# LPTMS Publications

Archives :

• ## A functional central limit theorem for interacting particle systems on transitive graphs

### Paul Doukhan 1, 2, Gabriel Lang 3, Sana Louhichi 4, Bernard Ycart 5, 6

#### Markov Processes and Related Fields 14, 1 (2008) 79-114

A finite range interacting particle system on a transitive graph is considered. Assuming that the dynamics and the initial measure are invariant, the normalized empirical distribution process converges in distribution to a centered diffusion process. As an application, a central limit theorem for certain hitting times, interpreted as failure times of a coherent system in reliability, is derived.

• 1. Statistique Appliquée et MOdélisation Stochastique (SAMOS), Université Paris I - Panthéon Sorbonne
• 2. Centre d'économie de la Sorbonne (CES), CNRS : UMR8174 – Université Paris I - Panthéon Sorbonne
• 3. Mathématiques et Informatique Appliquées (MIA), Institut national de la recherche agronomique (INRA) : UMR0518 – AgroParisTech
• 4. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 5. Mathématiques appliquées Paris 5 (MAP5), CNRS : UMR8145 – Université Paris V - Paris Descartes
• 6. Laboratoire de Modélisation et Calcul (LMC - IMAG), CNRS : UMR5523 – Université Joseph Fourier - Grenoble I – Institut National Polytechnique de Grenoble (INPG)

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• ## A Lattice Model for Colloidal Gels and Glasses

### Florent Krzakala 1, Marco Tarzia 2, Lenka Zdeborová 3

#### Physical Review Letters 101 (2008) 165702

We study a lattice model of attractive colloids. It is exactly solvable on sparse random graphs. As the pressure and temperature are varied it reproduces many characteristic phenomena of liquids, glasses and colloidal systems such as ideal gel formation, liquid-glass phase coexistence, jamming, or the reentrance of the glass transition.

• 1. CNRS ESPCI, CNRS : UMR7083
• 2. Institut de Physique Théorique (ex SPhT) (IPHT), CNRS : URA2306 – CEA : DSM/IPHT
• 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

Details Citations to the Article (17)
• ## A note on limit shapes of minimal difference partitions

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

#### Journal of Mathematical Physics, Analysis, Geometry 4 (2008) 24

We provide a variational derivation of the limit shape of minimal difference partitions and discuss the link with exclusion statistics. Also see arXiv:0707.2312 for a related paper.

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

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• ## Absolute limit for the capillary rise of a fluid

### Z. Burda 1, A. Krzywicki 2, O. C. Martin 3

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 78 (2008) 046106

Multi-agent models have been used in many contexts to study generic collective behavior. Similarly, complex networks have become very popular because of the diversity of growth rules giving rise to scale-free behavior. Here we study adaptive networks where the agents trade wealth'' when they are linked together while links can appear and disappear according to the wealth of the corresponding agents; thus the agents influence the network dynamics and vice-versa. Our framework generalizes a multi-agent model of Bouchand and Mezard, and leads to a steady state with fluctuating connectivities. The system spontaneously self-organizes into a critical state where the wealth distribution has a fat tail and the network is scale-free; in addition, network heterogeneities lead to enhanced wealth condensation.

• 1. Marian Smoluchowski Institute of Physics and Mark Kac Complex Systems Research Center, Jagellonian University
• 2. Laboratoire de Physique Théorique d'Orsay (LPT), CNRS : UMR8627 – Université Paris XI - Paris Sud
• 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• ## Behavior of Ising Spin Glasses in a Magnetic Field

### Thomas Jorg 1, Helmut G. Katzgraber 2, Florent Krzakala 3

#### Physical Review Letters 100 (2008) 197202

We study the existence of a spin-glass phase in a field using Monte Carlo simulations performed along a nontrivial path in the field--temperature plane that must cross any putative de Almeida-Thouless instability line. The method is first tested on the Ising spin glass on a Bethe lattice where the instability line separating the spin glass from the paramagnetic state is also computed analytically. While the instability line is reproduced by our simulations on the mean-field Bethe lattice, no such instability line can be found numerically for the short-range three-dimensional model.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Theoretische Physik, ETH Zurich
• 3. Laboratoire de Physico-Chimie Théorique (LPCT), CNRS : UMR7083 – ESPCI ParisTech

Details Citations to the Article (39)

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• ## Bethe Ansatz in the Bernoulli Matching Model of Random Sequence Alignment

### Satya N. Majumdar 1, Kirone Mallick 2, Sergei K. Nechaev 1

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 77 (2008) 011110

For the Bernoulli Matching model of sequence alignment problem we apply the Bethe ansatz technique via an exact mapping to the 5-vertex model on a square lattice. Considering the terrace-like representation of the sequence alignment problem, we reproduce by the Bethe ansatz the results for the averaged length of the Longest Common Subsequence in Bernoulli approximation. In addition, we compute the average number of nucleation centers of the terraces.

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

Details Citations to the Article (2)
• ## Breakdown of fluctuation-dissipation relations in granular gases

### J. J. Brey 1, M. I. Garcia de Soria 2, P. Maynar 1, 3

#### Europhysics Letters (EPL) 84 (2008) 24002

A numerical molecular dynamics experiment measuring the two-time correlation function of the transversal velocity field in the homogeneous cooling state of a granular gas is reported. By measuring the decay rate and the amplitude of the correlations, the accuracy of the Landau-Langevin equation of fluctuating hydrodynamics is checked. The results indicate that although a Langevin approach can be valid, the fluctuation-dissipation relation must be modified, since the viscosity parameter appearing in it differs from the usual hydrodynamic shear viscosity.

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

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• ## Brownian motion under annihilation dynamics

### M. I. Garcia de Soria 1, P. Maynar 2, 3, E. Trizac 1

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 78 (2008) 061110

The behavior of a heavy tagged intruder immersed in a bath of particles evolving under ballistic annihilation dynamics is investigated. The Fokker-Planck equation for this system is derived and the peculiarities of the corresponding diffusive behavior are worked out. In the long time limit, the intruder velocity distribution function approaches a Gaussian form, but with a different temperature from its bath counterpart. As a consequence of the continuous decay of particles in the bath, the mean squared displacement increases exponentially in the collision per particle time scale. Analytical results are finally successfully tested against Monte Carlo numerical simulations.

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

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• ## Casimir forces between arbitrary compact objects: Scalar and electromagnetic field

### T. Emig 1, 2, R. L. Jaffe 3

#### Journal of Physics A General Physics 41 (2008) 164001

We develop an exact method for computing the Casimir energy between arbitrary compact objects, both with boundary conditions for a scalar field and dielectrics or perfect conductors for the electromagnetic field. The energy is obtained as an interaction between multipoles, generated by quantum source or current fluctuations. The objects' shape and composition enter only through their scattering matrices. The result is exact when all multipoles are included, and converges rapidly. A low frequency expansion yields the energy as a series in the ratio of the objects' size to their separation. As examples, we obtain this series for two spheres with Robin boundary conditions for a scalar field and dielectric spheres for the electromagnetic field. The full interaction at all separations is obtained for spheres with Robin boundary conditions and for perfectly conducting spheres.

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

Details Citations to the Article (27)
• ## Casimir Forces between Compact Objects: I. The Scalar Case

### T. Emig 1, 2, N. Graham 3, 4, R. L. Jaffe 4, M. Kardar 5

#### Physical Review D 77 (2008) 025005

We have developed an exact, general method to compute Casimir interactions between a finite number of compact objects of arbitrary shape and separation. Here, we present details of the method for a scalar field to illustrate our approach in its most simple form; the generalization to electromagnetic fields is outlined in Ref. [1]. The interaction between the objects is attributed to quantum fluctuations of source distributions on their surfaces, which we decompose in terms of multipoles. A functional integral over the effective action of multipoles gives the resulting interaction. Each object's shape and boundary conditions enter the effective action only through its scattering matrix. Their relative positions enter through universal translation matrices that depend only on field type and spatial dimension. The distinction of our method from the pairwise summation of two-body potentials is elucidated in terms of the scattering processes between three objects. To illustrate the power of the technique, we consider Robin boundary conditions $\phi -\lambda \partial_n \phi=0$, which interpolate between Dirichlet and Neumann cases as $\lambda$ is varied. We obtain the interaction between two such spheres analytically in a large separation expansion, and numerically for all separations. The cases of unequal radii and unequal $\lambda$ are studied. We find sign changes in the force as a function of separation in certain ranges of $\lambda$ and see deviations from the proximity force approximation even at short separations, most notably for Neumann boundary conditions.

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

Details Citations to the Article (62)
• ## Casimir forces between cylinders and plates

### Sahand Jamal Rahi 1, Thorsten Emig 2, 3, Robert L. Jaffe 4, Mehran Kardar 1

#### Physical Review A: Atomic, Molecular and Optical Physics 78 (2008) 012104

We study collective interaction effects that result from the change of free quantum electrodynamic field fluctuations by one- and two-dimensional perfect metal structures. The Casimir interactions in geometries containing plates and cylinders is explicitly computed using partial wave expansions of constrained path integrals. We generalize previously obtained results and provide a more detailed description of the technical aspects of the approach \cite{Emig06}. We find that the interactions involving cylinders have a weak logarithmic dependence on the cylinder radius, reflecting that one-dimensional perturbations are marginally relevant in 4D space-time. For geometries containing two cylinders and one or two plates, we confirm a previously found non-monotonic dependence of the interaction on the object's separations which does not follow from pair-wise summation of two-body forces. Qualitatively, this effect is explained in terms of fluctuating charges and currents and their mirror images.

