# 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 ThÃ©orique et ModÃ¨les Statistiques (LPTMS), CNRS : UMR8626 – UniversitÃ© Paris XI - Paris Sud
• 2. Unite mixte de service de l'institut Henri PoincarÃ© (UMSIHP), CNRS : UMS839 – UniversitÃ© 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 ThÃ©orique (SPhT), CNRS : URA2306 – CEA : DSM/SPHT
• 2. Laboratoire de Physique ThÃ©orique et Hautes Energies (LPTHE), CNRS : UMR7589 – UniversitÃ© Paris VI - Pierre et Marie Curie – UniversitÃ© 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 ThÃ©orique et ModÃ¨les Statistiques (LPTMS), CNRS : UMR8626 – UniversitÃ© 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 ThÃ©orique et ModÃ¨les Statistiques (LPTMS), CNRS : UMR8626 – UniversitÃ© 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 ThÃ©orique et ModÃ¨les Statistiques (LPTMS), CNRS : UMR8626 – UniversitÃ© 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 ThÃ©orique et ModÃ¨les Statistiques (LPTMS), CNRS : UMR8626 – UniversitÃ© 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 ThÃ©orique et ModÃ¨les Statistiques (LPTMS), CNRS : UMR8626 – UniversitÃ© 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 ThÃ©orique et ModÃ¨les Statistiques (LPTMS), CNRS : UMR8626 – UniversitÃ© Paris XI - Paris Sud
• 2. Laboratoire de Physique ThÃ©orique des Liquides (LPTL), CNRS : UMR7600 – UniversitÃ© 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 ThÃ©orique et ModÃ¨les Statistiques (LPTMS), CNRS : UMR8626 – UniversitÃ© Paris XI - Paris Sud
• 2. Laboratoire de Physique des Solides (LPS), CNRS : UMR8502 – UniversitÃ© 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 – UniversitÃ© Paris VI - Pierre et Marie Curie – Ecole Normale SupÃ©rieure de Paris - ENS Paris
• 3. Laboratoire de Physique ThÃ©orique et ModÃ¨les Statistiques (LPTMS), CNRS : UMR8626 – UniversitÃ© 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 ThÃ©orique - IRSAMC (LPT), CNRS : UMR5152 – UniversitÃ© Paul Sabatier - Toulouse III
• 3. Laboratoire de Physique ThÃ©orique et ModÃ¨les Statistiques (LPTMS), CNRS : UMR8626 – UniversitÃ© 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 ThÃ©orique et ModÃ¨les Statistiques (LPTMS), CNRS : UMR8626 – UniversitÃ© 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 ThÃ©orique et ModÃ¨les Statistiques (LPTMS), CNRS : UMR8626 – UniversitÃ© 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 fÃ¼r Theoretische Physik, Universitat Regensburg
• 3. Laboratoire de Physique ThÃ©orique et ModÃ¨les Statistiques (LPTMS), CNRS : UMR8626 – UniversitÃ© 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 ThÃ©orique et ModÃ¨les Statistiques (LPTMS), CNRS : UMR8626 – UniversitÃ© Paris XI - Paris Sud
• 3. Laboratoire Kastler Brossel (LKB (Lhomond)), CNRS : UMR8552 – UniversitÃ© Paris VI - Pierre et Marie Curie – Ecole Normale SupÃ©rieure de Paris - ENS Paris
• 4. Van der Waalsâ€“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 ThÃ©orique et ModÃ¨les Statistiques (LPTMS), CNRS : UMR8626 – UniversitÃ© 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 ThÃ©orique d'Orsay (LPT), CNRS : UMR8627 – UniversitÃ© Paris XI - Paris Sud
• 2. Laboratoire de Physique ThÃ©orique et ModÃ¨les Statistiques (LPTMS), CNRS : UMR8626 – UniversitÃ© Paris XI - Paris Sud
• 3. MatiÃ¨re et SystÃ¨mes Complexes (MSC), CNRS : UMR7057 – UniversitÃ© 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\\Ã¶dinger 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 ThÃ©orique et ModÃ¨les Statistiques (LPTMS), CNRS : UMR8626 – UniversitÃ© Paris XI - Paris Sud
• 2. Unite mixte de service de l'institut Henri PoincarÃ© (UMSIHP), CNRS : UMS839 – UniversitÃ© Paris VI - Pierre et Marie Curie
• 3. Laboratoire de Physique des Solides (LPS), CNRS : UMR8502 – UniversitÃ© 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 ThÃ©orique et ModÃ¨les Statistiques (LPTMS), CNRS : UMR8626 – UniversitÃ© Paris XI - Paris Sud
• 2. Instituut voor Theoretische Fysica, Instituut voor Theoretische Fysica
• 3. Laboratoire de Physique Statistique de l'ENS (LPS), CNRS : UMR8550 – UniversitÃ© Paris VI - Pierre et Marie Curie – UniversitÃ© Paris VII - Paris Diderot – Ecole Normale SupÃ©rieure 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 ThÃ©orique d'Orsay (LPT), CNRS : UMR8627 – UniversitÃ© Paris XI - Paris Sud
• 2. Laboratoire de Physique ThÃ©orique et ModÃ¨les Statistiques (LPTMS), CNRS : UMR8626 – UniversitÃ© 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 ThÃ©orique d'Orsay (LPT), CNRS : UMR8627 – UniversitÃ© Paris XI - Paris Sud
• 2. Laboratoire de Physique ThÃ©orique et ModÃ¨les Statistiques (LPTMS), CNRS : UMR8626 – UniversitÃ© Paris XI - Paris Sud
• 3. MatiÃ¨re et SystÃ¨mes Complexes (MSC), CNRS : UMR7057 – UniversitÃ© 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 ThÃ©orique (SPhT), CNRS : URA2306 – CEA : DSM/SPHT
• 2. Laboratoire de Physique ThÃ©orique et ModÃ¨les Statistiques (LPTMS), CNRS : UMR8626 – UniversitÃ© Paris XI - Paris Sud
• 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 ThÃ©orique et ModÃ¨les Statistiques (LPTMS), CNRS : UMR8626 – UniversitÃ© 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 ThÃ©orique et ModÃ¨les Statistiques (LPTMS), CNRS : UMR8626 – UniversitÃ© 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 ThÃ©orique et ModÃ¨les Statistiques (LPTMS), CNRS : UMR8626 – UniversitÃ© Paris XI - Paris Sud
• 2. Departament de FÃ­sica Fonamental, Universitat de Barcelona

