# Publications

• ## Tunneling and the Band Structure of Chaotic Systems

### Leboeuf Patricio 1, Amaury Mouchet 2

#### Physical Review Letters 73 (1994) 1360

We compute the dispersion laws of chaotic periodic systems using the semiclassical periodic orbit theory to approximate the trace of the powers of the evolution operator. Aside from the usual real trajectories, we also include complex orbits. These turn out to be fundamental for a proper description of the band structure since they incorporate conduction processes through tunneling mechanisms. The results obtained, illustrated with the kicked-Harper model, are in excellent agreement with numerical simulations, even in the extreme quantum regime.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Laboratoire de Mathématiques et Physique Théorique (LMPT), CNRS : UMR6083 – Université François Rabelais - Tours

Details Citations to the Article (28)
• ## New evidence of GOE statistics for compound nuclear resonances

### M. Lombardi 1 O. Bohigas 2, 3 T. H. Seligman 3, 4

#### Physics Letters B, Elsevier, 1994, 324, pp.263-266. <10.1016/0370-2693(94)90191-0>

New statistical measures are applied to the previously compiled nuclear data ensemble in order to further test energy level fluctuations as well as the absence of correlations between levels and intensities. Data are found to be consistent with the predictions of the Wigner-Dyson random matrix model.

• 1. LSP - Laboratoire de Spectrométrie Physique
• 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
• 3. Wissenschaftskolleg zu Berlin
• 4. Laboratorio de Cuernavaca

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• ## Anyonic Partition Functions and Windings of Planar Brownian Motion

### Jean Desbois 1, Christine Heinemann 1, Stephane Ouvry 1

#### Physical Review D 51 (1995) 942-945

The computation of the $N$-cycle brownian paths contribution $F_N(\\alpha)$ to the $N$-anyon partition function is adressed. A detailed numerical analysis based on random walk on a lattice indicates that $F_N^{(0)}(\\alpha)= \\prod_{k=1}^{N-1}(1-{N\\over k}\\alpha)$. In the paramount $3$-anyon case, one can show that $F_3(\\alpha)$ is built by linear states belonging to the bosonic, fermionic, and mixed representations of $S_3$.

• 1. Division de Physique Théorique, IPN, Université Paris XI - Paris Sud

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• ## Bound states of 3He in 3He-4He mixture films.

### E. Bashkin 1, 2, N. Pavloff 3, J. Treiner. 3

#### Journal of Low Temperature Physics 99 (1995) 659-681

3He atoms dissolved in superfluid 4He may form dimers (3He)2 in two-dimensional geometries. We study dimer formation in films of dilute 3He-4He mixture. After designing a schematic 3He-3He interaction potential we calculate the dimer binding energy for various substrates. It is shown that 3He impurity states localized near the substrate give rise to the largest magnitudes of the binding energies.

• 1. Department of Physics and Material Sciences Center, Philipps University
• 2. Kapitza Institute for Physical Problems, Kapitza Institute for Physical Problems
• 3. Division de Physique Théorique, IPN, Université Paris XI - Paris Sud

Details Citations to the Article (9)
• ## Calogero Models for Distinguishable Particles

### Cyril Furtlehner 1, Stephane Ouvry 1

#### Modern Physics Letters B 9 (1995) 503-509

Motivated by topological bidimensional quantum models for distinguishable particles, and by Haldane\'s definition of mutual statistics for different species of particles, we propose a new class of one-dimensional $1/r_{ij}^2$ Calogero model with coupling constants $g_{ij}$ depending on the labels of the particles. We solve the groundstate problem, and show how to build some classes of excited states.

• 1. Division de Physique Théorique, IPN, Université Paris XI - Paris Sud

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• ## Comment on \’ Thermodynamics of a One- Dimensional Ideal Gas with fractional Exclusion Statistics \’

### Alain Dasnieres De Veigy 1, Stéphane Ouvry 1

#### Physical Review Letters 75 (1995) 352

In a recent letter -Phys. Rev. Lett. 73, 3331 (1995)-, the conclusion was reached that, in the one-dimensional Calogero model, only the second virial coefficient is affected by the statistical parameter $\\alpha$, where $\\alpha$ is related to the coupling constant $\\kappa/ x_{ij}^2$ of the Calogero interaction by $\\kappa=\\alpha(\\alpha+1)$. We argue that it is not so, i.e. all virial coefficients are affected, if the thermodynamic limit is properly taken.

• 1. Division de Physique Théorique, IPN, Université Paris XI - Paris Sud

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• ## Diffractive orbits in quantum billiards

### Nicolas Pavloff 1, Charles Schmit 1

#### Physical Review Letters 75 (1995) 61-64

We study diffractive effects in two dimensional polygonal billiards. We derive an analytical trace formula accounting for the role of non-classical diffractive orbits in the quantum spectrum. As an illustration the method is applied to a triangular billiard.

• 1. Division de Physique Théorique, IPN, Université Paris XI - Paris Sud

Details Citations to the Article (43)
• ## Diffusive transport in a one-dimensional disordered potential involving correlations

### Cecile Monthus 1, 2

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 52 (1995) 2569-2573

This article deals with transport properties of one dimensional Brownian diffusion under the influence of a correlated quenched random force, distributed as a two-level Poisson process. We find in particular that large time scaling laws of the position of the Brownian particle are analogous to the uncorrelated case. We discuss also the probability distribution of the stationary flux going through a sample between two prescribed concentrations, which differs significantly from the uncorrelated case.

• 1. Division de Physique Théorique, IPN, Université Paris XI - Paris Sud
• 2. L.P.T.P.E, Université Paris VI - Pierre et Marie Curie

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• ## Localization Properties in One Dimensional Disordered Supersymmetric Quantum Mechanics

### A. Comtet 1, J. Desbois 1, C. Monthus 1

#### Annals of Physics 239 (1995) 312-350

A model of localization based on the Witten Hamiltonian of supersymmetric quantum mechanics is considered. The case where the superpotential $\\phi(x)$ is a random telegraph process is solved exactly. Both the localization length and the density of states are obtained analytically. A detailed study of the low energy behaviour is presented. Analytical and numerical results are presented in the case where the intervals over which $\\phi(x)$ is kept constant are distributed according to a broad distribution. Various applications of this model are considered.

• 1. Division de Physique Théorique, IPN, Université Paris XI - Paris Sud

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• ## Magnetic Moment and Perturbation Theory with Singular Magnetic Fields

### Alain Comtet 1, Stefan Mashkevich 2, Stéphane Ouvry 1

#### Physical Review D 52 (1995) 2594-2597

The spectrum of a charged particle coupled to Aharonov-Bohm/anyon gauge fields displays a nonanalytic behavior in the coupling constant. Within perturbation theory, this gives rise to certain singularities which can be handled by adding a repulsive contact term to the Hamiltonian. We discuss the case of smeared flux tubes with an arbitrary profile and show that the contact term can be interpreted as the coupling of a magnetic moment spinlike degree of freedom to the magnetic field inside the flux tube. We also clarify the ansatz for the redefinition of the wave function.

• 1. Division de Physique Théorique, IPN, Université Paris XI - Paris Sud
• 2. Institut for Theoretical Physics, Institut for Theoretical Physics

Details Citations to the Article (13)

• ## On a dynamical model of glasses

### Jean-Philippe Bouchaud 1, Alain Comtet 2, 3, Cecile Monthus 2, 3

#### Journal de Physique I 5 (1995) 1521-1526

We analyze a simple dynamical model of glasses, based on the idea that each particle is trapped in a local potential well, which itself evolves due to hopping of neighbouring particles. The glass transition is signalled by the fact that the equilibrium distribution ceases to be normalisable, and dynamics becomes non-stationary. We generically find stretching of the correlation function at low temperatures and a Vogel-Fulcher like behaviour of the terminal time.

• 1. Service de physique de l'état condensé (SPEC), CNRS : URA2464 – CEA : DSM/IRAMIS
• 2. Division de Physique Théorique, IPN, Université Paris XI - Paris Sud
• 3. LPTPE, Université Paris VI - Pierre et Marie Curie

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• ## On the thermodynamics of multispecies anyons

### Serguei B. Isakov 1, Stefan Mashkevich 2, Stephane Ouvry 3

#### Nuclear Physics B 448 (1995) 457-469

We address the problem of multispecies anyons, i.e. particles of different species whose wave function is subject to anyonlike conditions. The cluster and virial coefficients are considered. Special attention is paid to the case of anyons in the lowest Landau level of a strong magnetic field, when it is possible (i) to prove microscopically the equation of state, in particular in terms of Aharonov-Bohm charge-flux composite systems, and (ii) to formulate the problem in terms of single-state statistical distributions.

• 2. Institute for Theoretical Physics, Institute for Theoretical Physics
• 3. Division de Physique Théorique, IPN, Université Paris XI - Paris Sud

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• ## One-Dimensional Statistical Mechanics for Identical Particles : The Calogero and Anyon Cases

### Alain Dasnieres De Veigy 1, Stephane Ouvry 1

#### Modern Physics Letters A 10 (1995) 1-13

The thermodynamic of particles with intermediate statistics interpolating between Bose and Fermi statistics is adressed in the simple case where there is one quantum number per particle. Such systems are essentially one-dimensional. As an illustration, one considers the anyon model restricted to the lowest Landau level of a strong magnetic field at low temperature, the generalization of this model to several particles species, and the one dimensional Calogero model. One reviews a unified algorithm to compute the statistical mechanics of these systems. It is pointed out that Haldane\'s generalization of the Pauli principle can be deduced from the anyon model in a strong magnetic field at low temperature.

• 1. Division de Physique Théorique, IPN, Université Paris XI - Paris Sud

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• ## Orbital Magnetism in Ensembles of Ballistic Billiards

### Denis Ullmo 1, Klaus Richter 1, Rodolfo A. Jalabert 1

#### Physical Review Letters 74 (1995) 383-386

We calculate the magnetic response of ensembles of small two-dimensional structures at finite temperatures. Using semiclassical methods and numerical calculation we demonstrate that only short classical trajectories are relevant. The magnetic susceptibility is enhanced in regular systems, where these trajectories appear in families. For ensembles of squares we obtain a large paramagnetic susceptibility, in good agreement with recent measurements in the ballistic regime.

• 1. Division de Physique Théorique, IPN, Université Paris XI - Paris Sud

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• ## Random Magnetic Impurities and the Landau Problem

### Jean Desbois 1, Cyril Furtlehner 1, Stephane Ouvry 1

#### Nuclear Physics B 453 (1995) 759-776

The 2-dimensional density of states of an electron is studied for a Poissonian random distribution of point vortices carrying $\\alpha$ flux in unit of the quantum of flux. It is shown that, for any given density of impurities, there is a transition, when $\\alpha\\simeq 0.3-0.4$, from an älmost free\' density of state -with only a depletion of states at the bottom of the spectrum characterized by a Lifschitz tail- to a Landau density of state with sharp Landau level oscillations. Several evidences and arguments for this transition -numerical and analytical- are presented.

• 1. Division de Physique Théorique, IPN, Université Paris XI - Paris Sud

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• ## Structural and dynamical properties of superfluid helium: a density functional approach

### F. Dalfovo 1, A. Lastri 1, L. Pricaupenko 2, S. Stringari 1, J. Treiner 2

#### Physical Review B 52 (1995) 1193-1209

We present a novel density functional for liquid 4He, properly accounting for the static response function and the phonon-roton dispersion in the uniform liquid. The functional is used to study both structural and dynamical properties of superfluid helium in various geometries. The equilibrium properties of the free surface, droplets and films at zero temperature are calculated. Our predictions agree closely to the results of ab initio Monte Carlo calculations, when available. The introduction of a phenomenological velocity dependent interaction, which accounts for backflow effects, is discussed. The spectrum of the elementary excitations of the free surface and films is studied.

• 1. Dipartimento di Fisica, UNIVERSITÀ DEGLI STUDI DI TRENTO
• 2. Division de Physique Théorique, IPN, Université Paris XI - Paris Sud

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• ## Trace formula for an ensemble of bumpy billiards.

### Nicolas Pavloff 1

#### Journal of Physics A 28 (1995) 4123-4132

We study the semiclassical quantization of an ensemble of billiards with a small random shape deformation. We derive a trace formula averaged over shape disorder. The results are illustrated by the study of supershells in rough metal clusters.

• 1. Division de Physique Théorique, IPN, Université Paris XI - Paris Sud

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• ## Complex Periodic Orbits and Tunnelling in Chaotic Potentials

### Stephen C. Creagh 1, Niall D. Whelan 1

#### Physical Review Letters 77 (1996) 4975-4979

We derive a trace formula for the splitting-weighted density of states suitable for chaotic potentials with isolated symmetric wells. This formula is based on complex orbits which tunnel through classically forbidden barriers. The theory is applicable whenever the tunnelling is dominated by isolated orbits, a situation which applies to chaotic systems but also to certain near-integrable ones. It is used to analyse a specific two-dimensional potential with chaotic dynamics. Mean behaviour of the splittings is predicted by an orbit with imaginary action. Oscillations around this mean are obtained from a collection of related orbits whose actions have nonzero real part.

• 1. Division de Physique Théorique, IPN, Université Paris XI - Paris Sud

Details Citations to the Article (53)
• ## Diffusion in one dimensional random medium and hyperbolic brownian motion

### Alain Comtet 1, 2, Cecile Monthus 1, 2

#### Journal of Physics A 29 (1996) 1331-1345

Classical diffusion in a random medium involves an exponential functional of Brownian motion. This functional also appears in the study of Brownian diffusion on a Riemann surface of constant negative curvature. We analyse in detail this relationship and study various distributions using stochastic calculus and functional integration.

• 1. Division de Physique Théorique, IPN, Université Paris XI - Paris Sud
• 2. LPTPE, Université Paris VI - Pierre et Marie Curie

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• ## Distribution of Eigenvalues for the Modular Group

### E. Bogomolny 1, F. Leyvraz 1, 2, C. Schmit 1

#### Communications in Mathematical Physics 176 (1996) 577-617

The two-point correlation function of energy levels for free motion on the modular domain, both with periodic and Dirichlet boundary conditions, are explicitly computed using a generalization of the Hardy-Littlewood method. It is shown that ion the limit of small separations they show an uncorrelated behaviour and agree with the Poisson distribution but they have prominent number-theoretical oscillations at larger scale. The results agree well with numerical simulations.

• 1. Division de Physique Théorique, IPN, Université Paris XI - Paris Sud
• 2. Instituto de Fisica, University of Mexico

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• ## Equation of State for Exclusion Statistics in a Harmonic Well

### Serguei B. Isakov 1, Stephane Ouvry 2

#### Journal of Physics A 29 (1996) 7401-7407

We consider the equations of state for systems of particles with exclusion statistics in a harmonic well. Paradygmatic examples are noninteracting particles obeying ideal fractional exclusion statistics placed in (i) a harmonic well on a line, and (ii) a harmonic well in the Lowest Landau Level (LLL) of an exterior magnetic field. We show their identity with (i) the Calogero model and (ii) anyons in the LLL of an exterior magnetic field and in a harmonic well.

• 2. Division de Physique Théorique, IPN, Université Paris XI - Paris Sud

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• ## Exponents appearing in heterogeneous reaction-diffusion models in one dimension

### Cecile Monthus 1, 2

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 54 (1996) 4844-4859

We study the following 1D two-species reaction diffusion model : there is a small concentration of B-particles with diffusion constant $D_B$ in an homogenous background of W-particles with diffusion constant $D_W$; two W-particles of the majority species either coagulate ($W+W \\longrightarrow W$) or annihilate ($W+W \\longrightarrow \\emptyset$) with the respective probabilities $p_c=(q-2)/(q-1)$ and $p_a=1/(q-1)$; a B-particle and a W-particle annihilate ($W+B \\longrightarrow \\emptyset$) with probability 1. The exponent $\\theta(q,\\lambda=D_B/D_W)$ describing the asymptotic time decay of the minority B-species concentration can be viewed as a generalization of the exponent of persistent spins in the zero-temperature Glauber dynamics of the 1D $q$-state Potts model starting from a random initial condition : the W-particles represent domain walls, and the exponent $\\theta(q,\\lambda)$ characterizes the time decay of the probability that a diffusive \'spectator\' does not meet a domain wall up to time $t$. We extend the methods introduced by Derrida, Hakim and Pasquier ({\\em Phys. Rev. Lett.} {\\bf 75} 751 (1995); Saclay preprint T96/013, to appear in {\\em J. Stat. Phys.} (1996)) for the problem of persistent spins, to compute the exponent $\\theta(q,\\lambda)$ in perturbation at first order in $(q-1)$ for arbitrary $\\lambda$ and at first order in $\\lambda$ for arbitrary $q$.

• 1. Service de Physique Théorique (SPhT), CNRS : URA2306 – CEA : DSM/SPHT
• 2. Division de Physique Théorique, IPN, Université Paris XI - Paris Sud

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• ## Integrability and Disorder in Mesoscopic Systems: Application to Orbital Magnetism

### K. Richter 1, 2, D. Ullmo 3, 4, R. A. Jalabert 5

#### Journal of Mathematical Physics 37 (1996) 5087-5110

We present a semiclassical theory of weak disorder effects in small structures and apply it to the magnetic response of non-interacting electrons confined in integrable geometries. We discuss the various averaging procedures describing different experimental situations in terms of one- and two-particle Green functions. We demonstrate that the anomalously large zero-field susceptibility characteristic of clean integrable structures is only weakly suppressed by disorder. This damping depends on the ratio of the typical size of the structure with the two characteristic length scales describing the disorder (elastic mean-free-path and correlation length of the potential) in a power-law form for the experimentally relevant parameter region. We establish the comparison with the available experimental data and we extend the study of the interplay between disorder and integrability to finite magnetic fields.

• 1. Institut für Physik, Institut für Physik
• 2. Max-Planck-Institut für Physik komplexer Systeme, Max-Planck-Institut
• 3. Bell Laboratories, Lucent Technologies, Bell Laboratories
• 4. Division de Physique Théorique, IPN, Université Paris XI - Paris Sud
• 5. Institut de Physique et Chimie des Matériaux de Strasbourg (IPCMS), CNRS : UMR7504 – Université Louis Pasteur - Strasbourg I

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• ## Models of traps and glass phenomenology

### Cecile Monthus 1, 2, Jean-Philippe Bouchaud 3

#### Journal of Physics A 29 (1996) 3847-3869

We study various models of independent particles hopping between energy traps\' with a density of energy barriers $\\rho(E)$, on a $d$ dimensional lattice or on a fully connected lattice. If $\\rho(E)$ decays exponentially, a true dynamical phase transition between a high temperature liquid\' phase and a low temperature aging\' phase occurs. More generally, however, one expects that for a large class of $\\rho(E)$, interrupted\' aging effects appear at low enough temperatures, with an ergodic time growing faster than exponentially. The relaxation functions exhibit a characteristic shoulder, which can be fitted as stretched exponentials. A simple way of introducing interactions between the particles leads to a modified model with an effective diffusion constant in energy space, which we discuss in detail.