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

Details Citations to the Article (31)
• ## Circular dielectric cavity and its deformations

### R. Dubertrand 1, E. Bogomolny 1, Nadia Djellali 2, Mélanie Lebental 1, 2, C. Schmit 1

#### Physical Review A: Atomic, Molecular and Optical Physics 77 (2008) 013804

The construction of perturbation series for slightly deformed dielectric circular cavity is discussed in details. The obtained formulae are checked on the example of cut disks. A good agreement is found with direct numerical simulations and far-field experiments.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Laboratoire de Photonique Quantique et Moléculaire (LPQM), CNRS : UMR8537 – École normale supérieure de Cachan - ENS Cachan

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• ## Collective excitations of trapped one-dimensional dipolar quantum gases

### P. Pedri 1, S. De Palo 2, 3, Edmond Orignac 4, R. Citro 5, M. L. Chiofalo 6, 7

#### Physical Review A: Atomic, Molecular and Optical Physics 77 (2008) 015601

We calculate the excitation modes of a 1D dipolar quantum gas confined in a harmonic trap with frequency $\omega_0$ and predict how the frequency of the breathing n=2 mode characterizes the interaction strength evolving from the Tonks-Girardeau value $\omega_2=2\omega_0$ to the quasi-ordered, super-strongly interacting value $\omega_2=\sqrt{5}\omega_0$. Our predictions are obtained within a hydrodynamic Luttinger-Liquid theory after applying the Local Density Approximation to the equation of state for the homogeneous dipolar gas, which are in turn determined from Reptation Quantum Monte Carlo simulations. They are shown to be in quite accurate agreement with the results of a sum-rule approach. These effects can be observed in current experiments, revealing the Luttinger-liquid nature of 1D dipolar Bose gases.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Dipartimento di Fisica Teorica, INFN – Università degli studi di Trieste
• 3. DEMOCRITOS, Consiglio Nazionale delle Ricerche
• 4. Laboratoire de Physique de l'ENS Lyon (Phys-ENS), CNRS : UMR5672 – École Normale Supérieure - Lyon
• 5. Dipartimento di Fisica "E. R. Caianiello" and CNISM, Università degli studi di Salerno
• 6. INFN Dipartimento di Matematica,, Università di Pisa
• 7. Centre Emile Borel, Institut Henri Poincaré

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• ## Collisional properties of weakly bound heteronuclear dimers

### B. Marcelis 1, 2, S. J. J. M. F. Kokkelmans 1, G. V. Shlyapnikov 2, 3, D. S. Petrov 2, 4

#### Physical Review A: Atomic, Molecular and Optical Physics 77 (2008) 032707

We consider collisional properties of weakly bound heteronuclear molecules (dimers) formed in a two-species mixture of atoms with a large mass difference. We focus on dimers containing light fermionic atoms as they manifest collisional stability due to an effective dimer-dimer repulsion originating from the exchange of the light atoms. In order to solve the dimer-dimer scattering problem we develop a theoretical approach, which provides a physically transparent and quantitative description of this four-atom system in terms of three- and two-body observables. We calculate the elastic scattering amplitude and the rates of inelastic processes such as the trimer formation and the relaxation of dimers into deeply bound molecular states. Irrespective of whether the heavy atoms are bosons or fermions, the inelastic rate can be significantly lower than the rate of elastic collisions. Moreover, the measurement of the inelastic rate which is a four-body observable, can be an efficient and precise tool for determining three-body observables such as the three-body parameter, positions of Efimov states and their lifetimes.

• 1. Eindhoven University of Technology (TUE), Eindhoven University of Technology
• 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
• 4. National Research Centre "Kurchatov Institute" (NRC KI), University of Moscow

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• ## Collisional statistics of the hard-sphere gas

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

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 77 (2008) 041117

We investigate the probability distribution function of the free flight time and of the number of collisions in a hard sphere gas at equilibrium. At variance with naive expectation, the latter quantity does not follow Poissonian statistics, even in the dilute limit which is the focus of the present analysis. The corresponding deviations are addressed both numerically and analytically. In writing an equation for the generating function of the cumulants of the number of collisions, we came across a perfect mapping between our problem and a previously introduced model: the probabilistic ballistic annihilation process [Coppex et al., Phys. Rev. E 69 11303 (2004)]. We exploit this analogy to construct a Monte-Carlo like algorithm able to investigate the asymptotically large time behavior of the collisional statistics within a reasonable computational time. In addition, our predictions are confronted against the results of Molecular Dynamics simulations and Direct Simulation Monte Carlo technique. An excellent agreement is reported.

• 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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• ## Comment on ‘Ultrametricity in the Edwards-Anderson Model’

### Thomas Jorg 1, Florent Krzakala 2

#### Physical Review Letters 100 (2008) 159701

In a recent interesting Letter Contucci {\it et al.} have investigated several properties of the three-dimensional (3d) Edwards-Anderson (EA) Ising spin glass. They claim to have found strong numerical evidence for the presence of a complex ultrametric structure similar to the one described by the replica symmetry breaking solution of the mean field model. We illustrate by numerical simulations that the relations used by Contucci {\it et al.} as evidence for an ultrametric structure in the 3d EA model are fulfilled to similar accuracy in the two-dimensional EA model, which is well-described by the droplet picture and has no spin glass phase at finite temperature. We conclude that the data presented in the Contucci {\it et al.} Letter is not sufficient to dismiss the possibility that, e.g., the droplet model might describe the behavior of the 3d EA model.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Laboratoire de Physico-Chimie Théorique (LPCT), CNRS : UMR7083 – ESPCI ParisTech

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• ## Condensation and Extreme Value Statistics

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

#### Journal of Statistical Mechanics (2008) 05004

We study the factorised steady state of a general class of mass transport models in which mass, a conserved quantity, is transferred stochastically between sites. Condensation in such models is exhibited when above a critical mass density the marginal distribution for the mass at a single site develops a bump, $p_{\rm cond}(m)$, at large mass $m$. This bump corresponds to a condensate site carrying a finite fraction of the mass in the system. Here, we study the condensation transition from a different aspect, that of extreme value statistics. We consider the cumulative distribution of the largest mass in the system and compute its asymptotic behaviour. We show 3 distinct behaviours: at subcritical densities the distribution is Gumbel; at the critical density the distribution is Fréchet, and above the critical density a different distribution emerges. We relate $p_{\rm cond}(m)$ to the probability density of the largest mass in the system.

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

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• ## Constraint satisfaction problems with isolated solutions are hard

### Lenka Zdeborová 1, 2, Marc Mézard 1

#### Journal of Statistical Mechanics: Theory and Experiment (2008) 12004

We study the phase diagram and the algorithmic hardness of the random locked' constraint satisfaction problems, and compare them to the commonly studied 'non-locked' problems like satisfiability of boolean formulas or graph coloring. The special property of the locked problems is that clusters of solutions are isolated points. This simplifies significantly the determination of the phase diagram, which makes the locked problems particularly appealing from the mathematical point of view. On the other hand we show empirically that the clustered phase of these problems is extremely hard from the algorithmic point of view: the best known algorithms all fail to find solutions. Our results suggest that the easy/hard transition (for currently known algorithms) in the locked problems coincides with the clustering transition. These should thus be regarded as new benchmarks of really hard constraint satisfaction problems.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Theorical Division (LANL), Los Alamos National Laboratory,

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• ## Critical Temperature Curve in the BEC-BCS Crossover

### Evgeni Burovski 1, Evgeny Kozik 2, Nikolay Prokof'Ev 3, 4, 5, Boris Svistunov 3, 4, Matthias Troyer 6

#### Physical Review Letters 101 (2008) 090402

The strongly-correlated regime of the BCS-BEC crossover can be realized by diluting a system of two-component fermions with a short-range attractive interaction. We investigate this system via a novel continuous-space-time diagrammatic determinant Monte Carlo method and determine the universal curve $T_c/\epsilon_F$ for the transition temperature between the normal and the superfluid states as a function of the scattering length with the maximum on the BEC side. At unitarity, we confirm that $T_c/\epsilon_F = 0.152(7)$.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Department of Physics, Department of Physics University of Massachussetts
• 3. Department of Physics, University of Massachussetts
• 4. National Research Centre "Kurchatov Institute" (NRC KI), University of Moscow
• 5. Theoretische Physik, EHT, Theoretische Physik, EHT
• 6. Institut für Theoretische Physik, ETH Zurich

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• ## Crowding at the Front of the Marathon Packs

### Sanjib Sabhapandit 1, Satya N. Majumdar 1, S. Redner 2

#### Journal of statistical mechanics-theory and experiment (2008) L03001

We study the crowding of near-extreme events in the time gaps between successive finishers in major international marathons. Naively, one might expect these gaps to become progressively larger for better-placing finishers. While such an increase does indeed occur from the middle of the finishing pack down to approximately 20th place, the gaps saturate for the first 10-20 finishers. We give a probabilistic account of this feature. However, the data suggests that the gaps have a weak maximum around the 10th place, a feature that seems to have a sociological origin.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Center for Polymer Studies (CPS), Boston University

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• ## Deformations of the Tracy-Widom distribution

### O. Bohigas 1, J. X. de Carvalho 2, 3, M. P. Pato 1, 2

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 79 (2008) 031117

In random matrix theory (RMT), the Tracy-Widom (TW) distribution describes the behavior of the largest eigenvalue. We consider here two models in which TW undergoes transformations. In the first one disorder is introduced in the Gaussian ensembles by superimposing an external source of randomness. A competition between TW and a normal (Gaussian) distribution results, depending on the spreading of the disorder. The second model consists in removing at random a fraction of (correlated) eigenvalues of a random matrix. The usual formalism of Fredholm determinants extends naturally. A continuous transition from TW to the Weilbull distribution, characteristc of extreme values of an uncorrelated sequence, is obtained.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Instituto de Fisica, Universidade de São Paulo
• 3. Max-Planck-Institut für Physik komplexer Systeme, Max-Planck-Institut

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• ## Dipole Oscillations of a Bose-Einstein Condensate in Presence of Defects and Disorder

### M. Albert 1, T. Paul 1, N. Pavloff 1, P. Leboeuf 1

#### Physical Review Letters 100 (2008) 250405

We consider dipole oscillations of a trapped dilute Bose-Einstein condensate in the presence of a scattering potential consisting either in a localized defect or in an extended disordered potential. In both cases the breaking of superfluidity and the damping of the oscillations are shown to be related to the appearance of a nonlinear dissipative flow. At supersonic velocities the flow becomes asymptotically dissipationless.