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

### Patricio Leboeuf 1

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• ## Fermi Edic d State K050oingsa qu class='pub_soustitre'>Retter, Jibhu Kheruntsyausup>1, C. J. Ullmo 1, 2, Hong&nbsSin densup>11, D. M.&nb. Baranger 1

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Details Citations to the Article (11)
• ## Interactr, and Sorttraint satisfaction problems, Fredeetter, JiNbtkizin;1< HonnbsTh Maryosal&nbiamarchhup>1, Matteo4 class='pub_refbib'>Physical Revie, T3PL) 72 (2005) 201310We ttionnvolvingnass="publoximatiois clalhey ain densitrstanding creasing ilyuS&dsime: A Qcts (gou noheat spbservht sa Theplestsaa Boseagnass="publ alhey atLwspro,gvv n oa theedee e ut-oons ted (SPsing 120y strdidarkdsObservg distsoew qortioof statEsteina theoretits sioci$\\ainglE. 1. Laboratoire de Physique ThÃ©orique et ModÃ¨les Statistiques (LPTMS), CNRS : UMR8626 – UniversitÃ©try, Duke University Down9oad PDF via arXiV.org Details Citati1s to the Article (45) • arlass='pub_r75nal de Ph343c-372ces de la Physique (2005) 213 • Jscsoustitre'>Alberto&nb'pub_soustZinn-Jeriansup>, Frederics Yua N.zard&nbajumd2, Hong&n4 class='pub_refbib'>Journal ofL815-L82tters 95 (2005) 200202 • 1. Laborat(SPhTModÃ¨les StaRA230ques (LPTMS), CNRS CEA StDSM/SPHTke Physics, Duke University • 2. LaboratoirHau-paeE distribue eHEModÃ¨les Stati7589ues (LPTMS), CNRS : UMR8626 &ndVsh;&n;Rosatoireic r Cuc rues (LPTMS), CNRS : UMR8626 &ndVssh; UDtry otersitÃ©try, Duke University • Down09ad PDF via arXiV.org Details Citati4ns to the Article (11) • 1, FrC. J. UllmoGctiessup>, umndambauxsup>, Frederics Yua N.zard&nbajumd2, Hong&n4 class='pub_refbib'>Journal of3455-347tters 95 (2005) 200202 e in a Rants oum flldvralodi, aftstiAAS lmeansMatteo4 n closd fromisderity c4> ac(0queo002ja, anl o den ofinglW d , duetpowtweee ffuserva betweewirbu randomnt satisfaac(0queocl ap o den ofts ing Couna, aftpowensarbitng nunet pretamainredue d oWekinkeyiegdip aum ions in quantum clatimong l class='pub_labos'> • 1. Laboratoire de Physique ThÃ©orique et ModÃ¨les Statistiques (LPTMS), CNRS : UMR8626 – UniversitÃ©ics, Duke University • Down09ad PDF via arXiV.org Details Citations to the Article (11) • Marc fua., Fournier, T., Mossang, E. Ph Mib'>risd:al of StatisEe armodehear,1tesical ReviP090etters 95 (2005) 110202We addr$Q$,on for cterizntum f thmces, denylfamilzing thproblroscdomnt up#3oabearikingtnves ideRier The$\\zd(0(3) two a$\\zd(0(2)$egdip aum ions in quantum clatimong l class='pub_labos'>
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Details Citati4s to the Article (11)
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Details Citatios to the Article (45)
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## Level omique : entre Ordre et Chaos., Fournier, T., Mossang, E.