• 1. Service de Physique Théorique (SPhT), CNRS : URA2306 – CEA : DSM/SPHT
• 2. Division de Physique Théorique, IPN, Université Paris XI - Paris Sud
• 3. Service de physique de l'état condensé (SPEC), CNRS : URA2464 – CEA : DSM/IRAMIS

Details Citations to the Article (247)

• ## Orbital Magnetism in the Ballistic Regime: Geometrical Effects

### K. Richter 1, 2, D. Ullmo 1, 3, R. A. Jalabert 1, 4

#### Physics Reports 276 (1996) 1-83

We present a general semiclassical theory of the orbital magnetic response of noninteracting electrons confined in two-dimensional potentials. We calculate the magnetic susceptibility of singly-connected and the persistent currents of multiply-connected geometries. We concentrate on the geometric effects by studying confinement by perfect (disorder free) potentials stressing the importance of the underlying classical dynamics. We demonstrate that in a constrained geometry the standard Landau diamagnetic response is always present, but is dominated by finite-size corrections of a quasi-random sign which may be orders of magnitude larger. These corrections are very sensitive to the nature of the classical dynamics. Systems which are integrable at zero magnetic field exhibit larger magnetic response than those which are chaotic. This difference arises from the large oscillations of the density of states in integrable systems due to the existence of families of periodic orbits. The connection between quantum and classical behavior naturally arises from the use of semiclassical expansions. This key tool becomes particularly simple and insightful at finite temperature, where only short classical trajectories need to be kept in the expansion. In addition to the general theory for integrable systems, we analyze in detail a few typical examples of experimental relevance: circles, rings and square billiards. In the latter, extensive numerical calculations are used as a check for the success of the semiclassical analysis. We study the weak-field regime where classical trajectories remain essentially unaffected, the intermediate field regime where we identify new oscillations characteristic for ballistic mesoscopic structures, and the high-field regime where the typical de Haas-van Alphen oscillations exhibit finite-size corrections. We address the comparison with experimental data obtained in high-mobility semiconductor microstructures discussing the differences between individual and ensemble measurements, and the applicability of the present model.

• 1. Division de Physique Théorique, IPN, Université Paris XI - Paris Sud
• 2. Institut für Physik, Institut für Physik
• 3. AT&T Bell Laboratories, Bell Laboratories
• 4. Institut de Physique et Chimie des Matériaux de Strasbourg (IPCMS), CNRS : UMR7504 – Université Louis Pasteur - Strasbourg I

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• ## Partial Dynamical Symmetry and Mixed Dynamics

### A. Leviatan 1, 2, N. D. Whelan 2, 3

#### Physical Review Letters 77 (1996) 5202-5205

Partial dynamical symmetry describes a situation in which some eigenstates have a symmetry which the quantum Hamiltonian does not share. This property is shown to have a classical analogue in which some tori in phase space are associated with a symmetry which the classical Hamiltonian does not share. A local analysis in the vicinity of these special tori reveals a neighbourhood of phase space foliated by tori. This clarifies the suppression of classical chaos associated with partial dynamical symmetry. The results are used to divide the states of a mixed system into chaotic\'\' and regular\'\' classes.

• 1. Racah Institute of Physics, Hebrew University of Jerusalem
• 2. Division de Physique Théorique, IPN, Université Paris XI - Paris Sud
• 3. Niels Bohr Institute (NBI), Niels Bohr Institute

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• ## Quantum Chaotic Dynamics and Random Polynomials

### E. Bogomolny 1, O. Bohigas 1, P. Leboeuf 1

#### Journal of Statistical Physics 85 (1996) 639-679

We investigate the distribution of roots of polynomials of high degree with random coefficients which, among others, appear naturally in the context of \'quantum chaotic dynamics\'. It is shown that under quite general conditions their roots tend to concentrate near the unit circle in the complex plane. In order to further increase this tendency, we study in detail the particular case of self-inversive random polynomials and show that for them a finite portion of all roots lies exactly on the unit circle. Correlation functions of these roots are also computed analytically, and compared to the correlations of eigenvalues of random matrices. The problem of ergodicity of chaotic wave-functions is also considered. For that purpose we introduce a family of random polynomials whose roots spread uniformly over phase space. While these results are consistent with random matrix theory predictions, they provide a new and different insight into the problem of quantum ergodicity. Special attention is devoted all over the paper to the role of symmetries in the distribution of roots of random polynomials.

• 1. Division Physique Théorique IPN, Université Paris XI - Paris Sud

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• ## Random Magnetic Impurities and the delta Impurity Problem

### Jean Desbois 1, Cyril Furtlehner 1, Stéphane Ouvry 1

#### Journal de Physique I 6 (1996) 641-648

One considers the effect of disorder on the 2-dimensional density of states of an electron in a constant magnetic field superposed onto a Poissonnian random distribution of point vortices. If one restricts the electron Hilbert space to the lowest Landau level of the total average magnetic field, the random magnetic impurity problem is mapped onto a contact $\\delta$ impurity problem. A brownian motion analysis of the model, based on brownian probability distributions for arithmetic area winding sectors, is also proposed. PACS numbers: 05.30.-d, 05.40.+j, 11.10.-

• 1. Division de Physique Théorique, IPN, Université Paris XI - Paris Sud

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• ## Random walk on Bethe lattice and hyperbolic geometry

### Cecile Monthus 1, Chistophe Texier 2

#### Journal of Physics A 29 (1996) 2399-2409

We give the exact solution to the problem of a random walk on the Bethe lattice through a mapping on an asymmetric random walk on the half-line. We also study the continuous limit of this model, and discuss in detail the relation between the random walk on the Bethe lattice and Brownian motion on a space of constant negative curvature.

• 1. Service de Physique Théorique (SPhT), CNRS : URA2306 – CEA : DSM/SPHT
• 2. Division de Physique Théorique, IPN, Université Paris XI - Paris Sud

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• ## Sample-size dependence of the ground-state energy in a one-dimensional localization problem

### C. Monthus 1, G. Oshanin 2, A. Comtet 2, 3, S. F. Burlatsky 4

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 54 (1996) 231

We study the sample-size dependence of the ground-state energy in a one-dimensional localization problem, based on a supersymmetric quantum mechanical Hamiltonian with random Gaussian potential. We determine, in the form of bounds, the precise form of this dependence and show that the disorder-average ground-state energy decreases with an increase of the size $R$ of the sample as a stretched-exponential function, $\\exp( - R^{z})$, where the characteristic exponent $z$ depends merely on the nature of correlations in the random potential. In the particular case where the potential is distributed as a Gaussian white noise we prove that $z = 1/3$. We also predict the value of $z$ in the general case of Gaussian random potentials with correlations.

• 1. Service de Physique Théorique (SPhT), CNRS : URA2306 – CEA : DSM/SPHT
• 2. Division de Physique Théorique, IPN, Université Paris XI - Paris Sud
• 3. LPTPE, Université Paris VI - Pierre et Marie Curie
• 4. Department of Chemistry, BG-10, University of Washington

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• ## The Level Splitting Distribution in Chaos-assisted Tunneling

### F. Leyvraz 1, D. Ullmo 1, 2

#### Journal of Physics A 29 (1996) 2529-2551

A compound tunneling mechanism from one integrable region to another mediated by a delocalized state in an intermediate chaotic region of phase space was recently introduced to explain peculiar features of tunneling in certain two-dimensional systems. This mechanism is known as chaos-assisted tunneling. We study its consequences for the distribution of the level splittings and obtain a general analytical form for this distribution under the assumption that chaos assisted tunneling is the only operative mechanism. %The validity of this form can then in %principle be checked either numerically or even experimentally. We have checked that the analytical form we obtain agrees with splitting distributions calculated numerically for a model system in which chaos-assisted tunneling is known to be the dominant mechanism. The distribution depends on two parameters: The first gives the scale of the splittings and is related to the magnitude of the classically forbidden processes, the second gives a measure of the efficiency of possible barriers to classical transport which may exist in the chaotic region. If these are weak, this latter parameter is irrelevant; otherwise it sets an energy scale at which the splitting distribution crosses over from one type of behavior to another. The detailed form of the crossover is also obtained and found to be in good agreement with numerical results for models for chaos-assisted tunneling.

• 1. Division de Physique Théorique, IPN, Université Paris XI - Paris Sud
• 2. Bell Laboratories 1D-265, Bell Laboratories 1D-265

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• ## Correlation functions for some conformal theories on Riemann surfaces

### Michael Monastyrsky 1, Sergei K. Nechaev 2, 3

#### Modern Physics Letters A 12 (1997) 589-596

We discuss the geometrical connection between 2D conformal field theories, random walks on hyperbolic Riemann surfaces and knot theory. For the wide class of CFTs with monodromies being the discrete subgroups of SL(2,R), the determination of four-point correlation functions are related to construction of topological invariants for random walks on multipunctured Riemann surfaces

• 1. Institute of Theoretical and Experimental Physics, Institute of Theoretical and Experimental Physics
• 2. Landau Institute for Theoretical Physics, Landau Institute for Theoretical Physics
• 3. Division de Physique Théorique, IPN, Université Paris XI - Paris Sud

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• ## Density Correlations of Magnetic Impurities and Disorder

### Jean Desbois 1, Cyril Furtlehner 1, Stéphane Ouvry 1

#### Journal of Physics A 30 (1997) 7291-7300

We consider an electron coupled to a random distribution of point vortices in the plane (magnetic impurities). We analyze the effect of the magnetic impurities on the density of states of the test particle, when the magnetic impurities have a spatial probability distribution governed by Bose or Fermi statistic at a given temperature. Comparison is made with the Poisson distribution, showing that the zero temperature Fermi distribution corresponds to less disorder. A phase diagram describing isolated impurities versus Landau level oscillations is proposed.

• 1. Division de Physique Théorique, IPN, Université Paris XI - Paris Sud

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• ## Hall Conductivity for Two Dimensional Magnetic Systems

### Jean Desbois 1, Stephane Ouvry 1, Christophe Texier 1

#### Nuclear Physics B 500 (1997) 486-510

A Kubo inspired formalism is proposed to compute the longitudinal and transverse dynamical conductivities of an electron in a plane (or a gas of electrons at zero temperature) coupled to the potential vector of an external local magnetic field, with the additional coupling of the spin degree of freedom of the electron to the local magnetic field (Pauli Hamiltonian). As an example, the homogeneous magnetic field Hall conductivity is rederived. The case of the vortex at the origin is worked out in detail. This system happens to display a transverse Hall conductivity ($P$ breaking effect) which is subleading in volume compared to the homogeneous field case, but diverging at small frequency like $1/\\omega^2$. A perturbative analysis is proposed for the conductivity in the random magnetic impurity problem (Poissonian vortices in the plane). At first order in perturbation theory, the Hall conductivity displays oscillations close to the classical straight line conductivity of the mean magnetic field.

• 1. Division de Physique Théorique, IPN, Université Paris XI - Paris Sud

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• ## Mean field and corrections for the Euclidean Minimum Matching problem

### Jacques Boutet de Monvel 1, Olivier C. Martin 1

#### Physical Review Letters 79 (1997) 167-170

Consider the length $L_{MM}^E$ of the minimum matching of N points in d-dimensional Euclidean space. Using numerical simulations and the finite size scaling law $< L_{MM}^E > = \\beta_{MM}^E(d) N^{1-1/d}(1+A/N+... )$, we obtain precise estimates of $\\beta_{MM}^E(d)$ for $2 \\le d \\le 10$. We then consider the approximation where distance correlations are neglected. This model is solvable and gives at $d \\ge 2$ an excellent random link\'\' approximation to $\\beta_{MM}^E(d)$. Incorporation of three-link correlations further improves the accuracy, leading to a relative error of 0.4% at d=2 and 3. Finally, the large d behavior of this expansion in link correlations is discussed.

• 1. Division de Physique Théorique, IPN, Université Paris XI - Paris Sud

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• ## On the distribution of the Wigner time delay in one-dimensional disordered systems

### Alain Comtet 1, 2, Christophe Texier 2

#### Journal of Physics A 30 (1997) 8017-8025

We consider the scattering by a one-dimensional random potential and derive the probability distribution of the corresponding Wigner time delay. It is shown that the limiting distribution is the same for two different models and coincides with the one predicted by random matrix theory. It is also shown that the corresponding stochastic process is given by an exponential functional of the potential.

• 1. Division de Physique Théorique, IPN, Université Paris XI - Paris Sud
• 2. LPTPE, Université Paris VI - Pierre et Marie Curie

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• ## Percolation Transition in the random antiferromagnetic spin-1 chain

### C. Monthus 1, O. Golinelli 1, Th. Jolicoeur 1

#### Physical Review Letters 79 (1997) 3254-3257

We give a physical description in terms of percolation theory of the phase transition that occurs when the disorder increases in the random antiferromagnetic spin-1 chain between a gapless phase with topological order and a random singlet phase. We study the statistical properties of the percolation clusters by numerical simulations, and we compute exact exponents characterizing the transition by a real-space renormalization group calculation.

• 1. Service de Physique Théorique (SPhT), CNRS : URA2306 – CEA : DSM/SPHT

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• ## Semiclassical Approach to Orbital Magnetism of Interacting Diffusive Quantum Systems

### D. Ullmo 1, 2, K. Richter 3, H. U. Baranger 1, F. Von Oppen 4, R. A. Jalabert 5

#### Physica E: Low-dimensional Systems and Nanostructures 1 (1997) 238-273

We study interaction effects on the orbital magnetism of diffusive mesoscopic quantum systems. By combining many-body perturbation theory with semiclassical techniques, we show that the interaction contribution to the ensemble averaged quantum thermodynamic potential can be reduced to an essentially classical operator. We compute the magnetic response of disordered rings and dots for diffusive classical dynamics. Our semiclassical approach reproduces the results of previous diagrammatic quantum calculations.

• 1. Bell Laboratories-Lucent Technologies, Bell Laboratories
• 2. Division de Physique Théorique, IPN, Université Paris XI - Paris Sud
• 3. Max-Planck-Institut für Physik komplexer Systeme, Max-Planck-Institut
• 4. Department of Condensed Matter Physics, Weizmann Institute of Science
• 5. Institut de Physique et Chimie des Matériaux de Strasbourg (IPCMS), CNRS : UMR7504 – Université Louis Pasteur - Strasbourg I

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• ## The random link approximation for the Euclidean traveling salesman problem

### N. J. Cerf 1, J. Boutet de Monvel 1, O. Bohigas 1, O. C. Martin 1, A. G. Percus 1

#### Journal de Physique I 7 (1997) 117-136

The traveling salesman problem (TSP) consists of finding the length of the shortest closed tour visiting N cities\'\'. We consider the Euclidean TSP where the cities are distributed randomly and independently in a d-dimensional unit hypercube. Working with periodic boundary conditions and inspired by a remarkable universality in the kth nearest neighbor distribution, we find for the average optimum tour length = beta_E(d) N^{1-1/d} [1+O(1/N)] with beta_E(2) = 0.7120 +- 0.0002 and beta_E(3) = 0.6979 +- 0.0002. We then derive analytical predictions for these quantities using the random link approximation, where the lengths between cities are taken as independent random variables. From the cavity\'\' equations developed by Krauth, Mezard and Parisi, we calculate the associated random link values beta_RL(d). For d=1,2,3, numerical results show that the random link approximation is a good one, with a discrepancy of less than 2.1% between beta_E(d) and beta_RL(d). For large d, we argue that the approximation is exact up to O(1/d^2) and give a conjecture for beta_E(d), in terms of a power series in 1/d, specifying both leading and subleading coefficients.

• 1. Division de Physique Théorique, IPN, Université Paris XI - Paris Sud

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• ## Uniform approximation for diffractive contributions to the trace formula in billiard systems

### Martin Sieber 1, 2, Nicolas Pavloff 1, Charles Schmit 1

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 55 (1997) 2279-2299

We derive contributions to the trace formula for the spectral density accounting for the role of diffractive orbits in two-dimensional billiard systems with corners. This is achieved by using the exact Sommerfeld solution for the Green function of a wedge. We obtain a uniformly valid formula which interpolates between formerly separate approaches (the geometrical theory of diffraction and Gutzwiller\'s trace formula). It yields excellent numerical agreement with exact quantum results, also in cases where other methods fail.

• 1. Division de Physique Théorique, IPN, Université Paris XI - Paris Sud
• 2. Abteilung Theoretische Physik, Universität Ulm

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• ## Chaos and Interacting Electrons in Ballistic Quantum Dots

### D. Ullmo 1, 2, H. U. Baranger 1, K. Richter 3, F. Von Oppen 4, R. A. Jalabert 5

#### Physical Review Letters 80 (1998) 895-899

We show that the classical dynamics of independent particles can determine the quantum properties of interacting electrons in the ballistic regime. This connection is established using diagrammatic perturbation theory and semiclassical finite-temperature Green functions. Specifically, the orbital magnetism is greatly enhanced over the Landau susceptibility by the combined effects of interactions and finite size. The presence of families of periodic orbits in regular systems makes their susceptibility parametrically larger than that of chaotic systems, a difference which emerges from correlation terms.

• 1. Bell Laboratories–Lucent Technologies, Bell Laboratories
• 2. Division de Physique Théorique, IPN, Université Paris XI - Paris Sud
• 3. Max-Planck-Institut für Physik komplexer Systeme, Max-Planck-Institut
• 4. Department of Condensed Matter Physics, Weizmann Institute of Science
• 5. Institut de Physique et Chimie des Matériaux de Strasbourg (IPCMS), CNRS : UMR7504 – Université Louis Pasteur - Strasbourg I

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• ## Comparing Mean Field and Euclidean Matching Problems

### J. Houdayer 1, J. H. Boutet de Monvel 1, 2, O. C. Martin 1

#### European Physical Journal B 6 (1998) 383-393

Combinatorial optimization is a fertile testing ground for statistical physics methods developed in the context of disordered systems, allowing one to confront theoretical mean field predictions with actual properties of finite dimensional systems. Our focus here is on minimum matching problems, because they are computationally tractable while both frustrated and disordered. We first study a mean field model taking the link lengths between points to be independent random variables. For this model we find perfect agreement with the results of a replica calculation. Then we study the case where the points to be matched are placed at random in a d-dimensional Euclidean space. Using the mean field model as an approximation to the Euclidean case, we show numerically that the mean field predictions are very accurate even at low dimension, and that the error due to the approximation is O(1/d^2). Furthermore, it is possible to improve upon this approximation by including the effects of Euclidean correlations among k link lengths. Using k=3 (3-link correlations such as the triangle inequality), the resulting errors in the energy density are already less than 0.5% at d>=2. However, we argue that the Euclidean model\'s 1/d series expansion is beyond all orders in k of the expansion in k-link correlations.

• 1. Division de Physique Théorique, IPN, Université Paris XI - Paris Sud
• 2. Forschungszentrum BiBos, Fakultät für Physik, Universität Bielefeld

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• ## Droplet Phenomenology and Mean Field in a Frustrated and Disordered System

### J. Houdayer 1, O. C. Martin 1

#### Physical Review Letters 81 (1998) 2554-2557

The low lying excited states of the three-dimensional minimum matching problem are studied numerically. The excitations\' energies grow with their size and confirm the droplet picture. However, some low energy, infinite size excitations create multiple valleys in the energy landscape. These states violate the droplet scaling ansatz, and are consistent with mean field predictions. A similar picture may apply to spin glasses whereby the droplet picture describes the physics at small length scales, while mean field describes that at large length scales.