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

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• ## Disordered ensembles of random matrices

### O. Bohigas 1, J. X. de Carvalho 2, 3, M. P. Pato 1, 2

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 77 (2008) 011122

It is shown that the families of generalized matrix ensembles recently considered which give rise to an orthogonal invariant stable L\'{e}vy ensemble can be generated by the simple procedure of dividing Gaussian matrices by a random variable. The nonergodicity of this kind of disordered ensembles is investigated. It is shown that the same procedure applied to random graphs gives rise to a family that interpolates between the Erd\'{o}s-Renyi and the scale free models.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Instituto de Fisica, Universidade de São Paulo
• 3. Max-Planck-Institut für Physik komplexer Systeme, Max-Planck-Institut

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• ## Distance matrices and isometric embeddings

### E. Bogomolny 1, O. Bohigas 1, C. Schmit 1

#### Journal of Mathematical Physics, Analysis, Geometry 4 (2008) 7

We review the relations between distance matrices and isometric embeddings and give simple proofs that distance matrices defined on euclidean and spherical spaces have all eigenvalues except one non-negative. Several generalizations are discussed.

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

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• ## Distributions of Conductance and Shot Noise and Associated Phase Transitions

### Pierpaolo Vivo 1, Satya N. Majumdar 2, Oriol Bohigas 2

#### Physical Review Letters 101 (2008) 216809

For a chaotic cavity with two indentical leads each supporting N channels, we compute analytically, for large N, the full distribution of the conductance and the shot noise power and show that in both cases there is a central Gaussian region flanked on both sides by non-Gaussian tails. The distribution is weakly singular at the junction of Gaussian and non-Gaussian regimes, a direct consequence of two phase transitions in an associated Coulomb gas problem.

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

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• ## Dynamics of Annihilation I : Linearized Boltzmann Equation and Hydrodynamics

### M. I. Garcia de Soria 1, P. Maynar 2, 3, G. Schehr 2, A. Barrat 2, E. Trizac 1

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 77 (2008) 051127

We study the non-equilibrium statistical mechanics of a system of freely moving particles, in which binary encounters lead either to an elastic collision or to the disappearance of the pair. Such a system of {\em ballistic annihilation} therefore constantly looses particles. The dynamics of perturbations around the free decay regime is investigated from the spectral properties of the linearized Boltzmann operator, that characterize linear excitations on all time scales. The linearized Boltzmann equation is solved in the hydrodynamic limit by a projection technique, which yields the evolution equations for the relevant coarse-grained fields and expressions for the transport coefficients. We finally present the results of Molecular Dynamics simulations that validate the theoretical predictions.

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

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• ## Dynamics of Annihilation II: Fluctuations of Global Quantities

### P. Maynar 1, 2, M. I. Garcia de Soria 3, G. Schehr 1, A. Barrat 1, E. Trizac 3

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 77 (2008) 051128

We develop a theory for fluctuations and correlations in a gas evolving under ballistic annihilation dynamics. Starting from the hierarchy of equations governing the evolution of microscopic densities in phase space, we subsequently restrict to a regime of spatial homogeneity, and obtain explicit predictions for the fluctuations and time correlation of the total number of particles, total linear momentum and total kinetic energy. Cross-correlations between these quantities are worked out as well. These predictions are successfully tested against Molecular Dynamics and Monte-Carlo simulations. This provides strong support for the theoretical approach developed, including the hydrodynamic treatment of the spectrum of the linearized Boltzmann operator. This article is a companion paper to arXiv:0801.2299 and makes use of the spectral analysis reported there.

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

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• ## Entropic effects in the very-low-temperature regime of diluted Ising spin glasses with discrete couplings

### Thomas Jorg 1, Federico Ricci-Tersenghi 2, 3

#### Physical Review Letters 100 (2008) 177203

We study link-diluted $\pm J$ Ising spin glass models on the hierarchical lattice and on a three-dimensional lattice close to the percolation threshold. We show that previously computed zero temperature fixed points are unstable with respect to temperature perturbations and do not belong to any critical line in the dilution-temperature plane. We discuss implications of the presence of such spurious unstable fixed points on the use of optimization algorithms, and we show how entropic effects should be taken into account to obtain the right physical behavior and critical points.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Dipartimento di Fisica and INFM, Università degli studi di Roma I - La Sapienza
• 3. International Centre for Theoretical Physics (ICTP), the Abdus Salam International Centre for Theoretical Physics

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• ## Equation of state and effective mass of the unitary Fermi gas in a 1D periodic potential

### Gentaro Watanabe 1, 2, Giuliano Orso 3, Franco Dalfovo 4, Lev P. Pitaevskii 5, 6, Sandro Stringari 7

#### Physical Review A: Atomic, Molecular and Optical Physics 78 (2008) 063619

By solving the Bogoliubov -- de Gennes equations at zero temperature, we study the effects of a one-dimensional optical lattice on the behavior of a superfluid Fermi gas at unitarity. We show that, due to the lattice, at low densities the gas becomes highly compressible and the effective mass is large, with a consequent significant reduction of the sound velocity. We discuss the role played by the lattice in the formation of molecules and the emergence of two-dimensional effects in the equation of state. Predictions for the density profiles and for the frequency of the collective oscillations in the presence of harmonic trapping are also given.

• 1. CNR INFM-BEC and Departement of physics, University of Trento
• 2. RIKEN The Insititute of Chemical and Physical Research, RIKEN the insititute of chemical and physical research
• 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 4. CNR INFM BEC and Departement of physics, University of Trento
• 5. Kapitza Institute for Physical Problems, Kapitza Institute for Physical Problems
• 6. CNR INFM BEC and Departement of Physics, University of Trento
• 7. CNR-INFM BEC Center, Universita di Trento

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• ## Equation of state for hard sphere fluids with and without Kac tails

### E. Trizac 1, I. Pagonabarraga 2

#### American Journal of Physics 76 (2008) 777

In this note, we propose a simple derivation of the one dimensional hard rod equation of state, with and without a Kac tail (appended long range and weak potential). The case of hard spheres in higher dimension is also addressed and it is shown there that our arguments --which avoid any mathematical complication-- allow to recover the virial form of the equation of state in a direct way.

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

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• ## Evidence for universal scaling in the spin-glass phase

### Thomas Jorg 1, Helmut G. Katzgraber 2

#### Physical Review Letters 101 (2008) 197205

We perform Monte Carlo simulations of Ising spin-glass models in three and four dimensions, as well as of Migdal-Kadanoff spin glasses on a hierarchical lattice. Our results show strong evidence for universal scaling in the spin-glass phase in all three models. Not only does this allow for a clean way to compare results obtained from different coupling distributions, it also suggests that a so far elusive renormalization group approach within the spin-glass phase may actually be feasible.

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

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• ## Exact distribution of the maximal height of watermelons

### Gregory Schehr 1, Satya N. Majumdar 2, Alain Comtet 2, Julien Randon-Furling 2

#### Physical Review Letters 101 (2008) 150601

We study p non intersecting one-dimensional Brownian walks, either excursions (p-watermelons with a wall) or bridges (p-watermelons without wall). We focus on the maximal height H_p of these p-watermelons configurations on the unit time interval. Using path integral techniques associated to corresponding models of free Fermions, we compute exactly the distribution of H_p for generic integer p. For large p, one obtains < H_p > \sim \sqrt{2p} for p-watermelons with a wall whereas < H_p > \sim \sqrt{p} for p-watermelons without wall. We point out and solve a discrepancy between these exact asymptotic behaviors and numerical experiments, which recently attracted much attention, and we show that only the pre-asymptotic behaviors of these averages were actually measured. In addition, our method, using tools of many-body physics, provides a simpler physical derivation of the connection between vicious walkers and random matrix theory.

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

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• ## Exact Minimum Eigenvalue Distribution of an Entangled Random Pure State

### Satya N. Majumdar 1, Oriol Bohigas 1, Arul Lakshminarayan 2, 3

#### Journal of Statistical Physics 131 (2008) 33-49

A recent conjecture regarding the average of the minimum eigenvalue of the reduced density matrix of a random complex state is proved. In fact, the full distribution of the minimum eigenvalue is derived exactly for both the cases of a random real and a random complex state. Our results are relevant to the entanglement properties of eigenvectors of the orthogonal and unitary ensembles of random matrix theory and quantum chaotic systems. They also provide a rare exactly solvable case for the distribution of the minimum of a set of N {\em strongly correlated} random variables for all values of N (and not just for large N).

