 2, Riccardo Zecchina 3

#### Journal of Statistical Mechanics: Theory and Experiment P (2005) P11016

We discuss the implementation of two distributed solvers of the random K-SAT problem, based on some development of the recently introduced survey-propagation (SP) algorithm. The first solver, called the \'SP diffusion algorithm\', diffuses as dynamical information the maximum bias over the system, so that variable nodes can decide to freeze in a self-organized way, each variable making its decision on the basis of purely local information. The second solver, called the \'SP reinforcement algorithm\', makes use of time-dependent external forcing messages on each variable, which let the variables get completely polarized in the direction of a solution at the end of a single convergence. Both methods allow us to find a solution of the random 3-SAT problem in a range of parameters comparable with the best previously described serialized solvers. The simulated time of convergence towards a solution (if these solvers were implemented on a distributed device) grows as log(N).

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

Details Citations to the Article (9)

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• ## The cavity method for large deviations

### Olivier Rivoire 1

#### Journal of Statistical Mechanics: Theory and Experiment 1 (2005) P04007

A method is introduced for studying large deviations in the context of statistical physics of disordered systems. The approach, based on an extension of the cavity method to atypical realizations of the quenched disorder, allows us to compute exponentially small probabilities (rate functions) over different classes of random graphs. It is illustrated with two combinatorial optimization problems, the vertex-cover and coloring problems, for which the presence of replica symmetry breaking phases is taken into account. Applications include the analysis of models on adaptive graph structures.

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

Details Citations to the Article (5)
• ## The Nature of the Condensate in Mass Transport Models

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

#### Physical Review Letters 94 (2005) 180601

We study the phenomenon of real space condensation in the steady state of a class of one dimensional mass transport models. We derive the criterion for the occurrence of a condensation transition and analyse the precise nature of the 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. We interpret these results within the framework of sums of random variables.

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

Details Citations to the Article (44)
• ## The statistical mechanics of traveling salesman type problems

### David S. Dean 1, 2, David Lancaster 3, Satya Majumdar 4

#### Journal of Statistical Mechanics: Theory and Experiment 1 (2005) L01001

We study the finite temperature statistical mechanics of Hamiltonian paths between a set of N quenched randomly distributed points in a finite domain D. The energy of the path is a function of the distance between neighboring points on the path, an example is the traveling salesman problem where the energy is the total distance between neighboring points on the path. We show how the system can be analyzed in the limit of large N without using the replica method.

• 1. DAMTP, CMS, University of Cambridge
• 2. Laboratoire de Physique Théorique - IRSAMC (LPT), CNRS : UMR5152 – Université Paul Sabatier - Toulouse III
• 3. Harrow School of Computer Science - University of Westminster, University of Westminster
• 4. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

Details Citations to the Article (4)
• ## The theoretical capacity of the Parity Source Coder

### Stefano Ciliberti 1, Marc Mezard 1

#### Journal of Statistical Mechanics: Theory and Experiment 1 (2005) P10003

The Parity Source Coder is a protocol for data compression which is based on a set of parity checks organized in a sparse random network. We consider here the case of memoryless unbiased binary sources. We show that the theoretical capacity saturate the Shannon limit at large K. We also find that the first corrections to the leading behavior are exponentially small, so that the behavior at finite K is very close to the optimal one.

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

Details Citations to the Article (3)

• ## Two-dimensional Bose-Einstein Condensate under extreme rotation

### S. Sinha 1, G. V. Shlyapnikov 2, 3

#### Physical Review Letters 94 (2005) 150401

We show that a Bose-condensed gas under extreme rotation in a 2D anisotropic trap, forms a novel elongated quantum fluid which has a roton-maxon excitation spectrum. For a sufficiently large interaction strength, the roton energy reaches zero and the system undergoes a second order quantum transition to the state with a periodic structure - rows of vortices. The number of rows increases with the interaction, and the vortices eventually form a triangular Abrikosov lattice.

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

Details Citations to the Article (24)
• ## Victor J. Emery and recent applications of his ideas

### Serguei Brazovskii 1, 2

#### Synthetic Metals 152 (2005) 309-312

Victor Emery made seminal contributions to the theory of one-dimensional electronic systems and to its applications to organic metals. His inventions became illuminated recently when the joint effect of the ferroelectricity and the charge disproportionation has been discovered in (TMTTF)2X compounds and beyond. Several of his contributions came to agenda at once: separate gaps in spin/charge channels and the route to solitons, 4kF anomaly, dimerization gap, role of ionic transitions. New phenomena unify an unusual variety of concepts: ferroelectricity of good conductors, structural instability towards Mott-Hubbard state, Wigner crystallization in a dense electronic system, ordered 4kF density wave, richness of physics of solitons, interplay of structural and electronic symmetries. The ferroelectric state gives rise to several types of solitons carrying the electron charge, a noninteger charge, spin or both the spin and the charge in special cases. They are clearly observed via conductivity, electric and magnetic susceptibilities. Solitons are challenging for optics where they already seem to determine the pseudogap in absorption. Various features also appear, or are expected, from collective electronic and coupled electron-phonon modes. The last topic, as well as some aspects of physics of solitons, recalls also the contributions of M.J. Rice. Moreover, the observation of Mott-Hubbard states refers to classical results of A.A. Ovchinnikov.

• 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