• 1. Division de Physique Théorique, IPN, Université Paris XI - Paris Sud

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• ## Exact Results on Sinai’s Diffusion

### Alain Comtet 1, David S. Dean 1

#### Journal of Physics A 31 (1998) 8595

We study the continuum version of Sinai\'s problem of a random walker in a random force field in one dimension. A method of stochastic representations is used to represent various probability distributions in this problem (mean probability density function and first passage time distributions). This method reproduces already known rigorous results and also confirms directly some recent results derived using approximation schemes. We demonstrate clearly, in the Sinai scaling regime, that the disorder dominates the problem and that the thermal distributions tend to zero-one laws.

• 1. Division de Physique Théorique, IPN, Université Paris XI - Paris Sud

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• ## Exponential functionals of Brownian motion and disordered systems

### Alain Comtet 1, Cecile Monthus 1, Marc Yor 2

#### Journal of Applied Probability 35 (1998) 255-271

The paper deals with exponential functionals of the linear Brownian motion which arise in different contexts such as continuous time finance models and one-dimensional disordered models. We study some properties of these exponential functionals in relation with the problem of a particle coupled to a heat bath in a Wiener potential. Explicit expressions for the distribution of the free energy are presented.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Laboratoire de Probabilités et Modèles Aléatoires (LPMA), CNRS : UMR7599 – Université Paris VI - Pierre et Marie Curie – Université Paris VII - Paris Diderot

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• ## Kinetics of Anchoring of Polymer Chains on Substrates with Chemically Active Sites

### G. Oshanin 1, S. Nechaev 2, A. M. Cazabat 3, M. Moreau 1

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 58 (1998) 6134-6144

We consider dynamics of an isolated polymer chain with a chemically active end-bead on a 2D solid substrate containing immobile, randomly placed chemically active sites (traps). For a particular situation when the end-bead can be irreversibly trapped by any of these sites, which results in a complete anchoring of the whole chain, we calculate the time evolution of the probability $P_{ch}(t)$ that the initially non-anchored chain remains mobile until time $t$. We find that for relatively short chains $P_{ch}(t)$ follows at intermediate times a standard-form 2D Smoluchowski-type decay law $ln P_{ch}(t) \\sim - t/ln(t)$, which crosses over at very large times to the fluctuation-induced dependence $ln P_{ch}(t) \\sim - t^{1/2}$, associated with fluctuations in the spatial distribution of traps. We show next that for long chains the kinetic behavior is quite different; here the intermediate-time decay is of the form $ln P_{ch}(t) \\sim - t^{1/2}$, which is the Smoluchowski-type law associated with subdiffusive motion of the end-bead, while the long-time fluctuation-induced decay is described by the dependence $ln P_{ch}(t) \\sim - t^{1/4}$, stemming out of the interplay between fluctuations in traps distribution and internal relaxations of the chain.

• 1. Laboratoire de Physique Théorique des Liquides (LPTL), CNRS : UMR7600 – Université Paris VI - Pierre et Marie Curie
• 2. Division de Physique Théorique, IPN, Université Paris XI - Paris Sud
• 3. Laboratoire de Physique de la Matière Condensée (LPMC), CNRS : UMR7125 – Collège de France

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• ## Normal and Anomalous Diffusion in a Deterministic Area-preserving Map

### P. Leboeuf 1

#### Physica D: Nonlinear Phenomena 116 (1998) 8-20

Chaotic deterministic dynamics of a particle can give rise to diffusive Brownian motion. In this paper, we compute analytically the diffusion coefficient for a particular two-dimensional stochastic layer induced by the kicked Harper map. The variations of the transport coefficient as a parameter is varied are analyzed in terms of the underlying classical trajectories with particular emphasis in the appearance and bifurcations of periodic orbits. When accelerator modes are present, anomalous diffusion of the L\\évy type can occur. The exponent characterizing the anomalous diffusion is computed numerically and analyzed as a function of the parameter.

• 1. Division de Physique Théorique, IPN, Université Paris XI - Paris Sud

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• ## Persistent Currents and Magnetization in two-dimensional Magnetic Quantum Systems

### Jean Desbois 1, Stephane Ouvry 1, Christophe Texier 1

#### Nuclear Physics B 528 (1998) 727-745

Persistent currents and magnetization are considered for a two-dimensional electron (or gas of electrons) coupled to various magnetic fields. Thermodynamic formulae for the magnetization and the persistent current are established and the classical\'\' relationship between current and magnetization is shown to hold for systems invariant both by translation and rotation. Applications are given, including the point vortex superposed to an homogeneous magnetic field, the quantum Hall geometry (an electric field and an homogeneous magnetic field) and the random magnetic impurity problem (a random distribution of point vortices).

• 1. Division de Physique Théorique, IPN, Université Paris XI - Paris Sud

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• ## Phases of random antiferromagnetic spin-1 chains

### C. Monthus 1, O. Golinelli 2, Th. Jolicoeur 2

#### Physical Review B 58 (1998) 805-815

We formulate a real-space renormalization scheme that allows the study of the effects of bond randomness in the Heisenberg antiferromagnetic spin-1 chain. There are four types of bonds that appear during the renormalization flow. We implement numerically the decimation procedure. We give a detailed study of the probability distributions of all these bonds in the phases that occur when the strength of the disorder is varied. Approximate flow equations are obtained in the weak-disorder regime as well as in the strong disorder case where the physics is that of the random singlet phase.

• 1. Division de Physique Théorique, IPN, Université Paris XI - Paris Sud
• 2. Service de Physique Théorique (SPhT), CNRS : URA2306 – CEA : DSM/SPHT

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• ## Quantum liquids of particles with generalized statistics

### Serguei B. Isakov 1, 2

#### Physics Letters A 242 (1998) 130-138

We propose a phenomenological approach to quantum liquids of particles obeying generalized statistics of a fermionic type, in the spirit of the Landau Fermi liquid theory. The approach is developed for fractional exclusion statistics. We discuss both equilibrium (specific heat, compressibility, and Pauli spin susceptibility) and nonequilibrium (current and thermal conductivities, thermopower) properties. Low temperature quantities have the same temperature dependences as for the Fermi liquid, with the coefficients depending on the statistics parameter. The novel quantum liquids provide explicit realization of systems with a non-Fermi liquid Lorentz ratio in two and more dimensions. Consistency of the theory is verified by deriving the compressibility and $f$-sum rules.

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

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• ## Random Operator Approach for Word Enumeration in Braid Groups

### Alain Comtet 1, Sergei K. Nechaev 1, 2

#### Journal of Physics A 31 (1998) 5609-5630

We investigate analytically the problem of enumeration of nonequivalent primitive words in the braid group B_n for n >> 1 by analysing the random word statistics and the target space on the basis of the locally free group approximation. We develop a \'symbolic dynamics\' method for exact word enumeration in locally free groups and bring arguments in support of the conjecture that the number of very long primitive words in the braid group is not sensitive to the precise local commutation relations. We consider the connection of these problems with the conventional random operator theory, localization phenomena and statistics of systems with quenched disorder. Also we discuss the relation of the particular problems of random operator theory to the theory of modular functions

• 1. Division de Physique Théorique, IPN, Université Paris XI - Paris Sud
• 2. L.D. Landau Institute for Theoretical Physics, Landau Institute for Theoretical Physics

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• ## Random Walks, Reaction-Diffusion, and Nonequilibrium Dynamics of Spin Chains in One-dimensional Random Environments

### Daniel Fisher 1, Pierre Le Doussal 2, Cecile Monthus 3

#### Physical Review Letters 80 (1998) 3539-3542

Sinai\'s model of diffusion in one-dimension with random local bias is studied by a real space renormalization group which yields asymptotically exact long time results. The distribution of the position of a particle and the probability of it not returning to the origin are obtained, as well as the two-time distribution which exhibits äging\' with $\\frac{\\ln t}{\\ln t\'}$ scaling and a singularity at $\\ln t =\\ln t\'$. The effects of a small uniform force are also studied. Extension to motion of many domain walls yields non-equilibrium time dependent correlations for the 1D random field Ising model with Glauber dynamics and \'persistence\' exponents of 1D reaction-diffusion models with random forces.

• 1. Lyman Laboratory of Physics, University of Harvard
• 2. Laboratoire de Physique Théorique de l'ENS (LPTENS), CNRS : UMR8549 – Université Paris VI - Pierre et Marie Curie – Ecole Normale Supérieure de Paris - ENS Paris
• 3. Service de Physique Théorique (SPhT), CNRS : URA2306 – CEA : DSM/SPHT

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• ## Rough droplet model for spherical metal clusters

### N. Pavloff 1, C. Schmit 1

#### Physical Review B 58 (1998) 4942-4951

We study the thermally activated oscillations, or capillary waves, of a neutral metal cluster within the liquid drop model. These deformations correspond to a surface roughness which we characterize by a single parameter $\\Delta$. We derive a simple analytic approximate expression determining $\\Delta$ as a function of temperature and cluster size. We then estimate the induced effects on shell structure by means of a periodic orbit analysis and compare with recent data for shell energy of sodium clusters in the size range $50 < N < 250$. A small surface roughness $\\Delta\\simeq 0.6$ \Å~ is seen to give a reasonable account of the decrease of amplitude of the shell structure observed in experiment. Moreover -- contrary to usual Jahn-Teller type of deformations -- roughness correctly reproduces the shape of the shell energy in the domain of sizes considered in experiment.

• 1. Division de Physique Théorique, IPN, Université Paris XI - Paris Sud

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• ## Scaling universalities of kth-nearest neighbor distances on closed manifolds

### A. G. Percus 1, O. C. Martin 2

#### Advances in Applied Mathematics 21 (1998) 424-436

Take N sites distributed randomly and uniformly on a smooth closed surface. We express the expected distance from an arbitrary point on the surface to its kth-nearest neighboring site, in terms of the function A(l) giving the area of a disc of radius l about that point. We then find two universalities. First, for a flat surface, where A(l)=\\pi l^2, the k-dependence and the N-dependence separate in . All kth-nearest neighbor distances thus have the same scaling law in N. Second, for a curved surface, the average \\int d\\mu over the surface is a topological invariant at leading and subleading order in a large N expansion. The 1/N scaling series then depends, up through O(1/N), only on the surface\'s topology and not on its precise shape. We discuss the case of higher dimensions (d>2), and also interpret our results using Regge calculus.

• 1. CIC-3 and Center for Nonlinear Studies, Los Alamos National Laboratory
• 2. Division de Physique Théorique, IPN, Université Paris XI - Paris Sud

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• ## Statistics of reduced words in locally free and braid groups: Abstract studies and application to ballistic growth model

### Jean Desbois 1, Sergei K. Nechaev 1, 2

#### Journal of Physics A 31 (1998) 2767-2784

We study numerically and analytically the average length of reduced (primitive) words in so-called locally free and braid groups. We consider the situations when the letters in the initial words are drawn either without or with correlations. In the latter case we show that the average length of the reduced word can be increased or lowered depending on the type of correlation. The ideas developed are used for analytical computation of the average number of peaks of the surface appearing in some specific ballistic growth model

• 1. Division de Physique Théorique, IPN, Université Paris XI - Paris Sud
• 2. L D Landau Institute for Theoretical Physics, Landau Institute for Theoretical Physics

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• ## Many body heat radiation and heat transfer in the presence of a non-absorbing background medium – Archive ouverte HAL

### Muller Boris 1 Incardone Roberta 1 Mauro Antezza 2, 3 Emig Thorsten 4, 5 Kruger Matthias 1

#### Muller Boris, Incardone Roberta, Mauro Antezza, Emig Thorsten, Kruger Matthias. Many body heat radiation and heat transfer in the presence of a non-absorbing background medium. Physical Review B: Condensed Matter and Materials Physics (1998-2015), American Physical Society, 2017, 95, pp.085413. ⟨10.1103/PhysRevB.95.085413⟩. ⟨hal-01464078⟩

Heat radiation and near-field radiative heat transfer can be strongly manipulated by adjusting geometrical shapes, optical properties, or the relative positions of the objects involved. Typically, these objects are considered as embedded in vacuum. By applying the methods of fluctuational electrodynamics, we derive general closed-form expressions for heat radiation and heat transfer in a system of N arbitrary objects embedded in a passive nonabsorbing background medium. Taking into account the principle of reciprocity, we explicitly prove the symmetry and positivity of transfer in any such system. Regarding applications, we find that the heat radiation of a sphere as well as the heat transfer between two parallel plates is strongly enhanced by the presence of a background medium. Regarding near- and far-field transfer through a gas like air, we show that a microscopic model (based on gas particles) and a macroscopic model (using a dielectric contrast) yield identical results. We also compare the radiative transfer through a medium like air and the energy transfer found from kinetic gas theory.

• 1. Max Planck Institute for Intelligent Systems
• 2. L2C - Laboratoire Charles Coulomb
• 3. Théorie du rayonnement matière et phénomènes quantiques
• 4. (MSC)2 UMI3466 CNRS-MIT - Multi-Scale Material Science for Energy and Environment
• 5. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

• ## A Matrix Element for Chaotic Tunnelling Rates and Scarring Intensities

### Stephen C. Creagh 1, 2, Niall D. Whelan 2, 3

#### Annals of Physics 272 (1999) 196-242

It is shown that tunnelling splittings in ergodic double wells and resonant widths in ergodic metastable wells can be approximated as easily-calculated matrix elements involving the wavefunction in the neighbourhood of a certain real orbit. This orbit is a continuation of the complex orbit which crosses the barrier with minimum imaginary action. The matrix element is computed by integrating across the orbit in a surface of section representation, and uses only the wavefunction in the allowed region and the stability properties of the orbit. When the real orbit is periodic, the matrix element is a natural measure of the degree of scarring of the wavefunction. This scarring measure is canonically invariant and independent of the choice of surface of section, within semiclassical error. The result can alternatively be interpretated as the autocorrelation function of the state with respect to a transfer operator which quantises a certain complex surface of section mapping. The formula provides an efficient numerical method to compute tunnelling rates while avoiding the need for the exceedingly precise diagonalisation endemic to numerical tunnelling calculations.

• 1. Service de Physique Théorique (SPhT), CNRS : URA2306 – CEA : DSM/SPHT
• 2. Division de Physique Théorique, IPN, Université Paris XI - Paris Sud
• 3. Department of Physics and Astronomy, McMaster University

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• ## Conductance and Shot Noise for Particles with Exclusion Statistics

### Serguei B. Isakov 1, Thierry Martin 2, Stephane Ouvry 1

#### Physical Review Letters 83 (1999) 580-583

The first quantized Landauer approach to conductance and noise is generalized to particles obeying exclusion statistics. We derive an explicit formula for the crossover between the shot and thermal noise limits and argue that such a crossover can be used to determine experimentally whether charge carriers in FQHE devices obey exclusion statistics.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Centre de Physique Théorique (CPT), CNRS : UMR6207 – CNRS : FR2291 – Université de Provence - Aix-Marseille I – Université de la Méditerranée - Aix-Marseille II – Université Sud Toulon Var

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• ## Coupled Potts models: Self-duality and fixed point structure

### Vladimir S. Dotsenko 1, Jesper Lykke Jacobsen 2, Marc-André Lewis 1, Marco Picco 1

#### Nuclear Physics B 546 (FS) (1999) 505

We consider q-state Potts models coupled by their energy operators. Restricting our study to self-dual couplings, numerical simulations demonstrate the existence of non-trivial fixed points for 2 <= q <= 4. These fixed points were first predicted by perturbative renormalisation group calculations. Accurate values for the central charge and the multiscaling exponents of the spin and energy operators are calculated using a series of novel transfer matrix algorithms employing clusters and loops. These results compare well with those of the perturbative expansion, in the range of parameter values where the latter is valid. The criticality of the fixed-point models is independently verified by examining higher eigenvalues in the even sector, and by demonstrating the existence of scaling laws from Monte Carlo simulations. This might be a first step towards the identification of the conformal field theories describing the critical behaviour of this class of models.

• 1. Laboratoire de Physique Théorique et Hautes Energies (LPTHE), CNRS : UMR7589 – Université Paris VI - Pierre et Marie Curie – Université Paris VII - Paris Diderot
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• ## Cut Size Statistics of Graph Bisection Heuristics

### G. R. Schreiber, O. C. Martin 1

#### SIAM Journal on Optimization 10 (1999) 231-251

We investigate the statistical properties of cut sizes generated by heuristic algorithms which solve approximately the graph bisection problem. On an ensemble of sparse random graphs, we find empirically that the distribution of the cut sizes found by local\'\' algorithms becomes peaked as the number of vertices in the graphs becomes large. Evidence is given that this distribution tends towards a Gaussian whose mean and variance scales linearly with the number of vertices of the graphs. Given the distribution of cut sizes associated with each heuristic, we provide a ranking procedure which takes into account both the quality of the solutions and the speed of the algorithms. This procedure is demonstrated for a selection of local graph bisection heuristics.

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

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• ## Determinant Formulae for some Tiling Problems and Application to Fully Packed Loops

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

We present determinant formulae for the number of tilings of various domains in relation with Alternating Sign Matrix and Fully Packed Loop enumeration.

• 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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• ## Experimental vs. Numerical Eigenvalues of a Bunimovich Stadium Billiard — A Comparison

### H. Alt 1, C. Dembowski 1, H. -D. Graef 1, R. Hofferbert 1, H. Rehfeld 1, A. Richter 1, 2, C. Schmit 3

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 60 (1999) 2851-2857

We compare the statistical properties of eigenvalue sequences for a gamma=1 Bunimovich stadium billiard. The eigenvalues have been obtained by two ways: one set results from a measurement of the eigenfrequencies of a superconducting microwave resonator (real system) and the other set is calculated numerically (ideal system). The influence of the mechanical imperfections of the real system in the analysis of the spectral fluctuations and in the length spectra compared to the exact data of the ideal system are shown. We also discuss the influence of a family of marginally stable orbits, the bouncing ball orbits, in two microwave stadium billiards with different geometrical dimensions.

• 1. Institut für Kernphysik, Technische Universität Darmstadt
• 2. Wissenschaftskolleg zu Berlin, Berlin
• 3. Division de Physique Théorique, IPN, Université Paris XI - Paris Sud

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• ## Hall Conductivity in the presence of repulsive magnetic impurities

### Jean Desbois 1, Stephane Ouvry 1, Christophe Texier 1

#### European Physical Journal B 7 (1999) 527-528

The Hall conductivity of disordered magnetic systems consisting of hard-core point vortices randomly dropped on the plane with a Poissonian distribution, has a behavior analogous to the one observed experimentally by R.~J.~Haug, R.~R.~Gerhardts, K.~v.~Klitzling and K.~Ploog, with repulsive scatterers \\cite {1}. We also argue that models of homogeneous magnetic field with disordered potential, have necessarily vanishing Hall conductivities when their Hilbert space is restricted to a given Landau level subspace.