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Max-Planck-Institut für Physik komplexer Systeme, Max-Planck-Institut
• 3. Department of Physics, Indian Institute of Technology Madras

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• ## Exact treatment of exciton-polaron formation by Diagrammatic Monte Carlo

### Evgeni Burovski 1, Holger Fehske 2, Andrei S. Mishchenko 3, 4

#### Physical Review Letters 101 (2008) 116403

We develop an approximation-free Diagrammatic Monte Carlo technique to study fermionic particles interacting with each other simultaneously through both an attractive Coulomb potential and bosonic excitations of the underlying medium. Exemplarily we apply the method to the long-standing exciton-polaron problem and present numerically exact results for the wave function, ground-state energy, binding energy and effective mass of this quasiparticle. Focusing on the electron-hole pair bound-state formation, we discuss various limiting cases of a generic exciton-polaron model. The frequently used instantaneous approximation to the retarded interaction due to the phonon exchange is found to be of very limited applicability. For the case of a light electron and heavy hole the system is well approximated by a particle in the field of a static attractive impurity.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Institut Fur Physik, Ernst-Moritz-Arndt-Universitat Greifswald
• 3. CMRG Cross-Correlated Materials Research Group, CMRG
• 4. "Kurchakov Institute" Russian Research Centre, Kurchakov Institute

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• ## Exhaustive enumeration unveils clustering and freezing in random 3-SAT

### John Ardelius 1, Lenka Zdeborová 2

#### Physica E: Low-dimensional Systems and Nanostructures 78 (2008) 040101

We study geometrical properties of the complete set of solutions of the random 3-satisfiability problem. We show that even for moderate system sizes the number of clusters corresponds surprisingly well with the theoretic asymptotic prediction. We locate the freezing transition in the space of solutions which has been conjectured to be relevant in explaining the onset of computational hardness in random constraint satisfaction problems.

• 1. Swedish Institute of Computeur science (SICS), SICS Swedish Institute of Computeur science
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• ## Extreme statistics of complex random and quantum chaotic states

### Arul Lakshminarayan 1, Steven Tomsovic 1, Oriol Bohigas 2, Satya N. Majumdar 2

#### Physical Review Letters 100 (2008) 044103

An exact analytical description of extreme intensity statistics in complex random states is derived. These states have the statistical properties of the Gaussian and Circular Unitary Ensemble eigenstates of random matrix theory. Although the components are correlated by the normalization constraint, it is still possible to derive compact formulae for all values of the dimensionality N. The maximum intensity result slowly approaches the Gumbel distribution even though the variables are bounded, whereas the minimum intensity result rapidly approaches the Weibull distribution. Since random matrix theory is conjectured to be applicable to chaotic quantum systems, we calculate the extreme eigenfunction statistics for the standard map with parameters at which its classical map is fully chaotic. The statistical behaviors are consistent with the finite-N formulae.

• 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

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• ## Fermions out of Dipolar Bosons in the lowest Landau level

### Brice Chung 1, Thierry Jolicoeur 1

#### Physical Review A: Atomic, Molecular and Optical Physics 77 (2008) 043608

In the limit of very fast rotation atomic Bose-Einstein condensates may reside entirely in the lowest two-dimensional Landau level (LLL). For small enough filling factor of the LLL, one may have formation of fractional quantum Hall states. We investigate the case of bosons with dipolar interactions as may be realized with Chromium-52 atoms. We show that at filling factor equal to unity the ground state is a Moore-Read (a.k.a Pfaffian) paired state as is the case of bosons with purely s-wave scattering interactions. This Pfaffian state is destabilized when the interaction in the s-wave channel is small enough and the ground state is a stripe phase with unidimensional density modulation. For filling factor 1/3, we show that there is formation of a Fermi sea of composite fermions''. These composites are made of one boson bound with three vortices. This phase has a wide range of stability and the effective mass of the fermions depends essentially only of the scattering amplitude in momentum channels larger or equal to 2. The formation of such a Fermi sea opens up a new possible route to detection of the quantum Hall correlations.

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

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• ## Finite Layer Thickness Stabilizes the Pfaffian State for the 5/2 Fractional Quantum Hall Effect: Wavefunction Overlap and Topological Degeneracy

### Michael. R. Peterson 1, Th. Jolicoeur 2, S. Das Sarma 3

#### Physical Review Letters 101 (2008) 016807

We find the finite-width, i.e., the layer thickness, of experimental quasi-two dimensional systems produces a physical environment sufficient to stabilize the Moore-Read Pfaffian state thought to describe the fractional quantum Hall effect at filling factor $\nu=5/2$. This conclusion is based on exact calculations performed in the spherical and torus geometries, studying wavefunction overlap and ground state degeneracy

• 1. Condensed Matter theory center, departement of physic., Condensed matter theory center
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 3. Condensed Matter Theory Center, Department of Physics, University of Maryland at College Park

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• ## Fluctuation induced quantum interactions between compact objects and a plane mirror

### Thorsten Emig 1

#### Journal of Statistical Mechanics: Theory and Experiment (2008) P04007

The interaction of compact objects with an infinitely extended mirror plane due to quantum fluctuations of a scalar or electromagnetic field that scatters off the objects is studied. The mirror plane is assumed to obey either Dirichlet or Neumann boundary conditions or to be perfectly reflecting. Using the method of images, we generalize a recently developed approach for compact objects in unbounded space [1,2] to show that the Casimir interaction between the objects and the mirror plane can be accurately obtained over a wide range of separations in terms of charge and current fluctuations of the objects and their images. Our general result for the interaction depends only on the scattering matrices of the compact objects. It applies to scalar fields with arbitrary boundary conditions and to the electromagnetic field coupled to dielectric objects. For the experimentally important electromagnetic Casimir interaction between a perfectly conducting sphere and a plane mirror we present the first results that apply at all separations. We obtain both an asymptotic large distance expansion and the two lowest order correction terms to the proximity force approximation. The asymptotic Casimir-Polder potential for an atom and a mirror is generalized to describe the interaction between a dielectric sphere and a mirror, involving higher order multipole polarizabilities that are important at sub-asymptotic distances.

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

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• ## Geometrical dependence of decoherence by electronic interactions in a GaAs/GaAlAs square network

### M. Ferrier 1, A. C. H. Rowe 1, S. Gueron 1, 2, H. Bouchiat 1, C. Texier 1, 3, G. Montambaux 1

#### Physical Review Letters 100 (2008) 146802

We investigate weak localization in metallic networks etched in a two dimensional electron gas between $25\:$mK and $750\:$mK when electron-electron (e-e) interaction is the dominant phase breaking mechanism. We show that, at the highest temperatures, the contributions arising from trajectories that wind around the rings and trajectories that do not are governed by two different length scales. This is achieved by analyzing separately the envelope and the oscillating part of the magnetoconductance. For $T\gtrsim0.3\:$K we find $\Lphi^\mathrm{env}\propto{T}^{-1/3}$ for the envelope, and $\Lphi^\mathrm{osc}\propto{T}^{-1/2}$ for the oscillations, in agreement with the prediction for a single ring \cite{LudMir04,TexMon05}. This is the first experimental confirmation of the geometry dependence of decoherence due to e-e interaction.

• 1. Laboratoire de Physique des Solides (LPS), CNRS : UMR8502 – Université Paris XI - Paris Sud
• 2. Quantronics group, Service de Physique de l'Etat Condensé, IRAMIS (QUANTRONICS), CEA : DSM/IRAMIS – CNRS : URA2464
• 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• ## Ground states of colloidal molecular crystals on periodic substrates

### Samir El Shawish 1, Jure Dobnikar 1, Emmanuel Trizac 2

#### Soft Matter 4 (2008) 1491-1498

Two dimensional suspensions of spherical colloids subject to periodic external fields exhibit a rich variety of molecular crystalline phases. We study in simulations the ground state configurations of dimeric and trimeric systems, that are realized on square and triangular lattices, when either two or three macroions are trapped in each external potential minimum. Bipartite orders of the checkerboard or stripe types are reported together with more complex quadripartite orderings, and the shortcomings of envisioning the colloids gathered in a single potential minimum as a composite rigid object are discussed. This work also sheds light on simplifying assumptions underlying previous theoretical treatments and that made possible the mapping onto spin models.

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

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• ## Ising model with memory: coarsening and persistence properties

### Fabio Caccioli 1, 2, Silvio Franz 3, Matteo Marsili 4

#### Journal of Statistical Mechanics: Theory and Experiment (2008) 07006

We consider the coarsening properties of a kinetic Ising model with a memory field. The probability of a spin-flip depends on the persistence time of the spin in a state. The more a spin has been in a given state, the less the spin-flip probability is. We numerically studied the growth and persistence properties of such a system on a two dimensional square lattice. The memory introduces energy barriers which freeze the system at zero temperature. At finite temperature we can observe an apparent arrest of coarsening for low temperature and long memory length. However, since the energy barriers introduced by memory are due to local effects, there exists a timescale on which coarsening takes place as for the Ising model. Moreover the two point correlation functions of the Ising model with and without memory are the same, indicating that they belong to the same universality class.

• 1. international school for advenced stydy, international school
• 2. Istituto Nazionale di Fisica Nucleare, Istituto Nazionale di Fisica Nucleare
• 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 4. The Abdus Salam International Centre for Theoretical Physics, ICTP Trieste

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• ## Kramers degeneracy in a magnetic field and Zeeman spin-orbit coupling in antiferromagnetic conductors

### Revaz Ramazashvili 1, 2

#### Physical Review Letters 101 (2008) 137202

In this article, I study magnetic response of electron wavefunctions in a commensurate collinear antiferromagnet. I show that, at a special set of momenta, hidden anti-unitary symmetry protects Kramers degeneracy of Bloch eigenstates against a magnetic field, pointing transversely to staggered magnetization. Hence a substantial momentum dependence of the transverse g-factor in the Zeeman term, turning the latter into a spin-orbit coupling, that may be present in materials from chromium to borocarbides, cuprates, pnictides, as well as organic and heavy fermion conductors.