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Details Citati102s to the Article (45)
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Details Citati4s to the Article (11)
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Details Citati2ns to the Article (11)
• ## Interactr, and Sortivngthse-Ein Pthatory traint satisfaction problems2,/h3>

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• Fermi Edic d State K050oingJoesoustitCharXioustitre'>Alberto&nbCyriltkizinFurtlehnersup>, Frederics YujaMarcangerC gasf thup>1, Fredeard&nb.N.B.van Wijlara&osup>1,/h3> Ph Mib'>risd:al of StatisEe armodehear,Ptesical ReviP1101tters 95 (2005) 110202aatn thegef= frgen1ereBydy e are li>owwus dotuilibtstols of tsCoes fGanx su3-SATe-oons tgvngth o fie th, taodcalnx o, $QAlasersolvilÃtwcse don- odehb the aris='mpareed syiy )igrows acdlog(N)amic aractoy ditwo-pardct in mir thelSIodÃlSIke Physics, l class='pub_labos'> • 1. Laboratoire de Physique ThÃ©orique et ModÃ¨les Statistiques (LPTMS), CNRS : UMR8626 – UniversitÃ©ics3e ICTPodÃICTPersitÃ© Paris XI - Paris Sud • 3. De Download PDF via arXiV.org Details Citati9s to the Article (11) • , CucasseoRr, Byshev, Yu.I., MGrÃƒ_bin,iG,p;Baranger 1 J 13nal de Ph125es de la Physique (2005) 213 • Fermi Edic d State K050oingJac SidnarJ.LAmo&JleutodHr., Fournier, T., Mossang, E. arlass='pubB 716al de Ph439-461ic, Singapore (2005) 248-255 Download PDF via arXiV.org Details • Fermi Edic d State K050oingOlivi aer&nPavlbsp;2tre'>Marc fua., Fournier, T., Mossang, E. Ph Mib'>risd:al of StatisEe armodehear,1tesical ReviP04007ters 95 (2005) 110202ows uttion.), se ueoinvevi • ONnn'rmdes idetadue d oe co be nd lucdap'pviegrapheforte n tutth from an RPA-lcal propertiet the l class='pub_labos'> • 1. Laboratoire de Physique ThÃ©orique et ModÃ¨les Statistiques (LPTMS), CNRS : UMR8626 – UniversitÃ© Paris XI - Paris Sud • 3. De Download PDF via arXiV.org Details Citatios to the Article (45) • 1, FredeSatya&nbsaroRrangerCEveucthup>1, Fredeard&nb.N.B.van Wijlara&osup>1,/h3> #### 4hysical Revie8060tters 95 (2005) 200202 thth>38ss d euc-thipo be n dh w srile distethealaoor prenifnoccucains calcts' and Sortions euche groredeaadue esfactalocergyd on the boundmidyna dentacrsehe sCoes fe and Sortivnges fe and StLw hhe ptWol ilibratris='pu_are and Sortireg>D\d:aldvrw tempemeie and Sortivf gaussianris='mpareed dentacr"> ## Inhn bulkd flK050oiore obree noeffn anis$L^{1/2}$rw temp$L$ipst'>Wesan batsehe, redea feef="greg>D\rw tempemei"> ## Inhn bulkd flK050oiore be whna doffne Klyroniq dentacre and Sortiteakipstall-gaussianedWi meeeraloto'>Wsevea. Then$L vnges f rahe pred frcumttalcGanx suSindiikesrth from an RPA-lcal propertiet the l class='pub_labos'> 1. Laboratoire de Physique ThÃ©orique et ModÃ¨les Statistiques (LPTMS), CNRS : UMR8626 – UniversitÃ©ics, Schoose denCeeelkd preStob'>goritPoocese devngScis/p> atisEnginealak ituVi-ai oteTib'ersitÃ© Paris XI - Paris Sud3. De Download PDF via arXiV.org Details Citati44s to the Article (11)

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