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

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• ## Homoclinic Structure Controls Chaotic Tunnelling

### Stephen C. Creagh 1, 2, Niall D. Whelan 2, 3

#### Physical Review Letters 82 (1999) 5237-5240

Tunnelling from a chaotic potential well is explained in terms of a set of complex periodic orbits which contain information about the real dynamics inside the well as well as the complex dynamics under the confining barrier. These orbits are associated with trajectories which are homoclinic to a real trajectory emerging from the optimal tunnelling path. The theory is verified by considering a model double-well problem.

• 1. Service de Physique Théorique (SPhT), CNRS : URA2306 – CEA : DSM/SPHT
• 2. Division de Physique Théorique, IPN, Université Paris XI - Paris Sud
• 3. Department of Physics and Astronomy, McMaster University

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• ## Ising Spin Glasses in a Magnetic Field

### J. Houdayer 1, O. C. Martin 1

#### Physical Review Letters 82 (1999) 4934-4937

Ground states of the three dimensional Edwards-Anderson spin glass are computed in the presence of an external magnetic field. Our algorithm is sufficiently powerful for us to treat systems with up to 600 spins. We perform a statistical analysis of how the ground state changes as the field is increased, and reach the conclusion that the spin glass phase at zero temperature does not survive in the presence of any finite field. This is in agreement with the droplet model or scaling predictions, but in sharp disagreement with the mean field picture. For comparison, we also investigate a dilute mean field spin glass model where an Almeida-Thouless line is present.

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

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• ## Nishimori point in random-bond Ising and Potts models in 2D

### Andreas Honecker 1, Jesper-Lykke Jacobsen 2, Marco Picco 3, Pierre Pujol 4

We study the universality class of the fixed points of the 2D random bond q-state Potts model by means of numerical transfer matrix methods. In particular, we determine the critical exponents associated with the fixed point on the Nishimori line. Precise measurements show that the universality class of this fixed point is inconsistent with percolation on Potts clusters for q=2, corresponding to the Ising model, and q=3

• 1. Technische Universität Braunschweig, Technische Universität Braunschweig
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 3. Laboratoire de Physique Théorique et Hautes Energies (LPTHE), CNRS : UMR7589 – Université Paris VI - Pierre et Marie Curie – Université Paris VII - Paris Diderot
• 4. Laboratoire de Physique de l'ENS Lyon (Phys-ENS), CNRS : UMR5672 – École Normale Supérieure - Lyon

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• ## Non-Abelian Chern-Simons Particles in an External Magnetic Field

### Serguei B. Isakov 1, Gustavo S. Lozano 1, Stephane Ouvry 1

#### Nuclear Physics B 552 (1999) 677

The quantum mechanics and thermodynamics of SU(2) non-Abelian Chern-Simons particles (non-Abelian anyons) in an external magnetic field are addressed. We derive the N-body Hamiltonian in the (anti-)holomorphic gauge when the Hilbert space is projected onto the lowest Landau level of the magnetic field. In the presence of an additional harmonic potential, the N-body spectrum depends linearly on the coupling (statistics) parameter. We calculate the second virial coefficient and find that in the strong magnetic field limit it develops a step-wise behavior as a function of the statistics parameter, in contrast to the linear dependence in the case of Abelian anyons. For small enough values of the statistics parameter we relate the N-body partition functions in the lowest Landau level to those of SU(2) bosons and find that the cluster (and virial) coefficients dependence on the statistics parameter cancels.

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

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

### Alejandro B. Kolton 1, A. Rosso 2, Thierry Giamarchi 1

We study the relaxation of an elastic string in a two dimensional pinning landscape using Langevin dynamics simulations. The relaxation of a line, initially flat, is characterized by a growing length, $L(t)$, separating the equilibrated short length scales from the flat long distance geometry that keep memory of the initial condition. We find that, in the long time limit, $L(t)$ has a non--algebraic growth, consistent with thermally activated jumps over barriers with power law scaling, $U(L) \\sim L^\\theta$.

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

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• ## Nonlinear conduction of sliding electronic crystals: Charge and Spin Density Waves

### S. Brazovskii 1, A. Larkin 2, 3

#### Journal de Physique IV Colloque 9 (1999) Pr10-77

A model of local metastable states due to the pinning induces plastic deformations allows to describe the nonlinear I-V curves in sliding density waves -DW. With increasing the DW velocity v, the metastable states of decreasing lifetimes ~1/v are accessed. The characteristic second threshold field is reached when configurations of shortest life time are accessed by the fast moving DW. Thus the DW works as a kind of a linear accelerator\'\' testing virtual states.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. ITP, Landau Institute for Theoretical Physics
• 3. William I. Fine Theoretical Physics Institute School of Physics and Astronomy, University of Minnesota-Crookston

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• ## Normal forms and complex periodic orbits in semiclassical expansions of Hamiltonian systems

### Patricio Leboeuf 1, Amaury Mouchet 2

#### Annals of Physics 275 (1999) 54

Bifurcations of periodic orbits as an external parameter is varied are a characteristic feature of generic Hamiltonian systems. Meyer's classification of normal forms provides a powerful tool to understand the structure of phase space dynamics in their neighborhood. We provide a pedestrian presentation of this classical theory and extend it by including systematically the periodic orbits lying in the complex plane on each side of the bifurcation. This allows for a more coherent and unified treatment of contributions of periodic orbits in semiclassical expansions. The contribution of complex fixed points is find to be exponentially small only for a particular type of bifurcation (the extremal one). In all other cases complex orbits give rise to corrections in powers of $\hbar$ and, unlike the former one, their contribution is hidden in the 'shadow' of a real periodic orbit.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Laboratoire de Mathématiques et Physique Théorique (LMPT), CNRS : UMR6083 – Université François Rabelais - Tours

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• ## On shape and electrostatics: competing anisotropies in charged colloidal platelets

### S. Jabbari-Farouji 1, J. -J. Weis 2, P. Davidson 3, P. Levitz 4, E. Trizac 1

Charged platelet suspensions, such as swelling clays, disc-like mineral crystallites or exfoliated nanosheets, are ubiquitous in nature. Their puzzling phase behaviours are nevertheless still poorly understood: while Laponite and Bentonite clay suspensions form arrested states at low densities, others, like Beidellite and Gibbsite, exhibit an equilibrium isotropic-nematic transition at moderate densities. These observations raise fundamental questions about the influence of electrostatic interactions on the isotropic-nematic transition and more generally on the organisation of charged platelets. We investigate the competition between anisotropic excluded-volume and electrostatic interactions in suspensions of thin charged disks, by means of Monte-Carlo simulations. We show that the original intrinsic anisotropy of the electrostatic potential between charged platelets, obtained within the non-linear Poisson-Boltzmann formalism, not only captures the generic features of the complex phase diagram of charged colloidal platelets, but also predicts the existence of novel structures and arrested states upon varying density and ionic strength.

• 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
• 3. Laboratoire de Physique des Solides (LPS), CNRS : UMR8502 – Université Paris XI - Paris Sud
• 4. Physicochimie des Electrolytes, Colloïdes et Sciences Analytiques (PECSA), Université Paris VI - Pierre et Marie Curie – ESPCI ParisTech – CNRS : UMR7195

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• ## On the distribution of the total energy of a system on non-interacting fermions: random matrix and semiclassical estimates

### O. Bohigas 1, P. Leboeuf 1, M. J. Sanchez 2

#### Physica D: Nonlinear Phenomena 131 (1999) 186-204

We consider a single particle spectrum as given by the eigenvalues of the Wigner-Dyson ensembles of random matrices, and fill consecutive single particle levels with n fermions. Assuming that the fermions are non-interacting, we show that the distribution of the total energy is Gaussian and its variance grows as n^2 log n in the large-n limit. Next to leading order corrections are computed. Some related quantities are discussed, in particular the nearest neighbor spacing autocorrelation function. Canonical and gran canonical approaches are considered and compared in detail. A semiclassical formula describing, as a function of n, a non-universal behavior of the variance of the total energy starting at a critical number of particles is also obtained. It is illustrated with the particular case of single particle energies given by the imaginary part of the zeros of the Riemann zeta function on the critical line.

• 1. Division de Physique Théorique, IPN, Université Paris XI - Paris Sud
• 2. Departmento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires

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• ## On the limiting power of set of knots generated by 1+1- and 2+1- braids

### R. Bikbov 1, S. Nechaev 1, 2

#### Journal of Mathematical Physics 40 (1999) 6598-6608

We estimate from above the set of knots, $\\Omega(n,\\mu)$, generated by closure of n-string 1+1- and 2+1-dimensional braids of irreducible length $\\mu$ ($\\mu>>1$) in the limit n>>1.

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

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• ## One-Dimensional Disordered Supersymmetric Quantum Mechanics: A Brief Survey

### Alain Comtet 1, Christophe Texier 1

We consider a one-dimensional model of localization based on the Witten Hamiltonian of supersymmetric quantum mechanics. The low energy spectral properties are reviewed and compared with those of other models with off-diagonal disorder. Using recent results on exponential functionals of a Brownian motion we discuss the statistical properties of the ground state wave function and their multifractal behaviour.

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

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• ## Random Analytic Chaotic Eigenstates

### P. Leboeuf 1

#### Journal of Statistical Physics 95 (1999) 651-664

The statistical properties of random analytic functions psi(z) are investigated as a phase-space model for eigenfunctions of fully chaotic systems. We generalize to the plane and to the hyperbolic plane a theorem concerning the equidistribution of the zeros of psi(z) previously demonstrated for a spherical phase space (SU(2) polynomials). For systems with time reversal symmetry, the number of real roots is computed for the three geometries. In the semiclassical regime, the local correlation functions are shown to be universal, independent of the system considered or the geometry of phase space. In particular, the autocorrelation function of psi is given by a Gaussian function. The connections between this model and the Gaussian random function hypothesis as well as the random matrix theory are discussed.

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

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• ## Random Walkers in 1-D Random Environments: Exact Renormalization Group Analysis

### Daniel S. Fisher 1, Pierre Le Doussal 2, Cecile Monthus 3

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 59 (1999) 4795

Sinai\'s model of diffusion in one-dimension with random local bias is studied by a real space renormalization group which yields exact results at long times. The effects of an additional small uniform bias force are also studied. We obtain analytically the scaling form of the distribution of the position $x(t)$ of a particle, the probability of it not returning to the origin and the distributions of first passage times, in an infinite sample as well as in the presence of a boundary and in a finite size sample. We compute the distribution of meeting time of two particles. We also obtain a detailed analytic description of thermally averaged trajectories: we compute the distributions of the number of returns and of the number of jumps forward. They obey multifractal scaling, characterized by generalized persistence exponents $\\theta(g)$ which we compute. With a small bias, the number of returns is finite, characterized by a universal scaling function. The statistics of the successive times of return of thermally averaged trajectories is obtained. The two time distribution of the positions of a particle, $x(t)$ and $x(t\')$ ($t>t\'$) is computed exactly. It exhibits aging\'\' with several regimes: without a bias, for $t-t\' \\sim t\'^\\alpha, \\alpha > 1$, it exhibits a $(\\ln t)/(\\ln t\')$ scaling, with a novel singularity at rescaled positions $x(t)=x(t\')$. For closer times $\\alpha<1$ there is a quasi-equilibrium regime with $\\ln(t-t\')/\\ln t\'$ scaling. The crossover to a $t/t\'$ aging form under a small bias is obtained analytically. Rare events, e.g. splitting of the thermal packet between wells, are also studied. Connections with the Green\'s function of a 1D Schr\\ödinger problem and quantum spin chains are discussed.

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

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• ## Reaction Diffusion Models in One Dimension with Disorder

### Pierre Le Doussal 1, Cecile Monthus 2, 3

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 60 (1999) 1212-1238

We study a large class of 1D reaction diffusion models with quenched disorder using a real space renormalization group method (RSRG) which yields exact results at large time. Particles (e.g. of several species) undergo diffusion with random local bias (Sinai model) and react upon meeting. We obtain the large time decay of the density of each specie, their associated universal amplitudes, and the spatial distribution of particles. We also derive the spectrum of exponents which characterize the convergence towards the asymptotic states. For reactions with several asymptotic states, we analyze the dynamical phase diagram and obtain the critical exponents at the transitions. We also study persistence properties for single particles and for patterns. We compute the decay exponents for the probability of no crossing of a given point by, respectively, the single particle trajectories ($\\theta$) or the thermally averaged packets ($\\bar{\\theta}$). The generalized persistence exponents associated to n crossings are also obtained. Specifying to the process $A+A \\to \\emptyset$ or A with probabilities $(r,1-r)$, we compute exactly the exponents $\\delta(r)$ and $\\psi(r)$ characterizing the survival up to time t of a domain without any merging or with mergings respectively, and $\\delta_A(r)$ and $\\psi_A(r)$ characterizing the survival up to time t of a particle A without any coalescence or with coalescences respectively. $\\bar{\\theta}, \\psi, \\delta$ obey hypergeometric equations and are numerically surprisingly close to pure system exponents (though associated to a completely different diffusion length). Additional disorder in the reaction rates, as well as some open questions, are also discussed.

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

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• ## Renormalization for Discrete Optimization

### J. Houdayer 1, O. C. Martin 1

#### Physical Review Letters 83 (1999) 1030-1033

The renormalization group has proven to be a very powerful tool in physics for treating systems with many length scales. Here we show how it can be adapted to provide a new class of algorithms for discrete optimization. The heart of our method uses renormalization and recursion, and these processes are embedded in a genetic algorithm. The system is self-consistently optimized on all scales, leading to a high probability of finding the ground state configuration. To demonstrate the generality of such an approach, we perform tests on traveling salesman and spin glass problems. The results show that our genetic renormalization algorithm\'\' is extremely powerful.

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

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• ## Semiclassical description of resonant tunneling

### E. B. Bogomolny 1, D. C. Rouben 1

#### European Physical Journal B 9 (1999) 695-718

We derive a semiclassical formula for the tunneling current of electrons trapped in a potential well which can tunnel into and across a wide quantum well. The calculations idealize an experimental situation where a strong magnetic field tilted with respect to an electric field is used. The resulting semiclassical expression is written as the sum over special periodic orbits which hit both walls of the quantum well and are perpendicular to the first wall.

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

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• ## Statistical properties of the time evolution of complex systems. I

### P. Leboeuf 1, G. Iacomelli

The time evolution of a bounded quantum system is considered in the framework of the orthogonal, unitary and symplectic circular ensembles of random matrix theory. For an $N$ dimensional Hilbert space we prove that in the large $N$ limit the return amplitude to the initial state and the transition amplitude to any other state of Hilbert space are Gaussian distributed. We further compute the exact first and second moments of the distributions. The return and transition probabilities turn out to be non self-averaging quantities with a Poisson distribution. Departures from this universal behaviour are also discussed.

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

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• ## Statistics of knots and entangled random walks

### Sergei K. Nechaev 1

The lectures review the state of affairs in modern branch of mathematical physics called probabilistic topology. In particular we consider the following problems: (i) We estimate the probability of a trivial knot formation on the lattice using the Kauffman algebraic invariants and show the connection of this problem with the thermodynamic properties of 2D disordered Potts model; (ii) We investigate the limit behavior of random walks in multi-connected spaces and on non-commutative groups related to the knot theory. We discuss the application of the above mentioned problems in statistical physics of polymer chains. On the basis of non-commutative probability theory we derive some new results in statistical physics of entangled polymer chains which unite rigorous mathematical facts with more intuitive physical arguments.

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

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• ## The stochastic traveling salesman problem: Finite size scaling and the cavity prediction

### A. G. Percus 1, O. C. Martin 2

#### Journal of Statistical Physics 94 (1999) 739-758

We study the random link traveling salesman problem, where lengths l_ij between city i and city j are taken to be independent, identically distributed random variables. We discuss a theoretical approach, the cavity method, that has been proposed for finding the optimal tour length over this random ensemble, given the assumption of replica symmetry. Using finite size scaling and a renormalized model, we test the cavity predictions against the results of simulations, and find excellent agreement over a range of distributions. We thus provide numerical evidence that the replica symmetric solution to this problem is the correct one. Finally, we note a surprising result concerning the distribution of kth-nearest neighbor links in optimal tours, and invite a theoretical understanding of this phenomenon.

• 1. CIC-3 and Center for Nonlinear Studies, Los Alamos National Laboratory
• 2. Division de Physique Théorique, IPN, Université Paris XI - Paris Sud

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• ## Theory of plastic flows of CDWs in application to the current conversion

### S. Brazovski 1, N. Kirova 1

#### Journal de Physique IV Colloque 9 (1999) Pr10-143

We suggest a theoretical picture for distributions of plastic deformations experienced by a sliding Charge Density Wave in the course of the conversion from the normal current at the contact to the collective one in the bulk. Several mechanisms of phase slips via creation and proliferation of dislocations are compared. The results are applied to space resolved X-ray, multi-contact and optical studies. Numerical simulations are combined with model independent relations.

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

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• ## Topological coupling of dislocations and magnetization vorticity in Spin Density Waves

### S. Brazovski 1, N. Kirova 1

#### Journal de Physique IV Colloque 9 (1999) Pr10-121

The rich order parameter of Spin Density Waves allows for an unusual object of a complex topological nature: a half-integer dislocation combined with a semi-vortex of the staggered magnetization. It becomes energetically preferable to ordinary dislocation due to enhanced Coulomb interactions in the semiconducting regime. Generation of these objects changes the narrow band noise frequency.

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

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• ## Universality in quantum parametric correlations

### P. Leboeuf 1, M. Sieber 1, 2

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 60 (1999) 3969-3972

We investigate the universality of correlation functions of chaotic and disordered quantum systems as an external parameter is varied. A new, general scaling procedure is introduced which makes the theory invariant under reparametrizations. Under certain general conditions we show that this procedure is unique. The approach is illustrated with the particular case of the distribution of eigenvalue curvatures. We also derive a semiclassical formula for the non-universal scaling factor, and give an explicit expression valid for arbitrary deformations of a billiard system.

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

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• ## Universality of the Wigner time delay distribution for one-dimensional random potentials

### Christophe Texier 1, Alain Comtet 1

#### Physical Review Letters 82 (1999) 4220-4223

We show that the distribution of the time delay for one-dimensional random potentials is universal in the high energy or weak disorder limit. Our analytical results are in excellent agreement with extensive numerical simulations carried out on samples whose sizes are large compared to the localisation length (localised regime). The case of small samples is also discussed (ballistic regime). We provide a physical argument which explains in a quantitative way the origin of the exponential divergence of the moments. The occurence of a log-normal tail for finite size systems is analysed. Finally, we present exact results in the low energy limit which clearly show a departure from the universal behaviour.

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

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• ## Vortices in Ginzburg-Landau billiards

### E. Akkermans 1, K. Mallick 1

#### Journal of Physics A 32 (1999) 7133-7143

We present an analysis of the Ginzburg-Landau equations for the description of a two-dimensional superconductor in a bounded domain. Using the properties of a special integrability point of these equations which allows vortex solutions, we obtain a closed expression for the energy of the superconductor. The role of the boundary of the system is to provide a selection mechanism for the number of vortices. A geometrical interpretation of these results is presented and they are applied to the analysis of the magnetization recently measured on small superconducting disks. Problems related to the interaction and nucleation of vortices are discussed.