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

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• ## Localization for one-dimensional random potentials with large local fluctuations

### Tom Bienaime 1, Christophe Texier 1

#### Journal of Physics A Mathematical and Theoretical 41 (2008) 475001

We study the localization of wave functions for one-dimensional Schrödinger Hamiltonians with random potentials $V(x)$ with short range correlations and large local fluctuations such that $\int\D{x} \smean{V(x)V(0)}=\infty$. A random supersymmetric Hamiltonian is also considered. Depending on how large the fluctuations of $V(x)$ are, we find either new energy dependences of the localization length, $\ell_\mathrm{loc}\propto{}E/\ln{E}$, $\ell_\mathrm{loc}\propto{}E^{\mu/2}$ with $0<\mu<2$ or $\ell_\mathrm{loc}\propto\ln^{\mu-1}E$ for $\mu>1$, or superlocalization (decay of the wave functions faster than a simple exponential).

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

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• ## Locked constraint satisfaction problems

### Lenka Zdeborová 1, Marc Mézard 1

#### Physical Review Letters 101 (2008) 078702

We introduce and study the random 'locked' constraint satisfaction problems. When increasing the density of constraints, they display a broad 'clustered' phase in which the space of solutions is divided into many isolated points. While the phase diagram can be found easily, these problems, in their clustered phase, are extremely hard from the algorithmic point of view: the best known algorithms all fail to find solutions. We thus propose new benchmarks of really hard optimization problems and provide insight into the origin of their typical hardness.

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

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• ## Many-Body Physics and Quantum Chaos

### Denis Ullmo 1

#### Reports on Progress in Physics 71 (2008) 026001

Experimental progresses in the miniaturisation of electronic devices have made routinely available in the laboratory small electronic systems, on the micron or sub-micron scale, which at low temperature are sufficiently well isolated from their environment to be considered as fully coherent. Some of their most important properties are dominated by the interaction between electrons. Understanding their behaviour therefore requires a description of the interplay between interference effects and interactions. The goal of this review is to address this relatively broad issue, and more specifically to address it from the perspective of the quantum chaos community. I will therefore present some of the concepts developed in the field of quantum chaos which have some application to study many-body effects in mesoscopic and nanoscopic systems. Their implementation is illustrated on a few examples of experimental relevance such as persistent currents, mesoscopic fluctuations of Kondo properties or Coulomb blockade. I will furthermore try to bring out, from the various physical illustrations, some of the specific advantages on more general grounds of the quantum chaos based approach.

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

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• ## Mesoscopic Fluctuations of the Pairing Gap

### S. Åberg 1, H. Olofsson 1, P. Leboeuf 2

#### AIP Conference Proceedings 995 (2008) 173-184

A description of mesoscopic fluctuations of the pairing gap in finite-sized quantum systems based on periodic orbit theory is presented. The size of the fluctuations are found to depend on quite general properties. We distinguish between systems where corresponding classical motion is regular or chaotic, and describe in detail fluctuations of the BCS gap as a function of the size of the system. The theory is applied to different mesoscopic systems: atomic nuclei, metallic grains, and ultracold fermionic gases. We also present a detailed description of pairing gap variation with particle number for nuclei based on a deformed cavity potential.

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

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• ## New Routes to Solitons in Quasi One-Dimensional Conductors

### S. Brazovskii 1

#### Solid State Sciences 10 (2008) 1786

We collect evidences on existence of microscopic solitons, and their determining role in electronic processes of quasi-1D conductors. The ferroelectric charge ordering gives access to several types of solitons in conductivity and permittivity, and to solitons' bound pairs in optics - both in insulating and conducting cases of TMTTF and TMTSF subfamilies. The excursion to physics of conjugated polymers allows to suggest further experiments. Internal tunnelling in Charge Density Waves goes through the channel of 'amplitude solitons', which correspond to the long sought quasi-particle - the spinon. The same experiment gives an access to the reversible reconstruction of the junction via spontaneous creation of a lattice of 2Pi solitons - a grid of dislocations. The individual 2Pi solitons have been visually captured in recent STM experiments. Junctions of organic and oxide conductors are anticipated to show similar effects of reconstruction.

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

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• ## Non Poissonian statistics in a low density fluid

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

#### The Journal of Physical Chemistry B 112, 17 (2008) 5412

Our interest goes to the collisional statistics in an arbitrary interacting fluid. We show that even in the low density limit and contrary to naive expectation, the number of collisions experienced by a tagged particle in a given time does not obey Poisson law, and that conversely, the free flight time distribution is not a simple exponential. As an illustration, the hard sphere fluid case is worked out in detail. For this model, we quantify analytically those deviations and successfully compare our predictions against molecular dynamics simulations.

• 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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• ## Nonmonotonic effects of parallel sidewalls on Casimir forces between cylinders

### Sahand Jamal Rahi 1, Alejandro W. Rodriguez 1, Thorsten Emig 2, 3, Robert L. Jaffe 4, Steven G. Johnson 5, Mehran Kardar 1

#### Physical Review A: Atomic, Molecular and Optical Physics 77 (2008) 030101

We analyze the Casimir force between two parallel infinite metal cylinders, with nearby metal plates (sidewalls), using complementary methods for mutual confirmation. The attractive force between cylinders is shown to have a nonmonotonic dependence on the separation to the plates. This intrinsically multi-body phenomenon, which occurs with either one or two sidewalls (generalizing an earlier result for squares between two sidewalls), does not follow from any simple two-body force description. We can, however, explain the nonmonotonicity by considering the screening (enhancement) of the interactions by the fluctuating charges (currents) on the two cylinders, and their images on the nearby plate(s). Furthermore, we show that this effect also implies a nonmonotonic dependence of the cylinder-plate force on the cylinder-cylinder separation.

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

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• ## Numerical studies of planar closed random walks

### Jean Desbois 1, Stephane Ouvry 1

#### Journal of Statistical Mechanics (2008) 08004

Lattice numerical simulations for planar closed random walks and their winding sectors are presented. The frontiers of the random walks and of their winding sectors have a Hausdorff dimension $d_H=4/3$. However, when properly defined by taking into account the inner 0-winding sectors, the frontiers of the random walks have a Hausdorff dimension $d_H\approx 1.77$.

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

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• ## On the Doubly Refined Enumeration of Alternating Sign Matrices and Totally Symmetric Self-Complementary Plane Partitions

### T. Fonseca 1, Paul Zinn-Justin 1

#### The Electronic Journal of Combinatorics 15 (2008) R81

We prove the equality of doubly refined enumerations of Alternating Sign Matrices and of Totally Symmetric Self-Complementary Plane Partitions using integral formulae originating from certain solutions of the quantum Knizhnik--Zamolodchikov equation.

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

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• ## On the spectrum of the Laplace operator of metric graphs attached at a vertex — Spectral determinant approach

### Christophe Texier 1, 2

#### Journal of Physics A General Physics 41 (2008) 085207

We consider a metric graph $\mathcal{G}$ made of two graphs $\mathcal{G}_1$ and $\mathcal{G}_2$ attached at one point. We derive a formula relating the spectral determinant of the Laplace operator $S_\mathcal{G}(\gamma)=\det(\gamma-\Delta)$ in terms of the spectral determinants of the two subgraphs. The result is generalized to describe the attachment of $n$ graphs. The formulae are also valid for the spectral determinant of the Schrödinger operator $\det(\gamma-\Delta+V(x))$.

• 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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• ## On the spin-liquid phase of one dimensional spin-1 bosons

### F. H. L. Essler 1, G. V. Shlyapnikov 2, 3, A. M. Tsvelik 4

#### Journal of Statistical Mechanics: Theory and Experiment (2008) 020027

We consider a model of one dimensional spin-1 bosons with repulsive density-density interactions and antiferromagnetic exchange. We show that the low energy effective field theory is given by a spin-charge separated theory of a Tomonaga-Luttinger Hamiltonian and the O(3) nonlinear sigma model describing collective charge and spin excitations respectively. At a particular ratio of the density-density to spin-spin interaction the model is integrable, and we use the exact solutions to provide an independent derivation of the low energy effective theory. The system is in a superfluid phase made of singlet pairs of bosons, and we calculate the long-distance asymptotics of certain correlation functions.

• 1. The Rudolf Peirls Centre for Theoretical Physics, University of Oxford
• 2. Van der Waals-Zeeman Institute, University of Amsterdam
• 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 4. Department of Condensed Matter Physics and Material Science, Brookhaven National Laboratory

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• ## Optimal Time to Sell a Stock in Black-Scholes Model: Comment on ‘Thou shall buy and hold’, by A. Shiryaev, Z. Xu and X.Y. Zhou

### Satya N. Majumdar 1, Jean-Philippe Bouchaud 2

#### Quantitative Finance 8 (2008) 753-760

We reconsider the problem of optimal time to sell a stock studied recently by Shiryaev, Xu and Zhou using path integral methods. This method allows us to confirm the results obtained by these authors and extend them to a parameter region inaccessible to the method used by Shiryaev et. al. We also obtain the full distribution of the time t_m at which the maximum of the price is reached for arbitrary values of the drift.

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

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• ## Orbital Landau level dependence of the fractional quantum Hall effect in quasi-two dimensional electron layers: finite-thickness effects

### Michael R. Peterson 1, Th. Jolicoeur 2, S. Das Sarma 3

#### Physical Review B 78 (2008) 155308

The fractional quantum Hall effect (FQHE) in the second orbital Landau level at filling factor 5/2 remains enigmatic and motivates our work. We consider the effect of the quasi-2D nature of the experimental FQH system on a number of FQH states (fillings 1/3, 1/5, 1/2) in the lowest, second, and third Landau levels (LLL, SLL, TLL,) by calculating the overlap, as a function of quasi-2D layer thickness, between the exact ground state of a model Hamiltonian and the consensus variational wavefunctions (Laughlin wavefunction for 1/3 and 1/5 and the Moore-Read Pfaffian wavefunction for 1/2). Using large overlap as a stability, or FQHE robustness, criterion we find the FQHE does not occur in the TLL (for any thickness), is the most robust for zero thickness in the LLL for 1/3 and 1/5 and for 11/5 in the SLL, and is most robust at finite-thickness (4-5 magnetic lengths) in the SLL for the mysterious 5/2 state and the 7/3 state. No FQHE is found at 1/2 in the LLL for any thickness. We examine the orbital effects of an in-plane (parallel) magnetic field finding its application effectively reduces the thickness and could destroy the FQHE at 5/2 and 7/3, while enhancing it at 11/5 as well as for LLL FQHE states. The in-plane field effects could thus be qualitatively different in the LLL and the SLL by virtue of magneto-orbital coupling through the finite thickness effect. In the torus geometry, we show the appearance of the threefold topological degeneracy expected for the Pfaffian state which is enhanced by thickness corroborating our findings from overlap calculations. Our results have ramifications for wavefunction engineering--the possibility of creating an optimal experimental system where the 5/2 FQHE state is more likely described by the Pfaffian state with applications to topological quantum computing.

• 1. Condensed Matter theory center, departement of physic., Condensed matter theory center
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 3. Condensed Matter Theory Center, Department of Physics, University of Maryland at College Park

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• ## Orientation dependence of Casimir forces

### T. Emig 1, 2, N. Graham 3, R. L. Jaffe 4, M. Kardar 5

#### Physical Review A: Atomic, Molecular and Optical Physics 79 (2008) 054901

The Casimir interaction between two objects, or between an object and a plane, depends on their relative orientations. We make these angular dependences explicit by considering prolate or oblate spheroids. The variation with orientation is calculated exactly at asymptotically large distances for the electromagnetic field, and at arbitrary separations for a scalar field. For a spheroid in front of a mirror, the leading term is orientation independent, and we find the optimal orientation from computations at higher order.

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

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• ## Overlap Interfaces in Hierarchical Spin-Glass models

### Silvio Franz 1, T Jorg 1, Giorgio Parisi 2

#### Journal of Statistical Mechanics: Theory and Experiment (2008) 02002

We discuss interfaces in spin glasses. We present new theoretical results and a numerical method to characterize overlap interfaces and the stability of the spin-glass phase in extended disordered systems. We use this definition to characterize the low temperature phase of hierarchical spin-glass models. We use the Replica Symmetry Breaking theory to evaluate the cost for an overlap interface, which in these models is particularly simple. A comparison of our results from numerical simulations with the theoretical predictions shows good agreement.

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

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• ## Phase Transition in a Random Minima Model: Mean Field Theory and Exact Solution on the Bethe Lattice

### Peter Sollich 1, Satya N Majumdar 2, Alan J Bray 3

#### Journal of Statistical Mechanics: Theory and Experiment (2008) 11011

We consider the number and distribution of minima in random landscapes defined on non-Euclidean lattices. Using an ensemble where random landscapes are reweighted by a fugacity factor $z$ for each minimum they contain, we construct first a two-box' mean field theory. This exhibits an ordering phase transition at $z\c=2$ above which one box contains an extensive number of minima. The onset of order is governed by an unusual order parameter exponent $\beta=1$, motivating us to study the same model on the Bethe lattice. Here we find from an exact solution that for any connectivity $\mu+1>2$ there is an ordering transition with a conventional mean field order parameter exponent $\beta=1/2$, but with the region where this behaviour is observable shrinking in size as $1/\mu$ in the mean field limit of large $\mu$. We show that the behaviour in the transition region can also be understood directly within a mean field approach, by making the assignment of minima soft'. Finally we demonstrate, in the simplest mean field case, how the analysis can be generalized to include both maxima and minima. In this case an additional first order phase transition appears, to a landscape in which essentially all sites are either minima or maxima.

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

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• ## Phase Transitions and Computational Difficulty in Random Constraint Satisfaction Problems

### Florent Krzakala 1, Lenka Zdeborová 2

#### Journal of Physics: Conference Series 95 (2008) 012012

We review the understanding of the random constraint satisfaction problems, focusing on the q-coloring of large random graphs, that has been achieved using the cavity method of the physicists. We also discuss the properties of the phase diagram in temperature, the connections with the glass transition phenomenology in physics, and the related algorithmic issues.

• 1. Laboratoire de Physico-Chimie Théorique (LPCT), CNRS : UMR7083 – ESPCI ParisTech
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• ## Potts Glass on Random Graphs

### Florent Krzakala 1, Lenka Zdeborová 2

#### Europhysics Letters (EPL) 81 (2008) 57005

We solve the q-state Potts model with anti-ferromagnetic interactions on large random lattices of finite coordination. Due to the frustration induced by the large loops and to the local tree-like structure of the lattice this model behaves as a mean field spin glass. We use the cavity method to compute the temperature-coordination phase diagram and to determine the location of the dynamic and static glass transitions, and of the Gardner instability. We show that for q>=4 the model possesses a phenomenology similar to the one observed in structural glasses. We also illustrate the links between the positive and the zero-temperature cavity approaches, and discuss the consequences for the coloring of random graphs. In particular we argue that in the colorable region the one-step replica symmetry breaking solution is stable towards more steps of replica symmetry breaking.

• 1. Laboratoire de Physico-Chimie Théorique (LPCT), CNRS : UMR7083 – ESPCI ParisTech
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• ## Quantum detection of electronic flying qubits

### G. Fève 1, 2, Pascal Degiovanni 3, 4, Th. Jolicoeur 5

#### Physical Review B 77 (2008) 035308

We consider a model of a detector of ballistic electrons at the edge of a two-dimensional electron gas in the integer quantum Hall regime. The electron is detected by capacitive coupling to a gate which is also coupled to a passive RC circuit. Using a quantum description of this circuit, we determine the signal over noise ratio of the detector in term of the detector characteristics. The back-action of the detector on the incident wavepacket is then computed using a Feynman-Vernon influence functional approach. Using information theory, we define the appropriate notion of quantum limit for such an 'on the fly' detector. We show that our particular detector can approach the quantum limit up to logarithms in the ratio of the measurement time over the RC relaxation time. We argue that such a weak logarithmic effect is of no practical significance. Finally we show that a two-electron interference experiment can be used to probe the detector induced decoherence.

• 1. Laboratoire Pierre Aigrain (LPA), CNRS : UMR8551 – Université Paris VI - Pierre et Marie Curie – Université Paris VII - Paris Diderot – Ecole Normale Supérieure de Paris - ENS Paris
• 2. Laboratoire de photonique et de nanostructures (LPN), CNRS : UPR20
• 3. Laboratoire de Physique de l'ENS Lyon (Phys-ENS), CNRS : UMR5672 – École Normale Supérieure - Lyon
• 4. Physics Department [Boston] (BU-Physics), Boston University
• 5. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• ## Quantum Knizhnik-Zamolodchikov Equation, Totally Symmetric Self-Complementary Plane Partitions and Alternating Sign Matrices

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

#### Theoretical and Mathematical Physics 154 (2008) 331-348

We present multiresidue formulae for partial sums in the basis of link patterns of the polynomial solution to the level 1 U_q(\hat sl_2) quantum Knizhnik--Zamolodchikov equation at generic values of the quantum parameter q. These allow for rewriting and generalizing a recent conjecture [Di Francesco '06] connecting the above to generating polynomials for weighted Totally Symmetric Self-Complementary Plane Partitions. We reduce the corresponding conjectures to a single integral identity, yet to be proved.

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

### Stefan Mashkevich 1, Stéphane Ouvry 2

#### Journal of statistical mechanics-theory and experiment (2008) P03018

At 6th order in perturbation theory, the random magnetic impurity problem at second order in impurity density narrows down to the evaluation of a single Feynman diagram with maximal impurity line crossing. This diagram can be rewritten as a sum of ordinary integrals and nested double integrals of products of the modified Bessel functions $K_{\nu}$ and $I_{\nu}$, with $\nu=0,1$. That sum, in turn, is shown to be a linear combination with rational coefficients of $(2^5-1)\zeta(5)$, $\int_0^{\infty} u K_0(u)^6 du$ and $\int_0^{\infty} u^3 K_0(u)^6 du$. Unlike what happens at lower orders, these two integrals are not linear combinations with rational coefficients of Euler sums, even though they appear in combination with $\zeta(5)$. On the other hand, any integral $\int_0^{\infty} u^{n+1} K_0(u)^p (uK_1(u))^q du$ with weight $p+q=6$ and an even $n$ is shown to be a linear combination with rational coefficients of the above two integrals and 1, a result that can be easily generalized to any weight $p+q=k$. A matrix recurrence relation in $n$ is built for such integrals. The initial conditions are such that the asymptotic behavior is determined by the smallest eigenvalue of the transition matrix.