• 1. Technion - Israel Institute of Technology (Technnion), Israel Institute of Technology

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• ## X-Ray Diffraction from Pinned Charge Density Waves

### S. Rouziere 1, S. Ravy 2, S. Brazovskii 3, J. -P. Pouget 2

#### Journal de Physique IV Colloque 9 (1999) Pr10-23

We present an x-ray study of doped charge density waves systems. When a 2k_f-charge density wave is strongly pinned to impurities, an interference effect gives rise to an asymmetry between the intensities of the +2k_f and -2k_f satellite reflections. Moreover, profile asymmetry of the satellite reflections indicates the existence of Friedel oscillations (FOs) around the defects. We have studied these effects in V- and W-doped blue bronzes. A syncrotron radiation study of the V-doped blue bronze clearly reveals the presence of FO around the V atoms.

• 1. School of Chemistry, Physics and Environmental Science, University of Sussex
• 2. Laboratoire de Physique des Solides (LPS), CNRS : UMR8502 – 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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• ## A geometrical picture for finite dimensional spin glasses

### Jérôme Houdayer 1, Olivier C. Martin 1

#### Europhysics Letters (EPL) 49 (2000) 794-800

A controversial issue in spin glass theory is whether mean field correctly describes 3-dimensional spin glasses. If it does, how can replica symmetry breaking arise in terms of spin clusters in Euclidean space? Here we argue that there exist system-size low energy excitations that are sponge-like, generating multiple valleys separated by diverging energy barriers. The droplet model should be valid for length scales smaller than the size of the system (theta > 0), but nevertheless there can be system-size excitations of constant energy without destroying the spin glass phase. The picture we propose then combines droplet-like behavior at finite length scales with a potentially mean field behavior at the system-size scale.

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

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• ## Action Correlations in Integrable Systems

### Eugene Bogomolny 1

#### Nonlinearity 13 (2000) 947-972

In many problems of quantum chaos the calculation of sums of products of periodic orbit contributions is required. A general method of computation of these sums is proposed for generic integrable models where the summation over periodic orbits is reduced to the summation over integer vectors uniquely associated with periodic orbits. It is demonstrated that in multiple sums over such integer vectors there exist hidden saddle points which permit explicit evaluation of these sums. Saddle point manifolds consist of periodic orbits vectors which are almost mutually parallel. Different problems has been treated by this saddle point method, e.g. Berry's bootstrap relations, mean values of Green function products etc. In particular, it is obtained that suitably defined 2-point correlation form-factor for periodic orbit actions in generic integrable models is proportional to quantum density of states and has peaks at quantum eigenenergies

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

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• ## Analyzing Fragmentation of Simple Fluids with Percolation Theory

### Xavier Campi 1, Hubert Krivine 1, Nicolas Sator 1, Eric Plagnol 2

#### European Physical Journal D 11 (2000) 233-238

We show that the size distributions of fragments created by high energy nuclear collisions are remarkably well reproduced within the framework of a parameter free percolation model. We discuss two possible scenarios to explain this agreement and suggest that percolation could be an universal mechanism to explain the fragmentation of simple fluids.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Institut de Physique Nucléaire d'Orsay (IPNO), CNRS : UMR8608 – IN2P3 – Université Paris XI - Paris Sud

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• ## Anchoring of polymers by traps randomly placed on a line

### S. Nechaev 1, 2, G. Oshanin 3, A. Blumen 4

#### Journal of Statistical Physics 98 (2000) 281-303

We study dynamics of a Rouse polymer chain, which diffuses in a three-dimensional space under the constraint that one of its ends, referred to as the slip-link, may move only along a one-dimensional line containing randomly placed, immobile, perfect traps. For such a model we compute exactly the time evolution of the probability $P_{sl}(t)$ that the chain slip-link will not encounter any of the traps until time $t$ and consequently, that until this time the chain will remain mobile.

• 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
• 3. Laboratoire de Physique Théorique des Liquides (LPTL), CNRS : UMR7600 – Université Paris VI - Pierre et Marie Curie
• 4. Université de Fribourg, Université de Fribourg

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• ## Copolymer at a selective interface and two dimensional wetting: a grand canonical approach

### C. Monthus 1, T. Garel 1, H. Orland 1

#### European Physical Journal B 17 (2000) 121

We consider two different problems involving the localization of a single polymer chain: (i) a periodic $AB$ copolymer at a selective fluid-fluid interface, with the upper (resp. lower) fluid attracting $A$ (resp. $B$) monomers (ii) a homopolymer chain attracted to a hard wall (wetting). Self avoidance is neglected in both models, which enables us to study their localization transition in a grand canonical approach. We recover the results obtained in previous studies via transfer matrix methods. Moreover, we calculate in this way the loop length distribution functions in the localized phase. Some finite size effects are also determined and tested numerically.

• 1. Service de Physique Théorique (SPhT), CNRS : URA2306 – CEA : DSM/SPHT

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• ## Correlations and fluctuations of a confined electron gas

### P. Leboeuf 1, A. Monastra 1

#### Physical Review B 62 (2000) 12617-12620

The grand potential $\\Omega$ and the response $R = - \\partial \\Omega /\\partial x$ of a phase-coherent confined noninteracting electron gas depend sensitively on chemical potential $\\mu$ or external parameter $x$. We compute their autocorrelation as a function of $\\mu$, $x$ and temperature. The result is related to the short-time dynamics of the corresponding classical system, implying in general the absence of a universal regime. Chaotic, diffusive and integrable motions are investigated, and illustrated numerically. The autocorrelation of the persistent current of a disordered mesoscopic ring is also computed.

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

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• ## Diffractive corrections in the trace formula for polygonal billiards

### Eugene Bogomolny 1, Nicolas Pavloff 1, Charles Schmit 1

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 61 (2000) 3689-3711

We derive contributions to the trace formula for the spectral density accounting for the role of diffractive orbits in two-dimensional polygonal billiards. In polygons, diffraction typically occurs at the boundary of a family of trajectories. In this case the first diffractive correction to the contribution of the family to the periodic orbit expansion is of order of the one of an isolated orbit, and gives the first $\sqrt{\hbar}$ correction to the leading semi-classical term. For treating these corrections Keller's geometrical theory of diffraction is inadequate and we develop an alternative approximation based on Kirchhoff's theory. Numerical checks show that our procedure allows to reduce the typical semi-classical error by about two orders of magnitude. The method permits to treat the related problem of flux-line diffraction with the same degree of accuracy.

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

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• ## Duality relations for M coupled Potts models

### Jesper Lykke Jacobsen 1

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 62 (2000) R1-R4

We establish explicit duality transformations for systems of M q-state Potts models coupled through their local energy density, generalising known results for M=1,2,3. The M-dimensional space of coupling constants contains a selfdual sub-manifold of dimension D_M = [M/2]. For the case M=4, the variation of the effective central charge along the selfdual surface is investigated by numerical transfer matrix techniques. Evidence is given for the existence of a family of critical points, corresponding to conformal field theories with an extended S_M symmetry algebra.

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

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• ## Elastic Rod Model of a Supercoiled DNA Molecule

### Claude Bouchiat 1, Marc Mezard 1, 2, 3

#### European Physical Journal E (2000) 337-402

We study the elastic behaviour of a supercoiled DNA molecule. The simplest model is that of a rod like chain, involving two elastic constants, the bending and the twist rigidities. We show that this model is singular and needs a small distance cut-off, which is a natural length scale giving the limit of validity of the model, of the order of the double helix pitch. The rod like chain in presence of the cutoff is able to reproduce quantitatively the experimentally observed effects of supercoiling on the elongation-force characteristics, in the small supercoiling regime. An exact solution of the model, using both transfer matrix techniques and its mapping to a quantum mechanics problem, allows to extract, from the experimental data,the value of the twist rigidity. We also analyse the variation of the torque and the writhe to twist ratio versus supercoiling, showing analytically the existence of a rather sharp crossover regime which can be related to the excitation of plectonemic-like structures. Finally we study the extension fluctuations of a stretched and supercoiled DNA molecule, both at fixed torque and at fixed supercoiling angle, and we compare the theoretical predictions to some preliminary experimental data.

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

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• ## Exact Meander Asymptotics: a Numerical Check

### Philippe Di Francesco 1, Emmanuel Guitter 1, Jesper Lykke Jacobsen 2

#### Nuclear Physics B 580 (2000) 757-795

This note addresses the meander enumeration problem: \'Count all topologically inequivalent configurations of a closed planar non self-intersecting curve crossing a line through a given number of points\'. We review a description of meanders introduced recently in terms of the coupling to gravity of a two-flavored fully-packed loop model. The subsequent analytic predictions for various meandric configuration exponents are checked against exact enumeration, using a transfer matrix method, with an excellent agreement.

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

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• ## Generalized model for dynamic percolation

### O. Benichou 1, 2, J. Klafter, M. Moreau 2, G. Oshanin 2

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 62 (2000) 3327-3339

We study the dynamics of a carrier, which performs a biased motion under the influence of an external field E, in an environment which is modeled by dynamic percolation and created by hard-core particles. The particles move randomly on a simple cubic lattice, constrained by hard-core exclusion, and they spontaneously annihilate and re-appear at some prescribed rates. Using decoupling of the third-order correlation functions into the product of the pairwise carrier-particle correlations we determine the density profiles of the 'environment' particles, as seen from the stationary moving carrier, and calculate its terminal velocity, V_c, as the function of the applied field and other system parameters. We find that for sufficiently small driving forces the force exerted on the carrier by the 'environment' particles shows a viscous-like behavior. An analog Stokes formula for such dynamic percolative environments and the corresponding friction coefficient are derived. We show that the density profile of the environment particles is strongly inhomogeneous: In front of the stationary moving carrier the density is higher than the average density, $\rho_s$, and approaches the average value as an exponential function of the distance from the carrier. Past the carrier the local density is lower than $\rho_s$ and the relaxation towards $\rho_s$ may proceed differently depending on whether the particles number is or is not explicitly conserved.

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

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• ## Individual energy level distributions for one-dimensional diagonal and off-diagonal disorder

### Christophe Texier 1

#### Journal of Physics A 33 (2000) 6095-6128

We study the distribution of the $n$-th energy level for two different one-dimensional random potentials. This distribution is shown to be related to the distribution of the distance between two consecutive nodes of the wave function. We first consider the case of a white noise potential and study the distributions of energy level both in the positive and the negative part of the spectrum. It is demonstrated that, in the limit of a large system ($L\\to\\infty$), the distribution of the $n$-th energy level is given by a scaling law which is shown to be related to the extreme value statistics of a set of independent variables. In the second part we consider the case of a supersymmetric random Hamiltonian (potential $V(x)=\\phi(x)^2+\\phi\'(x)$). We study first the case of $\\phi(x)$ being a white noise with zero mean. It is in particular shown that the ground state energy, which behaves on average like $\\exp{-L^{1/3}}$ in agreement with previous work, is not a self averaging quantity in the limit $L\\to\\infty$ as is seen in the case of diagonal disorder. Then we consider the case when $\\phi(x)$ has a non zero mean value.

• 1. Département de Physique Théorique, University of Geneva

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• ## Interaction-Induced Magnetization of the Two-Dimensional Electron Gas

### F. Von Oppen 1, D. Ullmo 2, H. U. Baranger 3

#### Physical Review B 62 (2000) 1935-1942

We consider the contribution of electron-electron interactions to the orbital magnetization of a two-dimensional electron gas, focusing on the ballistic limit in the regime of negligible Landau-level spacing. This regime can be described by combining diagrammatic perturbation theory with semiclassical techniques. At sufficiently low temperatures, the interaction-induced magnetization overwhelms the Landau and Pauli contributions. Curiously, the interaction-induced magnetization is third-order in the (renormalized) Coulomb interaction. We give a simple interpretation of this effect in terms of classical paths using a renormalization argument: a polygon must have at least three sides in order to enclose area. To leading order in the renormalized interaction, the renormalization argument gives exactly the same result as the full treatment.

• 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. Duke Physics, Duke University

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• ## Interactions and Interference in Quantum Dots: Kinks in Coulomb Blockade Peak Positions

### Harold U. Baranger 1, 2, Denis Ullmo 3, Leonid I. Glazman 4

#### Physical Review B 61 (2000) R2425-2428

We investigate the spin of the ground state of a geometrically confined many-electron system. For atoms, shell structure simplifies this problem-- the spin is prescribed by the well-known Hund's rule. In contrast, quantum dots provide a controllable setting for studying the interplay of quantum interference and electron-electron interactions in general cases. In a generic confining potential, the shell-structure argument suggests a singlet ground state for an even number of electrons. The interaction among the electrons produces, however, accidental occurrences of spin-triplet ground states, even for weak interaction, a limit which we analyze explicitly. Variaton of an external parameter causes sudden switching between these states and hence a kink in the conductance. Experimental study of these kinks would yield the exchange energy for the chaotic electron gas''.

• 1. Bell Laboratories, Lucent Technologies, Bell Laboratories
• 2. Duke Physics, Duke University
• 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 4. Theoretical Physics Institute, University of Minnesota

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• ## Large-scale low-energy excitations in 3-d spin glasses

### Jérôme Houdayer 1, Florent Krzakala 2, Olivier C. Martin 2

#### European Physical Journal B 18 (2000) 467-477

We numerically extract large-scale excitations above the ground state in the 3-dimensional Edwards-Anderson spin glass with Gaussian couplings. We find that associated energies are O(1), in agreement with the mean field picture. Of further interest are the position-space properties of these excitations. First, our study of their topological properties show that the majority of the large-scale excitations are sponge-like. Second, when probing their geometrical properties, we find that the excitations coarsen when the system size is increased. We conclude that either finite size effects are very large even when the spin overlap q is close to zero, or the mean field picture of homogeneous excitations has to be modified.

• 1. Institut für Physik [Mainz], Johannes Gutenberg-Universität Mainz
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• ## Multifractality of entangled random walks and non-uniform hyperbolic spaces

### R. Voituriez 1, S. Nechaev 1, 2

#### Journal of Physics A 33 (2000) 5631-5652

Multifractal properties of the distribution of topological invariants for a model of trajectories randomly entangled with a nonsymmetric lattice of obstacles are investigated. Using the equivalence of the model to random walks on a locally nonsymmetric tree, statistical properties of topological invariants, such as drift and return probabilities, have been studied by means of a renormalization group (RG) technique. The comparison of the analytical RG--results with numerical simulations as well as with the rigorous results of P.Gerl and W.Woess demonstrates clearly the validity of our approach. It is shown explicitly by direct counting for the discrete version of the model and by conformal methods for the continuous version that multifractality occurs when local uniformity of the phase space (which has an exponentially large number of states) has been broken.

• 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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• ## Multiscaling of energy correlations in the random-bond Potts model

### Jesper Lykke Jacobsen 1

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 61 (2000) R6060-R6062

We numerically calculate the exponent for the disorder averaged and fixed-sample decay of the energy-energy correlator in the q-state random-bond Potts model. Our results are in good agreement with a two-loop expansion (cond-mat/9910181) around q=2 recently found from perturbative renormalisation group techniques, fulfill the correlation length bound \\nu >= 2/d, and give further evidence against replica symmetry breaking in this class of models.

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

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• ## On the localization of random heteropolymers at the interface between two selective solvents

### Cecile Monthus 1

#### European Physical Journal B 13 (2000) 111-130

To study the localization of random heteropolymers at an interface separating two selective solvents within the model of Garel, Huse, Leibler and Orland, Europhys. Lett. {\\bf 8} 9 (1989), we propose an approach based on a disorder-dependent real space renormalization procedure. This approach allows to recover that a chain with a symmetric distribution in hydrophobic/hydrophilic components is localized at any temperature in the thermodynamic limit, whereas a dissymmetric distribution in hydrophobic/hydrophilic components leads to a delocalization phase transition. It yields in addition explicit expressions for the thermodynamic quantities as well as a very detailed description of the statistical properties of the behaviors of the heteropolymers in the high temperature limit. For the case of a small dissymmetry in hydrophobic/hydrophilic components, the renormalization approach yields explicit predictions for the delocalization transition temperature and for the critical behaviors of various quantities : in particular, the free energy presents an essential singularity at the transition, the typical length of blobs in the preferred solvent diverges with an essential singularity, whereas the typical length of blobs in the other solvent diverges algebraically. Finite-size properties are also characterized in details for both cases. In particular, we give the probability distribution of the delocalization temperature for the ensemble of chains of finite (large) length $L$. Finally, we discuss the non-equilibrium dynamics at temperature $T$ starting from a zero-temperature initial condition.

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

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• ## Plateau transitions in fractional quantum Hall liquids

### Ken-Ichiro Imura 1

#### European Physical Journal B 15 (2000) 155-160

Effects of backward scattering between fractional quantum Hall (FQH) edge modes are studied. Based on the edge-state picture for hierarchical FQH liquids, we discuss the possibility of the transitions between different plateaux of the tunneling conductance $G$. We find a selection rule for the sequence which begins with a conductance $G=m/(mp\pm 1)$ ($m$: integer, $p$: even integer) in units of $e^2/h$. The shot-noise spectrum as well as the scaling behavior of the tunneling current is calculated explicitly.

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

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• ## Quantum unique ergodicity for parabolic maps

### Jens Marklof 1, 2, Zeev Rudnick

#### GAFA Geometric And Functional Analysis 10 (2000) 1554-1578

We study the ergodic properties of quantized ergodic maps of the torus. It is known that these satisfy quantum ergodicity: For almost all eigenstates, the expectation values of quantum observables converge to the classical phase-space average with respect to Liouville measure of the corresponding classical observable. The possible existence of any exceptional subsequences of eigenstates is an important issue, which until now was unresolved in any example. The absence of exceptional subsequences is referred to as quantum unique ergodicity (QUE). We present the first examples of maps which satisfy QUE: Irrational skew translations of the two-torus, the parabolic analogues of Arnold\'s cat maps. These maps are classically uniquely ergodic and not mixing. A crucial step is to find a quantization recipe which respects the quantum-classical correspondence principle. In addition to proving QUE for these maps, we also give results on the rate of convergence to the phase-space average. We give upper bounds which we show are optimal. We construct special examples of these maps for which the rate of convergence is arbitrarily slow.

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

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• ## Random matrices, random polynomials and Coulomb systems

### P. Leboeuf 1

#### Journal de Physique IV Colloque 10 (2000) Pr5-45-52

It is well known that the joint probability density of the eigenvalues of Gaussian ensembles of random matrices may be interpreted as a Coulomb gas. We review these classical results for hermitian and complex random matrices, with special attention devoted to electrostatic analogies. We also discuss the joint probability density of the zeros of polynomials whose coefficients are complex Gaussian variables. This leads to a new two-dimensional solvable gas of interacting particles, with non-trivial interactions between particles.

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

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• ## Reply to Comment on ‘Ising Spin Glasses in a Magnetic Field’

### Jérôme Houdayer 1, Olivier C. Martin 1

#### Physical Review Letters 84 (2000) 1057

The problem of the survival of a spin glass phase in the presence of a field has been a challenging one for a long time. To date, all attempts using equilibrium Monte Carlo methods have been unconclusive. In their comment to our paper, Marinari, Parisi and Zuliani use out-of-equilibrium measurements to test for an Almeida-Thouless line. In our view such a dynamic approach is not based on very solid foundations in finite dimensional systems and so cannot be as compelling as equilibrium approaches. Nevertheless, the results of those authors suggests that there is a critical field near B=0.4 at zero temperature. In view of this quite small value (compared to the mean field value), we have reanalyzed our data. We find that if finite size scaling is to distinguish between that small field and a zero field, we would need to go to lattice sizes of about 20x20x20.

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

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• ## Spectral determinant on quantum graphs

### Eric Akkermans 1, 2, 3, Alain Comtet 3, Jean Desbois 3, Gilles Montambaux 2, Christophe Texier 3, 4

#### Annals of Physics 284 (2000) 10-51

We study the spectral determinant of the Laplacian on finite graphs characterized by their number of vertices V and of bonds B. We present a path integral derivation which leads to two equivalent expressions of the spectral determinant of the Laplacian either in terms of a V x V vertex matrix or a 2B x 2B link matrix that couples the arcs (oriented bonds) together. This latter expression allows us to rewrite the spectral determinant as an infinite product of contributions of periodic orbits on the graph. We also present a diagrammatic method that permits us to write the spectral determinant in terms of a finite number of periodic orbit contributions. These results are generalized to the case of graphs in a magnetic field. Several examples illustrating this formalism are presented and its application to the thermodynamic and transport properties of weakly disordered and coherent mesoscopic networks is discussed.

• 1. Department of Physics (Technion), Technion-Israel Institute of Technology
• 2. Laboratoire de Physique des Solides (LPS), CNRS : UMR8502 – Université Paris XI - Paris Sud
• 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 4. Département de Physique Théorique, University of Geneva

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• ## Spectral statistics of chaotic systems with a point-like scatterer

### Eugene Bogomolny 1, Patricio Leboeuf 1, Charles Schmit 1

#### Physical Review Letters 85 (2000) 2486-2489

The statistical properties of a Hamiltonian $H_0$ perturbed by a localized scatterer are considered. We prove that when $H_0$ describes a bounded chaotic motion, the universal part of the spectral statistics are not changed by the perturbation. This is done first within the random matrix model. Then it is shown by semiclassical techniques that the result is due to a cancellation between diagonal diffractive and off-diagonal periodic-diffractive contributions. The compensation is a very general phenomenon encoding the semiclassical content of the optical theorem.

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

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• ## Spin and link overlaps in 3-dimensional spin glasses

### F. Krzakala 1, O. C. Martin 1

#### Physical Review Letters 85 (2000) 3013-3016

Excitations of three-dimensional spin glasses are computed numerically. We find that one can flip a finite fraction of an LxLxL lattice with an O(1) energy cost, confirming the mean field picture of a non-trivial spin overlap distribution P(q). These low energy excitations are not domain-wall-like, rather they are topologically non-trivial and they reach out to the boundaries of the lattice. Their surface to volume ratios decrease as L increases and may asymptotically go to zero. If so, link and window overlaps between the ground state and these excited states become trivial\'\'.

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

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• ## Statistical properties of the 2D attached Rouse chain

### Olivier Benichou 1, 2, Jean Desbois 2

#### Journal of Statistical Physics 101 (2000) 921-931

We study various dynamical properties (winding angles, areas) of a set of harmonically bound Brownian particles (monomers), one endpoint of this chain being kept fixed at the origin 0. In particular, we show that, for long times t, the areas {A_i} enclosed by the monomers scale like t^{1/2}, with correlated gaussian distributions. This is at variance with the winding angles {\theta_i} around fixed points that scale like t and are distributed according to independent Cauchy laws.

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

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• ## Topological Defects in Spin Density Waves

### N. Kirova 1, S. Brazovskii 1

#### Journal de Physique IV Colloque 10 (2000) 3-189

The rich order parameter of Spin Density Waves allows for unusual object of a complex topological nature: a half-integer dislocation combined with a semi-vortex of a staggered magnetization. It becomes energetically preferable to ordinary dislocation due to enhanced Coulomb interactions in the semiconducting regime. Generation of these objects changes e.g. the narrow band noise frequency.

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

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• ## Windings of the 2D free Rouse chain

### Olivier Benichou 1, 2, Jean Desbois 2

#### Journal of Physics A 33 (2000) 6655-6665

We study long time dynamical properties of a chain of harmonically bound Brownian particles. This chain is allowed to wander everywhere in the plane. We show that the scaling variables for the occupation times T_j, areas A_j and winding angles \theta_j (j=1,...,n labels the particles) take the same general form as in the usual Brownian motion. We also compute the asymptotic joint laws P({T_j}), P({A_j}), P({\theta_j}) and discuss the correlations occuring in those distributions.

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

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• ## A ferromagnet with a glass transition

### Silvio Franz 1, Marc Mézard 2, Federico Ricci-Tersenghi 1, Martin Weigt 3, Riccardo Zecchina 1

#### Europhysics Letters (EPL) 55 (2001) 465

We introduce a finite-connectivity ferromagnetic model with a three-spin interaction which has a crystalline (ferromagnetic) phase as well as a glass phase. The model is not frustrated, it has a ferromagnetic equilibrium phase at low temperature which is not reached dynamically in a quench from the high-temperature phase. Instead it shows a glass transition which can be studied in detail by a one step replica-symmetry broken calculation. This spin model exhibits the main properties of the structural glass transition at a solvable mean-field level.

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

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• ## A hierarchical approach for computing spin glass ground states

### Jérôme Houdayer 1, Olivier C. Martin 2

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 64 (2001) 056704

We describe a numerical algorithm for computing spin glass ground states with a high level of reliability. The method uses a population based search and applies optimization on multiple scales. Benchmarks are given leading to estimates of the performance on large lattices.

• 1. Institut für Physik/Max Planck Institut für Polymerforschung, Max-Planck-Institut
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• ## A transfer matrix approach to the enumeration of colored links Authors: Jesper Jacobsen,

### Jesper-Lykke Jacobsen 1, Paul Zinn-Justin 1

#### Journal of Knot Theory and Its Ramifications 10 (2001) 1233-1267

We propose a transfer matrix algorithm for the enumeration of alternating link diagrams with external legs, giving a weight $n$ to each connected component. Considering more general tetravalent diagrams with self-intersections and tangencies allows us to treat topological (flype) equivalences. This is done by means of a finite renormalization scheme for an associated matrix model. We give results, expressed as polynomials in $n$, for the various generating functions up to order 19 (link diagrams), 15 (prime alternating tangles) and 11 (6-legged links) intersections. The limit $n\to\infty$ is solved explicitly. We then analyze the large-order asymptotics of the generating functions. For $0\le n \le 2$ good agreement is found with a conjecture for the critical exponent, based on the KPZ relation.

• 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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• ## Adsorption of a random heteropolymer at a potential well revisited: location of transition point and design of sequences

### Alexei A. Naidenov 1, Sergei K. Nechaev 1, 2

#### Journal of Physics A 34 (2001) 5625-5634

The adsorption of an ideal heteropolymer loop at a potential point well is investigated within the frameworks of a standard random matrix theory. On the basis of semi-analytical/semi-numerical approach the histogram of transition points for the ensemble of quenched heteropolymer structures with bimodal symmetric distribution of types of chain's links is constructed. It is shown that the sequences having the transition points in the tail of the histogram display the correlations between nearest-neighbor monomers.

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

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• ## Bose beams: coherent propagation through a guide

### Patricio Leboeuf 1, Nicolas Pavloff 1

#### Physical Review A: Atomic, Molecular and Optical Physics 64 (2001) 033602

We compute the stationary profiles of a coherent beam of Bose condensed atoms propagating through a guide. Special emphasis is put on the effect of an obstacle present on the trajectory of the beam. The obstacle considered (such as a bend in the guide, or a laser field perpendicular to the beam) results in a repulsive or an attractive potential acting on the condensate. Different behaviors are observed when varying the beam velocity (with respect to the speed of sound), the size of the obstacle (relative to the healing length) and the intensity and sign of the potential. The existence of bound states of the condensate is also considered.

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

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• ## Classification of Conformal Field Theories Based on Coulomb gases. Application to Loop Models

### Vladimir S. Dotsenko 1, Jesper Lykke Jacobsen 2, Marco Picco 1

#### Nuclear Physics B 618 (2001) 523

We present a method for classifying conformal field theories based on Coulomb gases (bosonic free-field construction). Given a particular geometric configuration of the screening charges, we give necessary conditions for the existence of degenerate representations and for the closure of the vertex-operator algebra. The resulting classification contains, but is more general than, the standard one based on classical Lie algebras. We then apply the method to the Coulomb gas theory for the two-flavoured loop model of Jacobsen and Kondev. The purpose of the study is to clarify the relation between Coulomb gas models and conformal field theories with extended symmetries.

• 1. Laboratoire de Physique Théorique et Hautes Energies (LPTHE), CNRS : UMR7589 – Université Paris VI - Pierre et Marie Curie – Université Paris VII - Paris Diderot
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• ## Discrete energy landscapes and replica symmetry breaking at zero temperature

### Florent Krzakala 1, Olivier C. Martin 1

#### Europhysics Letters (EPL) 53 (2001) 749-755

The order parameter P(q) for disordered systems with degenerate ground-states is reconsidered. We propose that entropy fluctuations lead to a trivial P(q) at zero temperature as in the non-degenerate case, even if there are zero-energy large-scale excitations (complex energy landscape). Such a situation should arise in the 3-dimensional +-J Ising spin glass and in MAX-SAT. Also, we argue that if the energy landscape is complex with a finite number of ground-state families, then replica symmetry breaking reappears at positive temperature.

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

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• ## Discrete thermodynamic Bethe ansatz

### Michel Bergere 1, Ken-Ichiro Imura 2, Stéphane Ouvry 2

#### Nuclear Physics B 608 (2001) 577

We propose discrete TBA equations for models with discrete spectrum. We illustrate our construction on the Calogero-Moser model and determine the discrete 2-body TBA function which yields the exact N-body Calogero-Moser thermodynamics. We apply this algorithm to the Lieb-Liniger model in a harmonic well, a model which is relevant for the microscopic description of harmonically trapped Bose-Einstein condensates in one dimension. We find that the discrete TBA reproduces correctly the N-body groundstate energy of the Lieb-Liniger model in a harmonic well at first order in perturbation theory, but corrections do appear at second order.

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

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• ## Equilibrium valleys in spin glasses at low temperature

### Enzo Marinari 1, Olivier C. Martin 2, Francesco Zuliani 2

#### Physical Review B 64 (2001) 184413

We investigate the 3-dimensional Edwards-Anderson spin glass model at low temperature on simple cubic lattices of sizes up to L=12. Our findings show a strong continuity among T>0 physical features and those found previously at T=0, leading to a scenario with emerging mean field like characteristics that are enhanced in the large volume limit. For instance, the picture of space filling sponges seems to survive in the large volume limit at T>0, while entropic effects play a crucial role in determining the free-energy degeneracy of our finite volume states. All of our analysis is applied to equilibrium configurations obtained by a parallel tempering on 512 different disorder realizations. First, we consider the spatial properties of the sites where pairs of independent spin configurations differ and we introduce a modified spin overlap distribution which exhibits a non-trivial limit for large L. Second, after removing the Z_2 (+-1) symmetry, we cluster spin configurations into valleys. On average these valleys have free-energy differences of O(1), but a difference in the (extensive) internal energy that grows significantly with L; there is thus a large interplay between energy and entropy fluctuations. We also find that valleys typically differ by sponge-like space filling clusters, just as found previously for low-energy system-size excitations above the ground state.

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

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• ## Force-velocity relation and density profiles for biased diffusion in an adsorbed monolayer

### O. Benichou 1, 2, A. M. Cazabat 3, J. De Coninck, M. Moreau 2, G. Oshanin 2

#### Physical Review B 63 (2001) 235413

In this paper, which completes our earlier short publication [Phys. Rev. Lett. 84, 511 (2000)], we study dynamics of a hard-core tracer particle (TP) performing a biased random walk in an adsorbed monolayer, composed of mobile hard-core particles undergoing continuous exchanges with a vapor phase. In terms of an approximate approach, based on the decoupling of the third-order correlation functions, we obtain the density profiles of the monolayer particles around the TP and derive the force-velocity relation, determining the TP terminal velocity, V_{tr}, as the function of the magnitude of external bias and other system's parameters. Asymptotic forms of the monolayer particles density profiles at large separations from the TP, and behavior of V_{tr} in the limit of small external bias are found explicitly.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Laboratoire de Physique Théorique des Liquides (LPTL), CNRS : UMR7600 – Université Paris VI - Pierre et Marie Curie
• 3. Laboratoire de Physique de la Matière Condensée (LPMC), CNRS : UMR7125 – Collège de France

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• ## Friedel Oscillations and Charge-density Waves Pinning in Quasi-one-dimensional Conductors: An X-ray Access

### Sylvain Ravy 1, Stephan Rouzière 2, Jean-Paul Pouget 1, Serguei Brazovskii 3

#### Synthetic Metals 120 (2001) 1075

We present an x-ray diffraction study of the Vanadium-doped blue bronze K0.3(Mo0.972V0.028)O3. At low temperature, we have observed both an intensity asymmetry of the +-2kF satellite reflections relative to the pure compound, and a profile asymmetry of each satellite reflections. We show that the profile asymmetry is due to Friedel oscillation around the V substituant and that the intensity asymmetry is related to the charge density wave (CDW) pinning. These two effects, intensity and profile asymmetries, gives for the first time access to the local properties of CDW in disordered systems, including the pinning and even the phase shift of FOs.

• 1. Laboratoire de Physique des Solides (LPS), CNRS : UMR8502 – Université Paris XI - Paris Sud
• 2. School of Chemistry, Physics and Environmental Science, University of Sussex
• 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• ## Interactions in Chaotic Nanoparticles: Fluctuations in Coulomb Blockade Peak Spacings

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

#### Physical Review B 64 (2001) 245324

We use random matrix models to investigate the ground state energy of electrons confined to a nanoparticle. Our expression for the energy includes the charging effect, the single-particle energies, and the residual screened interactions treated in Hartree-Fock. This model is applicable to chaotic quantum dots or nanoparticles--in these systems the single-particle statistics follows random matrix theory at energy scales less than the Thouless energy. We find the distribution of Coulomb blockade peak spacings first for a large dot in which the residual interactions can be taken constant: the spacing fluctuations are of order the mean level separation Delta. Corrections to this limit are studied using the small parameter 1/(kf L): both the residual interactions and the effect of the changing confinement on the single-particle levels produce fluctuations of order Delta/sqrt(kf L). The distributions we find are significantly more like the experimental results than the simple constant interaction model.

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

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• ## Marginal pinning of vortices at high temperature

### Markus Muller 1, 2, Denis A. Gorokhov 1, 3, Gianni Blatter 1

#### Physical Review B 64 (2001) 134523

We analyze the competition between thermal fluctuations and pinning of vortices in bulk type II superconductors subject to point-like disorder and derive an expression for the temperature dependence of the pinning length L_c(T) which separates different types of single vortex wandering. Given a disorder potential with a basic scale \xi and a correlator K_0(u) \sim K_0 (u/xi)^{-\beta} ln^alpha (u/xi) we determine the dependence of L_c(T) on the correlator range: correlators with \beta > 2 (short-range) and \beta <2 (long-range) lead to the known results L_c(T) \sim L_c(0) exp[C T^3] and L_c(T) \sim L_c(0) (C T)^{(4+beta)/(2-beta)}, respectively. Using functional renormalization group we show that for \beta =2 the result takes the interpolating form L_c(T) \sim L_c(0) exp[C T^{3/(2+alpha)}]. Pinning of vortices in bulk type II superconductors involves a long-range correlator with \beta=2, \alpha=1 on intermediate scales \xi

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

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• ## Microscopic Models for Long Ranged Volatility Correlations

### Irene Giardina 1, Jean-Philippe Bouchaud 2, 3, Marc Mézard 4

#### Physica A 299 (2001) 28-39

We propose a general interpretation for long-range correlation effects in the activity and volatility of financial markets. This interpretation is based on the fact that the choice between active' and inactive' strategies is subordinated to random-walk like processes. We numerically demonstrate our scenario in the framework of simplified market models, such as the Minority Game model with an inactive strategy, or a more sophisticated version that includes some price dynamics. We show that real market data can be surprisingly well accounted for by these simple models.

• 1. Service de Physique Théorique (SPhT), CNRS : URA2306 – CEA : DSM/SPHT
• 2. Service de physique de l'état condensé (SPEC), CNRS : URA2464 – CEA : DSM/IRAMIS
• 3. Science & Finance, Sciences et Finances
• 4. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• ## Multifractality in uniform hyperbolic lattices and in quasi-classical Liouville field theory

### Alain Comtet 1, Sergei K. Nechaev 1, Raphael Voituriez 1

#### Journal of Statistical Physics 102 (2001) 203-230

We introduce a deterministic model defined on a two dimensional hyperbolic lattice. This model provides an example of a non random system whose multifractal behaviour has a number theoretic origin. We determine the multifractal exponents, discuss the termination of multifractality and conjecture the geometric origin of the multifractal behavior in Liouville quasi--classical field theory.

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

Details
• ## On a universal mechanism for long ranged volatility correlations

### Jean-Philippe Bouchaud 1, 2, Irene Giardina 3, Marc Mézard 4

#### Quantitative Finance 1 (2001) 212-216

We propose a general interpretation for long-range correlation effects in the activity and volatility of financial markets. This interpretation is based on the fact that the choice between active' and inactive' strategies is subordinated to random-walk like processes. We numerically demonstrate our scenario in the framework of simplified market models, such as the Minority Game model with an inactive strategy. We show that real market data can be surprisingly well accounted for by these simple models.

• 1. Service de physique de l'état condensé (SPEC), CNRS : URA2464 – CEA : DSM/IRAMIS
• 2. Science & Finance, Science et Finances
• 3. Service de Physique Théorique (SPhT), CNRS : URA2306 – CEA : DSM/SPHT
• 4. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• ## On the Plants Leaves Boundary, ‘Jupe à Godets’ and Conformal Embeddings

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

#### Journal of Physics A 34 (2001) 11069-11082

he stable profile of the boundary of a plant's leaf fluctuating in the direction transversal to the leaf's surface is described in the framework of a model called a 'surface à godets'. It is shown that the information on the profile is encoded in the Jacobian of a conformal mapping (the coefficient of deformation) corresponding to an isometric embedding of a uniform Cayley tree into the 3D Euclidean space. The geometric characteristics of the leaf's boundary (like the perimeter and the height) are calculated. In addition a symbolic language allowing to investigate statistical properties of a 'surface à godets' with annealed random defects of curvature of density $q$ is developed. It is found that at $q=1$ the surface exhibits a phase transition with critical exponent $\alpha=1/2$ from the exponentially growing to the flat structure.

• 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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• ## On the Relation between the anyon and the Calogero Models

### Stéphane Ouvry 1

#### Physics Letters B 510 (2001) 335

In order to achieve a dimensional reduction from dimension two to one not only in phase space but also in configuration space, the lowest Landau level (LLL) projection is not sufficient. One has also, in the LLL, to take the vanishing magnetic field limit, a procedure which can be given a non ambiguous meaning by means of a long distance regulator. As an illustration, the equivalence of the LLL anyon model in the vanishing magnetic field limit to the Calogero model is established. A thermodynamical argument is proposed which supports this claim. Some general considerations in favor of an intimate connexion between anyon and Haldane statistics are also given.