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

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• ## Random subcubes as a toy model for constraint satisfaction problems

### Thierry Mora 1, 2, Lenka Zdeborova 1

#### Journal of Statistical Physics 131 (2008) 1121-1138

We present an exactly solvable random-subcube model inspired by the structure of hard constraint satisfaction and optimization problems. Our model reproduces the structure of the solution space of the random k-satisfiability and k-coloring problems, and undergoes the same phase transitions as these problems. The comparison becomes quantitative in the large-k limit. Distance properties, as well the x-satisfiability threshold, are studied. The model is also generalized to define a continuous energy landscape useful for studying several aspects of glassy dynamics.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Lewis-Sigler Institute for Integrative Genomics, Princeton University

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Details
• ## Residual Coulomb interaction fluctuations in chaotic systems: the boundary, random plane waves, and semiclassical theory

### Steven Tomsovic 1, Denis Ullmo 2, Arnd Baecker 3

#### Physical Review Letters 100 (2008) 164101

New fluctuation properties arise in problems where both spatial integration and energy summation are necessary ingredients. The quintessential example is given by the short-range approximation to the first order ground state contribution of the residual Coulomb interaction. The dominant features come from the region near the boundary where there is an interplay between Friedel oscillations and fluctuations in the eigenstates. Quite naturally, the fluctuation scale is significantly enhanced for Neumann boundary conditions as compared to Dirichlet. Elements missing from random plane wave modeling of chaotic eigenstates lead surprisingly to significant errors, which can be corrected within a purely semiclassical approach.

• 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. Institut für Theoretische Physik,, Technische Universität Dresden

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• ## Semiclassical Theory of Bardeen-Cooper-Schrieffer Pairing-Gap Fluctuations

### H. Olofsson 1, S. Åberg 1, P. Leboeuf 2

#### Physical Review Letters 100 (2008) 0370005

Superfluidity and superconductivity are genuine many-body manifestations of quantum coherence. For finite-size systems the associated pairing gap fluctuates as a function of size or shape. We provide a parameter free theoretical description of pairing fluctuations in mesoscopic systems characterized by order/chaos dynamics. The theory accurately describes experimental observations of nuclear superfluidity (regular system), predicts universal fluctuations of superconductivity in small chaotic metallic grains, and provides a global analysis in ultracold Fermi gases.

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

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• ## Semiclassical theory of non-local statistical measures: residual Coulomb interactions

### Denis Ullmo 1, Steven Tomsovic 1, 2, 3, Arnd Baecker 4

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 79 (2008) 056217

In a recent letter [Phys. Rev. Lett. {\bf 100}, 164101 (2008)] and within the context of quantized chaotic billiards, random plane wave and semiclassical theoretical approaches were applied to an example of a relatively new class of statistical measures, i.e. measures involving both complete spatial integration and energy summation as essential ingredients. A quintessential example comes from the desire to understand the short-range approximation to the first order ground state contribution of the residual Coulomb interaction. Billiards, fully chaotic or otherwise, provide an ideal class of systems on which to focus as they have proven to be successful in modeling the single particle properties of a Landau-Fermi liquid in typical mesoscopic systems, i.e. closed or nearly closed quantum dots. It happens that both theoretical approaches give fully consistent results for measure averages, but that somewhat surprisingly for fully chaotic systems the semiclassical theory gives a much improved approximation for the fluctuations. Comparison of the theories highlights a couple of key shortcomings inherent in the random plane wave approach. This paper contains a complete account of the theoretical approaches, elucidates the two shortcomings of the oft-relied-upon random plane wave approach, and treats non-fully chaotic systems as well.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Max-Planck-Institut für Physik komplexer Systeme, Max-Planck-Institut
• 3. Department of Physics, Washington State University
• 4. Institut für Theoretische Physik,, Technische Universität Dresden

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• ## Simple Glass Models and their Quantum Annealing

### Thomas Jorg 1, Florent Krzakala 2, Jorge Kurchan 3, A. C. Maggs 2

#### Physical Review Letters 101 (2008) 147204

We study first order quantum phase transitions in mean-field spin glasses. We solve the quantum Random Energy Model using elementary methods and show that at the transition the eigenstate suddenly projects onto the unperturbed ground state and that the gap between the lowest states is exponentially small in the system size. We argue that this is a generic feature of all Random First Order' models, which includes benchmarks such as random satisfiability. We introduce a two-time instanton to calculate this gap in general, and discuss the consequences for quantum annealing.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Laboratoire de Physico-Chimie Théorique (LPCT), CNRS : UMR7083 – ESPCI ParisTech
• 3. Physique et mécanique des milieux hétérogenes (PMMH), CNRS : UMR7636 – Université Paris VI - Pierre et Marie Curie – Université Paris VII - Paris Diderot – ESPCI ParisTech

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• ## Spin glass models with Kac interactions

### Silvio Franz 1

#### European Physical Journal B 64 (2008) 557-561

In this paper I will review my work on disordered systems -spin glass model with two body and $p>2$ body interactions- with long but finite interaction range $R$. I will describe the relation of these model with Mean Field Theory in the Kac limit and some attempts to go beyond mean field.

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

Details
• ## Stability of dark solitons in three dimensional dipolar Bose-Einstein condensates

### R. Nath 1, P. Pedri 2, 3, L. M.N.B.F. Santos 1

#### Physical Review Letters 101 (2008) 210402

The dynamical stability of dark solitons in dipolar Bose-Einstein condensates is studied. For standard short-range interacting condensates dark solitons are unstable against transverse excitations in two and three dimensions. On the contrary, due to its non local character, the dipolar interaction allows for stable 3D stationary dark solitons, opening a qualitatively novel scenario in nonlinear atom optics. We discuss in detail the conditions to achieve this stability, which demand the use of an additional optical lattice, and the stability regimes.

• 1. Institut fur Theoretische Physik, Leibniz Universität Hannover
• 2. Laboratoire de Physique Théorique de la Matière Condensée (LPTMC), CNRS : UMR7600 – Université Paris VI - Pierre et Marie Curie
• 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• ## Stability of the fermionic gases close to a p-wave Feshbach resonance

### J. Levinsen 1, N. R. Cooper 2, V. Gurarie 3

#### Physical Review A: Atomic, Molecular and Optical Physics 78 (2008) 063616

We study the stability of the paired fermionic p-wave superfluid made out of identical atoms all in the same hyperfine state close to a p-wave Feshbach resonance. First we reproduce known results concerning the lifetime of a 3D superfluid, in particular, we show that it decays at the same rate as its interaction energy, thus precluding its equilibration before it decays. Then we proceed to study its stability in case when the superfluid is confined to 2D by means of an optical harmonic potential. We find that the relative stability is somewhat improved in 2D in the BCS regime, such that the decay rate is now slower than the appropriate interaction energy scale. The improvement in stability, however, is not dramatic and one probably needs to look for other mechanisms to suppress decay to create a long lived 2D p-wave fermionic superfluid.

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

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• ## Statistical Properties of the Final State in One-dimensional Ballistic Aggregation

### Satya N. Majumdar 1, Kirone Mallick 2, Sanjib Sabhapandit 3

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 79 (2008) 021109

We investigate the long time behaviour of the one-dimensional ballistic aggregation model that represents a sticky gas of N particles with random initial positions and velocities, moving deterministically, and forming aggregates when they collide. We obtain a closed formula for the stationary measure of the system which allows us to analyze some remarkable features of the final fan' state. In particular, we identify universal properties which are independent of the initial position and velocity distributions of the particles. We study cluster distributions and derive exact results for extreme value statistics (because of correlations these distributions do not belong to the Gumbel-Frechet-Weibull universality classes). We also derive the energy distribution in the final state. This model generates dynamically many different scales and can be viewed as one of the simplest exactly solvable model of N-body dissipative dynamics.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Service de Physique Théorique (SPhT), CNRS : URA2306 – CEA : DSM/SPHT
• 3. Raman Research Institute, Raman Research Insitute

Details Citations to the Article (1)
• ## Statistics of the total number of collisions and the ordering time in a freely expanding hard-point gas

### Sanjib Sabhapandit 1, Ioana Bena 2, Satya N. Majumdar 1

#### Journal of statistical mechanics-theory and experiment (2008) P05012

We consider a Jepsen gas of $N$ hard-point particles undergoing free expansion on a line, starting from random initial positions of the particles having random initial velocities. The particles undergo binary elastic collisions upon contact and move freely in-between collisions. After a certain ordering time $T_{o}$, the system reaches a `fan'' state where all the velocities are completely ordered from left to right in an increasing fashion and there is no further collision. We compute analytically the distributions of (i) the total number of collisions and (ii) the ordering time $T_{o}$. We show that several features of these distributions are universal.

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

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• ## Structure and thermodynamics of a ferrofluid bilayer

### Carlos Alvarez 1, 2, Martial Mazars 1, Jean-Jacques Weis 1

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 77 (2008) 051501

We present extensive Monte Carlo simulations for the thermodynamic and structural properties of a planar bilayer of dipolar hard spheres for a wide range of densities, dipole moments and layer separations. Expressions for the stress and pressure tensors of the bilayer system are derived. For all thermodynamic states considered the interlayer energy is shown to be attractive and much smaller than the intralayer contribution to the energy. It vanishes at layer separations of the order of two hard sphere diameters. The normal pressure is negative and decays as a function of layer separation $h$ as $-1/h^5$. Intralayer and interlayer pair distribution functions and angular correlation functions are presented. Despite the weak interlayer energy strong positional and orientational correlations exist between particles in the two layers.

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

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• ## Superfluid pairing between fermions with unequal masses

### M. A. Baranov 1, 2, 3, C. Lobo 4, G. V. Shlyapnikov 5

#### Physical Review B 78 (2008) 033620

We consider a superfluid state in a two-component gas of fermionic atoms with equal densities and unequal masses in the BCS limit. We develop a perturbation theory along the lines proposed by Gorkov and Melik-Barkhudarov and find that for a large difference in the masses of heavy ($M$) and light ($m$) atoms one has to take into account both the second-order and third-order contributions. The result for the critical temperature and order parameter is then quite different from the prediction of the simple BCS approach. Moreover, the small parameter of the theory turns out to be $(p_{F}|a|)/\hbar)\sqrt{M/m}\ll1$, where $p_{F}$ is the Fermi momentum, and $a$ the scattering length. Thus, for a large mass ratio $M/m$ the conventional perturbation theory requires significantly smaller Fermi momenta (densities) or scattering lengths than in the case of $M\sim m$, where the small parameter is $(p_{F}|a|)/\hbar)\ll1$. We show that 3-body scattering resonances appearing at a large mass ratio due to the presence of 3-body bound Efimov states do not influence the result, which in this sense becomes universal.