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

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• ## Percolation line of stable clusters in supercritical fluids

### Xavier Campi 1, Hubert Krivine 1, Nicolas Sator 1

#### Physica A 296 (2001) 24-30

We predict that self-bound clusters of particles exist in the supercritical phase of simple fluids. These clusters, whose internal temperature is lower than the global temperature of the system, define a percolation line that starts at the critical point. This line should be physically observable. Possible experiments showing the validity of these predictions are discussed.

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

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• ## Periodic orbits contribution to the 2-point correlation form factor for pseudo-integrable systems

### Eugene Bogomolny 1, Olivier Giraud 1, Charles Schmit 1

#### Communications in Mathematical Physics 222 (2001) 327-369

The 2-point correlation form factor, $K_2(\tau)$, for small values of $\tau$ is computed analytically for typical examples of pseudo-integrable systems. This is done by explicit calculation of periodic orbit contributions in the diagonal approximation. The following cases are considered: (i) plane billiards in the form of right triangles with one angle $\pi/n$ and (ii) rectangular billiards with the Aharonov-Bohm flux line. In the first model, using the properties of the Veech structure, it is shown that $K_2(0)=(n+\epsilon(n))/(3(n-2))$ where $\epsilon(n)=0$ for odd $n$, $\epsilon(n)=2$ for even $n$ not divisible by 3, and $\epsilon(n)=6$ for even $n$ divisible by 3. For completeness we also recall informally the main features of the Veech construction. In the second model the answer depends on arithmetical properties of ratios of flux line coordinates to the corresponding sides of the rectangle. When these ratios are non-commensurable irrational numbers, $K_2(0)=1-3\bar{\alpha}+4\bar{\alpha}^2$ where $\bar{\alpha}$ is the fractional part of the flux through the rectangle when $0\le \bar{\alpha}\le 1/2$ and it is symmetric with respect to the line $\bar{\alpha}=1/2$ when $1/2 \le \bar{\alpha}\le 1$. The comparison of these results with numerical calculations of the form factor is discussed in detail. The above values of $K_2(0)$ differ from all known examples of spectral statistics, thus confirming analytically the peculiarities of statistical properties of the energy levels in pseudo-integrable systems.

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

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• ## Population dynamics in a random environment

### Irene Giardina 1, Jean-Philippe Bouchaud 2, Marc Mézard 3

#### Journal of Physics A 34 (2001) L245-L252

We investigate the competition between barrier slowing down and proliferation induced superdiffusion in a model of population dynamics in a random force field. Numerical results in $d=1$ suggest that a new intermediate diffusion behaviour appears. We introduce the idea of proliferation assisted barrier crossing and give a Flory like argument to understand qualitatively this non trivial diffusive behaviour. A one loop RG analysis close to the critical dimension d_c=2 confirms that the random force fixed point is unstable and flows towards an uncontrolled strong coupling regime.

• 1. Service de Physique Théorique (SPhT), CNRS : URA2306 – CEA : DSM/SPHT
• 2. Service de physique de l'état condensé (SPEC), CNRS : URA2464 – CEA : DSM/IRAMIS
• 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• ## Resonance-assisted tunneling in near-integrable systems

### Olivier Brodier 1, Peter Schlagheck 1, Denis Ullmo 1

#### Physical Review Letters 87 (2001) 064101

Dynamical tunneling between symmetry related invariant tori is studied in the near-integrable regime. Using the kicked Harper model as an illustration, we show that the exponential decay of the wave functions in the classically forbidden region is modified due to coupling processes that are mediated by classical resonances. This mechanism leads to a substantial deviation of the splitting between quasi-degenerate eigenvalues from the purely exponential decrease with 1 / hbar obtained for the integrable system. A simple semiclassical framework, which takes into account the effect of the resonance substructure on the KAM tori, allows to quantitatively reproduce the behavior of the eigenvalue splittings.

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

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• ## Scattering theory on graphs

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

#### Journal of Physics A 34 (2001) 10307-10326

We consider the scattering theory for the Schrödinger operator $-\Dc_x^2+V(x)$ on graphs made of one-dimensional wires connected to external leads. We derive two expressions for the scattering matrix on arbitrary graphs. One involves matrices that couple arcs (oriented bonds), the other involves matrices that couple vertices. We discuss a simple way to tune the coupling between the graph and the leads. The efficiency of the formalism is demonstrated on a few known examples.

• 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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• ## Semiclassical Density Functional Theory: Strutinsky Energy Corrections in Quantum Dots

### Denis Ullmo 1, Tatsuro Nagano 2, Steven Tomsovic 2, Harold U. Baranger 3

#### Physical Review B 63 (2001) 125339-1-13

We develop a semiclassical density functional theory in the context of quantum dots. Coulomb blockade conductance oscillations have been measured in several experiments using nanostructured quantum dots. The statistical properties of these oscillations remain puzzling, however, particularly the statistics of spacings between conductance peaks. To explore the role that residual interactions may play in the spacing statistics, we consider many-body systems which include electron-electron interactions through an explicit density functional. First, we develop an approximate series expansion for obtaining the ground state using the idea of the Strutinsky shell correction method. Next, we relate the second-order semiclassical corrections to the screened Coulomb potential. Finally, we investigate the validity of the approximation method by numerical calculation of a one-dimensional model system, and show the relative magnitudes of the successive terms as a function of particle number.

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

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• ## Short-range plasma model for intermediate spectral statistics

### Eugene Bogomolny 1, Ulrich Gerland 2, Charles Schmit 1

#### European Physical Journal B 19 (2001) 121-132

We propose a plasma model for spectral statistics displaying level repulsion without long-range spectral rigidity, i.e. statistics intermediate between random matrix and Poisson statistics similar to the ones found numerically at the critical point of the Anderson metal-insulator transition in disordered systems and in certain dynamical systems. The model emerges from Dysons one-dimensional gas corresponding to the eigenvalue distribution of the classical random matrix ensembles by restricting the logarithmic pair interaction to a finite number $k$ of nearest neighbors. We calculate analytically the spacing distributions and the two-level statistics. In particular we show that the number variance has the asymptotic form $\Sigma^2(L)\sim\chi L$ for large $L$ and the nearest-neighbor distribution decreases exponentially when $s\to \infty$, $P(s)\sim\exp (-\Lambda s)$ with $\Lambda=1/\chi=k\beta+1$, where $\beta$ is the inverse temperature of the gas ($\beta=$1, 2 and 4 for the orthogonal, unitary and symplectic symmetry class respectively). In the simplest case of $k=\beta=1$, the model leads to the so-called Semi-Poisson statistics characterized by particular simple correlation functions e.g. $P(s)=4s\exp(-2s)$. Furthermore we investigate the spectral statistics of several pseudointegrable quantum billiards numerically and compare them to the Semi-Poisson statistics.

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

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• ## Singular statistics

### Eugene Bogomolny 1, Ulrich Gerland 2, Charles Schmit 1

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 63 (2001) 036206

We consider the statistical distribution of zeros of random meromorphic functions whose poles are independent random variables. It is demonstrated that correlation functions of these zeros can be computed analytically and explicit calculations are performed for the 2-point correlation function. This problem naturally appears in e.g. rank-one perturbation of an integrable Hamiltonian and, in particular, when a $\delta$-function potential is added to an integrable billiard.

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

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• ## Some Matrix Integrals related to Knots and Links

### Paul Zinn-Justin 1

#### MSRI Publications 40 (2001) 1

The study of a certain class of matrix integrals can be motivated by their interpretation as counting objects of knot theory such as alternating prime links, tangles or knots. The simplest such model is studied in detail and allows to rederive recent results of Sundberg and Thistlethwaite. The second non-trivial example turns out to be essentially the so-called ABAB model, though in this case the analysis has not yet been carried out completely. Further generalizations are discussed. This is a review of work done (in part) in collaboration with J.-B. Zuber.

• 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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• ## Spectral determinant on graphs with generalized boundary conditions

### Jean Desbois 1

#### European Physical Journal B 24 (2001) 261-266

The spectral determinant of the Schrödinger operator ($- \Delta + V(x)$) on a graph is computed for general boundary conditions. ($\Delta$ is the Laplacian and $V(x)$ is some potential defined on the graph). Applications to restricted random walks on graphs are discussed.

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

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• ## Spectral spacing correlations for chaotic and disordered systems

### Oriol Bohigas 1, Patricio Leboeuf 1, Juan Mayor Sanchez 2

#### Foundations of Physics 31 (2001) 489-517

ew aspects of spectral fluctuations of (quantum) chaotic and diffusive systems are considered, namely autocorrelations of the spacing between consecutive levels or spacing autocovariances. They can be viewed as a discretized two point correlation function. Their behavior results from two different contributions. One corresponds to (universal) random matrix eigenvalue fluctuations, the other to diffusive or chaotic characteristics of the corresponding classical motion. A closed formula expressing spacing autocovariances in terms of classical dynamical zeta functions, including the Perron-Frobenius operator, is derived. It leads to a simple interpretation in terms of classical resonances. The theory is applied to zeros of the Riemann zeta function. A striking correspondence between the associated classical dynamical zeta functions and the Riemann zeta itself is found. This induces a resurgence phenomenon where the lowest Riemann zeros appear replicated an infinite number of times as resonances and sub-resonances in the spacing autocovariances. The theoretical results are confirmed by existing data''. The present work further extends the already well known semiclassical interpretation of properties of Riemann zeros.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Departamento de Física J. J. Giambiagi, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires

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• ## Star graphs and Seba billiards

### Gregory Berkolaiko 1, Eugene Bogomolny 2, J.P. Keating 3, 4

#### Journal of Physics A 34 (2001) 335-350

We derive an exact expression for the two-point correlation function for quantum star graphs in the limit as the number of bonds tends to infinity. This turns out to be identical to the corresponding result for certain Seba billiards in the semiclassical limit. Reasons for this are discussed. The formula we derive is also shown to be equivalent to a series expansion for the form factor - the Fourier transform of the two-point correlation function - previously calculated using periodic orbit theory.

• 1. Department of Physics of Complex Systems, Weizmann Institute of Science
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 3. School of Mathematics, University of Bristol
• 4. Basic Research Institute in Mathematical Sciences (BRIMS), Hewlett-Packard Labs

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• ## Statistical mechanics methods and phase transitions in optimization problems

### Olivier C. Martin 1, Rémi Monasson 2, Riccardo Zecchina 3

#### Theoretical Computer Science 265 (2001) 3-67

Recently, it has been recognized that phase transitions play an important role in the probabilistic analysis of combinatorial optimization problems. However, there are in fact many other relations that lead to close ties between computer science and statistical physics. This review aims at presenting the tools and concepts designed by physicists to deal with optimization or decision problems in an accessible language for computer scientists and mathematicians, with no prerequisites in physics. We first introduce some elementary methods of statistical mechanics and then progressively cover the tools appropriate for disordered systems. In each case, we apply these methods to study the phase transitions or the statistical properties of the optimal solutions in various combinatorial problems. We cover in detail the Random Graph, the Satisfiability, and the Traveling Salesman problems. References to the physics literature on optimization are provided. We also give our perspective regarding the interdisciplinary contribution of physics to computer science.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. The James Franck Institute, University of Chicago
• 3. International Centre for Theoretical Physics (ICTP), International Centre for Theoretical Physics

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• ## Statistics of charged solitons and formation of stripes

### Sofian Teber 1, Branko P. Stojkovic 2, Serguei Brazovskii 1, A. R. Bishop 2

#### Journal of Physics: Condensed Matter 13 (2001) 4015-4031

The 2-fold degeneracy of the ground state of a quasi-one-dimensional system allows it to support topological excitations such as solitons. We study the combined effects of Coulomb interactions and confinement due to interchain coupling on the statistics of such defects. We concentrate on a 2D case which may correspond to monolayers of polyacetylene or other charge density waves. The theory is developped by a mapping to the 2D Ising model with long-range 4-spin interactions. The phase diagram exhibits deconfined phases for liquids and Wigner crystals of kinks and confined ones for bikinks. Also we find aggregated phases with either infinite domain walls of kinks or finite rods of bikinks. Roughening effects due to both temperature and Coulomb repulsion are observed. Applications may concern the melting of stripes in doped correlated materials.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory

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• ## The Bethe lattice spin glass revisited

### Marc Mézard 1, Giorgio Parisi 2

#### European Physical Journal B 20 (2001) 217-240

So far the problem of a spin glass on a Bethe lattice has been solved only at the replica symmetric level, which is wrong in the spin glass phase. Because of some technical difficulties, attempts at deriving a replica symmetry breaking solution have been confined to some perturbative regimes, high connectivity lattices or temperature close to the critical temperature. Using the cavity method, we propose a general non perturbative solution of the Bethe lattice spin glass problem at a level of approximation which is equivalent to a one step replica symmetry breaking solution. The results compare well with numerical simulations. The method can be used for many finite connectivity problems appearing in combinatorial optimization.

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

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• ## The dynamical structure factor in topologically disordered systems

### Victor Martin-Mayor 1, Marc Mézard 2, Giorgio Parisi 3, Paolo Verrocchio 4

#### Journal of Chemical Physics 114 (2001) 8068-8081

A computation of the dynamical structure factor of topologically disordered systems, where the disorder can be described in terms of euclidean random matrices, is presented. Among others, structural glasses and supercooled liquids belong to that class of systems. The computation describes their relevant spectral features in the region of the high frequency sound. The analytical results are tested with numerical simulations and are found to be in very good agreement with them. Our results may explain the findings of inelastic X-ray scattering experiments in various glassy systems.

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

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• ## The ferroelectric Mott-Hubbard phase of organic (TMTTF)2X conductors

### Pierre Monceau 1, F. Ya Nad 1, 2, Serguei Brazovskii 3, 4

#### Physical Review Letters 86 (2001) 4080-4083

We present experimental evidences for a ferro-electric transition in the family of quasi one- dimensional conductors (TMTTF)2X. We interpret this new transition in the frame of the combined Mott-Hubbard state taking into account the double action of the spontaneous charge disproportionation on the TMTTF molecular stacks and of the X anionic potentials.

• 1. Centre de Recherches sur les Très Basses Températures (CRTBT), CNRS : UPR5001 – Université Joseph Fourier - Grenoble I – Institut National Polytechnique de Grenoble (INPG)
• 2. Institute of Radio-Engineering and Electronics, Institute of Radio-Engineering and Electronics
• 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 4. L.D. Landau Institute for Theoretical Physics, Landau Institute for Theoretical Physics

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• ## The Riemannium

### Patricio Leboeuf 1, Alejandro Monastra 1, Oriol Bohigas 1

#### Regular and Chaotic Dynamics 6 (2001) 205-210

The properties of a fictitious, fermionic, many-body system based on the complex zeros of the Riemann zeta function are studied. The imaginary part of the zeros are interpreted as mean-field single-particle energies, and one fills them up to a Fermi energy $E_F$. The distribution of the total energy is shown to be non-Gaussian, asymmetric, and independent of $E_F$ in the limit $E_F\to\infty$. The moments of the limit distribution are computed analytically. The autocorrelation function, the finite energy corrections, and a comparison with random matrix theory are also discussed.

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

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• ## Thermodynamics and Topology of Disordered Systems: Statistics of the Random Knot Diagrams on Finite Lattice

### Sergei K. Nechaev 1, 2, Oleg A. Vasilyev 2

#### JETP Letters 93 (2001) 1119-1136

The statistical properties of random lattice knots, the topology of which is determined by the algebraic topological Jones-Kauffman invariants was studied by analytical and numerical methods. The Kauffman polynomial invariant of a random knot diagram was represented by a partition function of the Potts model with a random configuration of ferro- and antiferromagnetic bonds, which allowed the probability distribution of the random dense knots on a flat square lattice over topological classes to be studied. A topological class is characterized by the highest power of the Kauffman polynomial invariant and interpreted as the free energy of a q-component Potts spin system for q->infinity. It is shown that the highest power of the Kauffman invariant is correlated with the minimum energy of the corresponding Potts spin system. The probability of the lattice knot distribution over topological classes was studied by the method of transfer matrices, depending on the type of local junctions and the size of the flat knot diagram. The obtained results are compared to the probability distribution of the minimum energy of a Potts system with random ferro- and antiferromagnetic bonds

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

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• ## Topological Confinement of Spins and Charges: Spinons as pi-junctions

### Serguei Brazovskii 1

#### EDP Sciences 1 (2001) 315

Topologically nontrivial states, the solitons, emerge as elementary excitations in 1D electronic systems. In a quasi 1D material the topological requirements originate the spin- or charge- roton like excitations with charge- or spin- kinks localized in the core. They result from the spin-charge recombination due to confinement and the combined symmetry. The rotons possess semi-integer winding numbers which may be relevant to configurations discussed in connection to quantum computing schemes. Practically important is the case of the spinon functioning as the single electronic pi- junction in a quasi 1D superconducting material.

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

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• ## Topological relaxation of entangled flux lattices: Single vs collective line dynamics

### Ruslan Bikbov 1, Sergei K. Nechaev 1, 2

#### Physical Review Letters 87 (2001) 150602

A symbolic language allowing to solve statistical problems for the systems with nonabelian braid-like topology in 2+1 dimensions is developed. The approach is based on the similarity between growing braid and 'heap of colored pieces'. As an application, the problem of a vortex glass transition in high-T_c superconductors is re-examined on microscopic level

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

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• ## Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models II. Extended Results for Square-Lattice Chromatic Polynomial

### Jesper-Lykke Jacobsen 1, Jesus Salas 2

#### Journal of Statistical Physics 104 (2001) 701-723

We study the chromatic polynomials for m \times n square-lattice strips, of width 9 <= m <= 13 (with periodic boundary conditions) and arbitrary length n (with free boundary conditions). We have used a transfer matrix approach that allowed us also to extract the limiting curves when n \to \infty. In this limit we have also obtained the isolated limiting points for these square-lattice strips and checked some conjectures related to the Beraha numbers.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Departamento de Física Teórica, Facultad de Ciencias, Universidad de Zaragoza

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• ## Unusual corrections to scaling in the 3-state Potts antiferromagnet on a square lattice

### John Cardy 1, Jesper-Lykke Jacobsen 2, Alan D. Sokal 3

#### Journal of Statistical Physics 105 (2001) 25-47

At zero temperature, the 3-state antiferromagnetic Potts model on a square lattice maps exactly onto a point of the 6-vertex model whose long-distance behavior is equivalent to that of a free scalar boson. We point out that at nonzero temperature there are two distinct types of excitation: vortices, which are relevant with renormalization-group eigenvalue 1/2; and non-vortex unsatisfied bonds, which are strictly marginal and serve only to renormalize the stiffness coefficient of the underlying free boson. Together these excitations lead to an unusual form for the corrections to scaling: for example, the correlation length diverges as \beta \equiv J/kT \to \infty according to \xi \sim A e^{2\beta} (1 + b\beta e^{-\beta} + ...), where b is a nonuniversal constant that may nevertheless be determined independently. A similar result holds for the staggered susceptibility. These results are shown to be consistent with the anomalous behavior found in the Monte Carlo simulations of Ferreira and Sokal.