• 1. Van der Waals-Zeeman Institute, Van der Waals-Zeeman Institute
• 2. Institut für Quantenoptik und Quanteninformation, Institut für Quantenoptik und Quanteninformation
• 3. National Research Centre "Kurchatov Institute" (NRC KI), University of Moscow
• 4. School of Physics and Astronomy, University of Nottingham
• 5. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• ## The Mott metal-insulator transition in the 1D Hubbard model in an external magnetic field

### Holger Frahm 1, Temo Vekua 2

#### Journal of statistical mechanics-theory and experiment (2008) P01007

We study the low energy behavior of the one dimensional Hubbard model across the Mott metal-insulator phase transition in an external magnetic field. In particular we calculate elements of the dressed charge matrix at the critical point of the Mott transition for arbitrary Hubbard repulsion and magnetization numerically and, in certain limiting cases, analytically. These results are combined with a non-perturbative effective field theory approach to reveal how the breaking of time reversal symmetry influences the Mott transition.

• 1. Institut fur Theoretische Physik, Leibniz Universitat Hannover
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• ## Theory of subgap interchain tunneling in quasi one-dimensional conductors

### S. Brazovskii 1, 2, S. I. Matveenko 1, 2

#### Physical Review B 77 (2008) 155432

We suggest a theory of internal coherent tunneling in the pseudogap region, when the applied voltage U is below the free electron gap 2Delta_0. We address quasi 1D systems, where the gap is originated by spontaneous lattice distortions of the Incommensurate Charge Density Wave (ICDW) type. Results can be adjusted also to quasi-1D superconductors. The instanton approach allows to calculate the interchain tunneling current both in single electron (amplitude solitons, i.e. spinons) and bi-electron (phase slips) channels. Transition rates are governed by a dissipative dynamics originated by emission of gapless phase excitations in the course of the instanton process. We find that the single-electron tunneling is allowed below the nominal gap 2Delta_0 down to the true pair-breaking threshold at 2W_as<2Delta, where W_as=2Delta/pi is the amplitude soliton energy. Most importantly, the bi-electronic tunneling stretches down to U=0 (in the 1D regime). In both cases, the threshold behavior is given by power laws J (U-U_c)^beta, where the exponent beta v_F/u is large as the ratio of the Fermi velocity v_F and the phase one u. In the 2D or 3D ordered phases, at temperature T

• 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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• ## Thermal Effects in the dynamics of disordered elastic systems

### S. Bustingorry 1, A. B. Kolton 2, A. Rosso 3, W. Krauth 4, T. Giamarchi 5

#### Physica B: Condensed Matter 404 (2008) 444-446

Many seemingly different macroscopic systems (magnets, ferroelectrics, CDW, vortices,..) can be described as generic disordered elastic systems. Understanding their static and dynamics thus poses challenging problems both from the point of view of fundamental physics and of practical applications. Despite important progress many questions remain open. In particular the temperature has drastic effects on the way these systems respond to an external force. We address here the important question of the thermal effect close to depinning, and whether these effects can be understood in the analogy with standard critical phenomena, analogy so useful to understand the zero temperature case. We show that close to the depinning force temperature leads to a rounding of the depinning transition and compute the corresponding exponent. In addition, using a novel algorithm it is possible to study precisely the behavior close to depinning, and to show that the commonly accepted analogy of the depinning with a critical phenomenon does not fully hold, since no divergent lengthscale exists in the steady state properties of the line below the depinning threshold.

• 1. Centro Atomico Bariloche, Centro Atomico
• 2. Centro Atomico Bariloche, Centro Atómico Bariloche
• 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 4. 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
• 5. DPMC (DPMC-MaNEP), University of Geneva

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• ## Trace formula for dieletric cavities : I. General properties

### E. Bogomolny 1, R. Dubertrand 1, C. Schmit 1

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 78 (2008) 056202

The construction of the trace formula for open dielectric cavities is examined in detail. Using the Krein formula it is shown that the sum over cavity resonances can be written as a sum over classical periodic orbits for the motion inside the cavity. The contribution of each periodic orbit is the product of the two factors. The first is the same as in the standard trace formula and the second is connected with the product of reflection coefficients for all points of reflection with the cavity boundary. Two asymptotic terms of the smooth resonance counting function related with the area and the perimeter of the cavity are derived. The coefficient of the perimeter term differs from the one for closed cavities due to unusual high-energy asymptotics of the $\mathbf{S}$-matrix for the scattering on the cavity. Corrections to the leading semi-classical formula are briefly discussed. Obtained formulas agree well with numerical calculations for circular dielectric cavities.

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

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• ## Two-component repulsive Fermi gases with population imbalance in elongated harmonic traps

### M. Colomé-Tatché 1

#### Physical Review A: Atomic, Molecular and Optical Physics 78 (2008) 033612

We study the two-component repulsive Fermi gas with imbalanced populations in one dimension. Starting from the Bethe Ansatz solution we calculate analytically the phase diagram for the homogeneous system. We show that two phases appear: the fully polarised phase and the partially polarised phase. By means of the local density approximation and the equation of state for the homogeneous system we calculate the density profile for the harmonically confined case. We show that a two-shell structure appears: at the center of the cloud we find the partially polarised phase and at the edges the fully polarised one. The radii of the inner and outer shells are calculated for different values of the polarisation and the coupling strength. We calculate the dependence of the magnetisation on the polarisation for different values of the coupling strength and we show that the susceptibility is always finite.

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

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• ## Universal Record Statistics of Random Walks and Lévy Flights

### Satya N. Majumdar 1, Robert M. Ziff 2

#### Physical Review Letters 101 (2008) 050601

It is shown that statistics of records for time series generated by random walks are independent of the details of the jump distribution, as long as the latter is continuous and symmetric. In N steps, the mean of the record distribution grows as the sqrt(4N/pi) while the standard deviation grows as sqrt((2-4/pi) N), so the distribution is non-self-averaging. The mean shortest and longest duration records grow as sqrt(N/pi) and 0.626508... N, respectively. The case of a discrete random walker is also studied, and similar asymptotic behavior is found.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Michigan Center for Theoretical Physics and Department of chemical Engineering, University of Michigan-Ann Arbor

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• ## Universality and universal finite-size scaling functions in four-dimensional Ising spin glasses

### Thomas Jorg 1, Helmut G. Katzgraber 2

#### Physical Review B 77 (2008) 214426

We study the four-dimensional Ising spin glass with Gaussian and bond-diluted bimodal distributed interactions via large-scale Monte Carlo simulations and show via an extensive finite-size scaling analysis that four-dimensional Ising spin glasses obey universality.

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

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• ## Unzipping of two random heteropolymers: Ground state energy and finite size effects

### M. V. Tamm 1, S. K. Nechaev 2

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 78 (2008) 011903

We have analyzed the dependence of average ground state energy per monomer, $e$, of the complex of two random heteropolymers with quenched sequences, on chain length, $n$, in the ensemble of chains with uniform distribution of primary sequences. Every chain monomer is randomly and independently chosen with the uniform probability distribution $p=1/c$ from a set of $c$ different types A, B, C, D, .... Monomers of the first chain could form saturating reversible bonds with monomers of the second chain. The bonds between similar monomer types (like A--A, B--B, C--C, etc.) have the attraction energy $u$, while the bonds between different monomer types (like A--B, A--D, B--D, etc.) have the attraction energy $v$. The main attention is paid to the computation of the normalized free energy $e(n)$ for intermediate chain lengths, $n$, and different ratios $a=\frac{v}{u}$ at sufficiently low temperatures when the entropic contribution of the loop formation is negligible compared to direct energetic interactions between chain monomers and the partition function of the chains is dominated by the ground state. The performed analysis allows one to derive the force, $f$, which is necessary to apply for unzipping of two random heteropolymer chains of equal lengths whose ends are separated by the distance $x$, averaged over all equally distributed primary structures at low temperatures for fixed values $a$ and $c$.

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

Details Citations to the Article (3)
• ## Wetting transition on a one-dimensional disorder

### D. M. Gangardt 1, S. K. Nechaev 2, 3

#### Journal of Statistical Physics 130 (2008) 483-502

We consider wetting of a one-dimensional random walk on a half-line $x\ge 0$ in a short-ranged potential located at the origin $x=0$. We demonstrate explicitly how the presence of a quenched chemical disorder affects the pinning-depinning transition point. For small disorders we develop a perturbative technique which enables us to compute explicitly the averaged temperature (energy) of the pinning transition. For strong disorder we compute the transition point both numerically and using the renormalization group approach. Our consideration is based on the following idea: the random potential can be viewed as a periodic potential with the period $n$ in the limit $n\to\infty$. The advantage of our approach stems from the ability to integrate exactly over all spatial degrees of freedoms in the model and to reduce the initial problem to the analysis of eigenvalues and eigenfunctions of some special non-Hermitian random matrix with disorder--dependent diagonal and constant off-diagonal coefficients. We show that even for strong disorder the shift of the averaged pinning point of the random walk in the ensemble of random realizations of substrate disorder is indistinguishable from the pinning point of the system with preaveraged (i.e. annealed) Boltzmann weight.

• 1. School of Physics and Astronomy, University of Birmingham, University of Birmingham
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 3. P.N. Lebedev Institute, The Russian Academy of Science