• 1. Oxford University (THEORETICAL PHYSICS), University of Oxford
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 3. New York University (DEPARTMENT OF PHYSICS), New York University

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• ## X-Ray Scattering Evidence for Macroscopic Strong Pinning Centers in the Sliding CDW state of NbSe_3

### D. Rideau 1, 2, Pierre Monceau 1, Roland Currat 2, Herwig Requardt 3, 4, F. Ya Nad 1, 5, J. Lorenzo 2, 4, Serguei Brazovskii 6, C. Detlefs 4, G. Gruebel 4

#### Europhysics Letters (EPL) 56 (2001) 289-295

Using high-resolution X-ray scattering techniques, we measure the variation, q(x), of the position in reciprocal space of the CDW satellite, in the sliding state, along the length of NbSe_3 whiskers. We show that structural defects and intentionally X-ray radiation-damaged regions increase locally the CDW pinning force, and induce CDW phase distortions which are consistent with those observed near contacts. Using the semi-microscopic model from Brazovskii describing the normal-condensed carrier conversion, with spatially varying parameters, we account for the experimental spatial dependence of the CDW phase gradient near both types of defects.

• 1. Centre de Recherches sur les Très Basses Températures (CRTBT), CNRS : UPR5001 – Université Joseph Fourier - Grenoble I – Institut National Polytechnique de Grenoble (INPG)
• 2. Institut Laue-Langevin, Institut Laue-Langevin
• 3. MPI für Metallforschung, MPI für Metallforschung
• 4. European Synchrotron Radiation Facility (ESRF), ESRF
• 5. Institute of Radio-Engineering and Electronics, Institute of Radio-Engineering and Electronics
• 6. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• ## Zero-temperature responses of a 3D spin glass in a magnetic field

### Florent Krzakala 1, Jérôme Houdayer 2, Enzo Marinari 3, Olivier C. Martin 1, Giorgio Parisi 3

#### Physical Review Letters 87 (2001) 197204

We probe the energy landscape of the 3D Edwards-Anderson spin glass in a magnetic field to test for a spin glass ordering. We find that the spin glass susceptibility is anomalously large on the lattice sizes we can reach. Our data suggest that a transition from the spin glass to the paramagnetic phase takes place at B_c=0.65, though the possibility B_c=0 cannot be excluded. We also discuss the question of the nature of the putative frozen phase.

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

Details Citations to the Article (37)
• ## Effect of Microscopic Noise on Front Propagation – Archive ouverte HAL

### Éric BrunetBernard Derrida 1, 2

#### Éric Brunet, Bernard Derrida. Effect of Microscopic Noise on Front Propagation. Journal of Statistical Physics, Springer Verlag, 2001, 103 (1-2), pp.269-282. ⟨10.1023/A:1004875804376⟩. ⟨hal-03282975⟩

We study the effect of the noise due to microscopic fluctuations on the position of a one dimensional front propagating from a stable to an unstable region in the “linearly marginal stability case.” By simulating a very simple system for which the effective number N of particles can be as large as N=10150, we measure the N dependence of the diffusion constant DN of the front and the shift of its velocity vN. Our results indicate that DN∼(log N)−3. They also confirm our recent claim that the shift of velocity scales like vmin−vN≃K(log N)−2 and indicate that the numerical value of K is very close to the analytical expression Kapprox obtained in our previous work using a simple cut-off approximation.

• 1. UPMC - Université Pierre et Marie Curie - Paris 6
• 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

• ## A theory of the subgap photoemission in one – dimensional electron – phonon systems. An instanton approach to pseudogaps

### Serguei Matveenko 1, Serguei Brazovskii 2

#### Physical Review B 65 (2002) 245108

For a one-dimensional electron-phonon system we consider the photon absorption involving electronic excitations within the pseudogap energy range. Within the adiabatic approximation for the electron - phonon interactions these processes are described by nonlinear configurations of an instanton type. We calculate intensities of the photoelectron spectroscopy PES including the momentum resolved one ARPES and supplement to known results for the optical subgap absorption. We start with the generic case of a one dimensional semiconductor with pronounced polaronic effect. In details we consider the Peierls model for a half-filled band of electrons coupled to the lattice which describes the polyacethylene and some commensurate Charge Density Waves. Particular attention was required for studies of momentum dependencies for the ARPES where we face an intriguing interference between the time evolution and the translational motion of the instantons.

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

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• ## A Transfer Matrix approach to the Enumeration of Knots

### Jesper-Lykke Jacobsen 1, Paul Zinn-Justin 1

#### Journal of Knot and its Theoretical Ramifications 11 (2002) 739-758

We propose a new method to enumerate alternating knots using a transfer matrix approach. We apply it to count numerically various objects, including prime alternating tangles with two connected components, up to order 18--22, and comment on the large-order behavior in connection with one of the authors' conjecture.

• 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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• ## A Transfer Matrix for the Backbone Exponent of Two-Dimensional Percolation

### Jesper-Lykke Jacobsen 1, Paul Zinn-Justin 1

#### Journal of Physics A 35 (2002) 2131-2144

Rephrasing the backbone of two-dimensional percolation as a monochromatic path crossing problem, we investigate the latter by a transfer matrix approach. Conformal invariance links the backbone dimension D_b to the highest eigenvalue of the transfer matrix T, and we obtain the result D_b=1.6431 \pm 0.0006. For a strip of width L, T is roughly of size 2^{3^L}, but we manage to reduce it to \sim L!. We find that the value of D_b is stable with respect to inclusion of additional blobs'' tangent to the backbone in a finite number of points.

• 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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• ## Absence of an equilibrium ferromagnetic spin glass phase in three dimensions

### Florent Krzakala 1, Olivier C. Martin 1

#### Physical Review Letters 89 (2002) 267202

Using ground state computations, we study the transition from a spin glass to a ferromagnet in 3-d spin glasses when changing the mean value of the spin-spin interaction. We find good evidence for replica symmetry breaking up till the critical value where ferromagnetic ordering sets in, and no ferromagnetic spin glass phase. This phase diagram is in conflict with the droplet/scaling and mean field theories of spin glasses. We also find that the exponents of the second order ferromagnetic transition do not depend on the microscopic Hamiltonian, suggesting universality of this transition.

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

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• ## Almost sure convergence of the minimum bipartite matching functional in Euclidean space

### J. Boutet De Monvel 1, Olivier C. Martin 2

#### COMBINATORICA 22 (2002) 523-530

Let $L_N = L_{MBM}(X_1,..., X_N; Y_1,..., Y_N)$ be the minimum length of a bipartite matching between two sets of points in $\mathbf{R}^d$, where $X_1,..., X_N,...$ and $Y_1,..., Y_N,...$ are random points independently and uniformly distributed in $[0,1]^d$. We prove that for $d \ge 3$, $L_N/N^{1-1/d}$ converges with probability one to a constant $\beta_{MBM}(d)>0$ as $N\to \infty$.

• 1. Center for Hearing and Communication Research, Karolinska Institutet
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• ## Breakdown of superfluidity of an atom laser past an obstacle

### Nicolas Pavloff 1

#### Physical Review A: Atomic, Molecular and Optical Physics 66 (2002) 013610

The 1D flow of a continuous beam of Bose-Einstein condensed atoms in the presence of an obstacle is studied as a function of the beam velocity and of the type of perturbing potential (representing the interaction of the obstacle with the atoms of the beam). We identify the relevant regimes: stationary/time-dependent and superfluid/dissipative; the absence of drag is used as a criterion for superfluidity. There exists a critical velocity below which the flow is superfluid. For attractive obstacles, we show that this critical velocity can reach the value predicted by Landau's approach. For penetrable obstacles, it is shown that superfluidity is recovered at large beam velocity. Finally, enormous differences in drag occur when switching from repulsive to attractive potential.

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

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• ## Chaotic temperature dependence in a model of spin glasses

### Florent Krzakala 1, Olivier C. Martin 1

#### European Physical Journal B 20 (2002) 199

We address the problem of chaotic temperature dependence in disordered glassy systems at equilibrium by following states of a random-energy random-entropy model in temperature; of particular interest are the crossings of the free-energies of these states. We find that this model exhibits strong, weak or no temperature chaos depending on the value of an exponent. This allows us to write a general criterion for temperature chaos in disordered systems, predicting the presence of temperature chaos in the Sherrington-Kirkpatrick and Edwards-Anderson spin glass models, albeit when the number of spins is large enough. The absence of chaos for smaller systems may justify why it is difficult to observe chaos with current simulations. We also illustrate our findings by studying temperature chaos in the naive mean field equations for the Edwards-Anderson spin glass.

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

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• ## Deviations from Perfect Memory in Spin Glass Temperature Cycling Experiments

### M. Sasaki 1, V. Dupuis 2, J. -P. Bouchaud 2, E. Vincent 2

#### European Physical Journal B 29 (2002) 469

We study the deviations from perfect memory in negative temperature cycle spin glass experiments. It is known that the a.c. susceptibility after the temperature is raised back to its initial value is superimposed to the reference isothermal curve for large enough temperature jumps DT (perfect memory). For smaller DT, the deviation from this perfect memory has a striking non monotonous behavior: the memory anomaly is negative for small DT's, becomes positive for intermediate DT's, before vanishing for still larger DT's. We show that this interesting behavior can be reproduced by simple Random Energy trap models. We discuss an alternative interpretation in terms of droplets and temperature chaos.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Service de physique de l'état condensé (SPEC), CNRS : URA2464 – CEA : DSM/IRAMIS

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• ## Discreteness and entropic fluctuations in GREM-like systems

### M. Sasaki 1, O. C. Martin 1, 2

#### Physical Review B 66 (2002) 174411

Within generalized random energy models, we study the effects of energy discreteness and of entropy extensivity in the low temperature phase. At zero temperature, discreteness of the energy induces replica symmetry breaking, in contrast to the continuous case where the ground state is unique. However, when the ground state energy has an extensive entropy, the distribution of overlaps P(q) instead tends towards a single delta function in the large volume limit. Considering now the whole frozen phase, we find that P(q) varies continuously with temperature, and that state-to-state fluctuations of entropy wash out the differences between the discrete and continuous energy models.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Service de physique de l'état condensé (SPEC), CNRS : URA2464 – CEA : DSM/IRAMIS

Details Citations to the Article (2)
• ## Dynamics of ballistic annihilation

### Jaroslaw Piasecki, Emmanuel Trizac 1, 2, Michel Droz

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 66 (2002) 066111

The problem of ballistically controlled annihilation is revisited for general initial velocity distributions and arbitrary dimension. An analytical derivation of the hierarchy equations obeyed by the reduced distributions is given, and a scaling analysis of the corresponding spatially homogeneous system is performed. This approach points to the relevance of the non-linear Boltzmann equation for dimensions larger than one and provides expressions for the exponents describing the decay of the particle density n(t) ~ t^{-\xi} and the root mean-square velocity ${\bar v} ~ t^{-\gamma}$ in term of a parameter related to the dissipation of kinetic energy. The Boltzmann equation is then solved perturbatively within a systematic expansion in Sonine polynomials. Analytical expressions for the exponents $\xi$ and $\gamma$ are obtained in arbitrary dimension as a function of the parameter $\mu$ characterizing the small velocity behavior of the initial velocity distribution. Moreover, the leading non-Gaussian corrections to the scaled velocity distribution are computed. These expressions for the scaling exponents are in good agreement with the values reported in the literature for continuous velocity distributions in $d=1$. For the two dimensional case, we implement Monte-Carlo and molecular dynamics simulations that turn out to be in excellent agreement with the analytical predictions.

• 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 Asymptotic Results for Persistence in the Sinai Model with Arbitrary Drift

### Alain Comtet 1, 2, Satya N. Majumdar 3

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 66 (2002) 061105

We obtain exact asymptotic results for the disorder averaged persistence of a Brownian particle moving in a biased Sinai landscape. We employ a new method that maps the problem of computing the persistence to the problem of finding the energy spectrum of a single particle quantum Hamiltonian, which can be subsequently found. Our method allows us analytical access to arbitrary values of the drift (bias), thus going beyond the previous methods which provide results only in the limit of vanishing drift. We show that on varying the drift, the persistence displays a variety of rich asymptotic behaviors including, in particular, interesting qualitative changes at some special values of the drift.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. IHP, Institut Henri Poincaré
• 3. Laboratoire de Physique Quantique (LPQ), CNRS : UMR5626 – Université Paul Sabatier - Toulouse III

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• ## First Steps in Glass Theory

### Marc Mézard 1

#### More is different, Ong and Bhatt editors 1 (2002) 1

This paper is an introduction to some of the main present issues in the theory of structural glasses. After recalling a few experimental facts, it gives a short account of the analogy between fragile glasses and the mean field discontinuous spin glasses. The many valley picture is presented, and a brief account of recent attempts to obtain quantitative results from first principle computations is summarised.

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

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• ## HCIZ integral and 2D Toda lattice hierarchy

### Paul Zinn-Justin 1

#### Nuclear Physics B 634 (2002) 417

The expression of the large $N$ Harish Chandra--Itzykson--Zuber (HCIZ) integral in terms of the moments of the two matrices is investigated using an auxiliary unitary two-matrix model, the associated biorthogonal polynomials and integrable hierarchy. We find that the large $N$ HCIZ integral is governed by the dispersionless Toda lattice hierarchy and derive its string equation. We use this to obtain various exact results on its expansion in powers of the moments.

• 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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• ## Inhomogeneous Six-Vertex Model with Domain Wall Boundary Conditions and Bethe Ansatz

### Vladimir Korepin 1, Paul Zinn-Justin 1

#### Journal of Mathematical Physics 43 (2002) 3261-3267

In this note, we consider the six-vertex model with domain wall boundary conditions, defined on a $M\times M$ lattice, in the inhomogeneous case where the partition function depends on 2M inhomogeneities $\lambda_j$ and $\mu_k$. For a particular choice of the set of $\lambda_j$ we find a new determinant representation for the partition function, which allows evaluation of the bulk free energy in the thermodynamic limit. This provides a new connection between two types of determinant formulae. We also show in a special case that spin correlations on the horizontal line going through the center coincide with the ones for periodic boundary conditions.

• 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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• ## Iterated Local Search

### Helena R. Lourenco 1, Olivier C. Martin 2, Thomas Stützle 3

#### Science Kluwer 57 (2002) 321-353

This is a survey of 'Iterated Local Search', a general purpose metaheuristic for finding good solutions of combinatorial optimization problems. It is based on building a sequence of (locally optimal) solutions by: (1) perturbing the current solution; (2) applying local search to that modified solution. At a high level, the method is simple, yet it allows for a detailed use of problem-specific properties. After giving a general framework, we cover the uses of Iterated Local Search on a number of well studied problems.

• 1. IMIM-Hospital del Mar, Generalitat de Catalunya
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• ## Lattice Glass Models

### Giulio Biroli 1, Marc Mézard 2

#### Physical Review Letters 88 (2002) 025501

Motivated by the concept of geometrical frustration, we introduce a class of statistical mechanics lattice models for the glass transition. Monte Carlo simulations in three dimensions show that they display a dynamical glass transition which is very similar to that observed in other off-lattice systems and which does not depend on a specific dynamical rule. Whereas their analytic solution within the Bethe approximation shows that they do have a discontinuous glass transition compatible with the numerical observations.

• 1. Center for Material Theory, Department of Physics and Astronomy, Rutgers University
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• ## Matrix Integrals and the Counting of Tangles and Links

### Paul Zinn-Justin 1, Jean-Bernard Zuber 2

#### Disc. Math. 246 (2002) 343

Using matrix model techniques for the counting of planar Feynman diagrams, recent results of Sundberg and Thistlethwaite on the counting of alternating tangles and links are reproduced.

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

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• ## Monochromatic path crossing exponents and graph connectivity in 2D percolation

### Jesper-Lykke Jacobsen 1, Paul Zinn-Justin 1

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 66 (2002) 055102

We consider the fractal dimensions d_k of the k-connected part of percolation clusters in two dimensions, generalizing the cluster (k=1) and backbone (k=2) dimensions. The codimensions X_k = 2-d_k describe the asymptotic decay of the probabilities P(r,R) ~ (r/R)^{X_k} that an annulus of radii r<>1 is traversed by k disjoint paths, all living on the percolation clusters. Using a transfer matrix approach, we obtain numerical results for X_k, k<=6. They are well fitted by the Ansatz X_k = 1/12 k^2 + 1/48 k + (1-k)C, with C = 0.0181+-0.0006.

• 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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• ## Nature of the glassy phase of RNA secondary structure

### Florent Krzakala 1, Marc Mézard 1, Markus Muller 1

#### Europhysics Letters (EPL) 57 (2002) 752-758

We characterize the low temperature phase of a simple model for RNA secondary structures by determining the typical energy scale E(l) of excitations involving l bases. At zero temperature, we find a scaling law E(l) \sim l^\theta with \theta \approx 0.23, and this same scaling holds at low enough temperatures. Above a critical temperature, there is a different phase characterized by a relatively flat free energy landscape resembling that of a homopolymer with a scaling exponent \theta=1. These results strengthen the evidence in favour of the existence of a glass phase at low temperatures.

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

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• ## Non-compact local excitations in spin glasses

### Julien Lamarcq 1, Jean-Philippe Bouchaud 1, Olivier C. Martin 2, Marc Mézard 2

#### Europhysics Letters (EPL) 58 (2002) 321

We study numerically the local low-energy excitations in the 3-d Edwards-Anderson model for spin glasses. Given the ground state, we determine the lowest-lying connected cluster of flipped spins with a fixed volume containing one given spin. These excitations are not compact, having a fractal dimension close to two, suggesting an analogy with lattice animals. Also, their energy does not grow with their size; the associated exponent is slightly negative whereas the one for compact clusters is positive. These findings call for a modification of the basic hypotheses underlying the droplet model.

• 1. Service de physique de l'état condensé (SPEC), CNRS : URA2464 – CEA : DSM/IRAMIS
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• ## Nuclear masses: evidence of order-chaos coexistence

### Oriol Bohigas 1, Patricio Leboeuf 1

#### Physical Review Letters 88 (2002) 092502

Shell corrections are important in the determination of nuclear ground-state masses and shapes. Although general arguments favor a regular single-particle dynamics, symmetry-breaking and the presence of chaotic layers cannot be excluded. The latter provide a natural framework that explains the observed differences between experimental and computed masses.

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

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• ## On the Reactions A+A+…+A->0 at a One-Dimensional Periodic Lattice of Catalytic Centers: Exact Solution

### Alexei A. Naidenov 1, Sergei K. Nechaev 2

#### JETP Letters 76 (2002) 61-65

The kinetics of the diffusion-controlled chemical reactions A+A+...+A->0 that occur at catalytic centers periodically arranged along a straight line is considered. Modes of the behavior of reaction probability W(t) were studied at different times and different densities of the catalyst. Within the Smoluchowski approximation, it was rigorously proved that at large times the function W(t) is independent of the lattice period. This means that, in the given asymptotic mode, the probability of the reaction on a lattice with a catalyst placed in each lattice site is the same as on a lattice with a catalyst placed in sparse sites

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

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• ## Percolation model for nodal domains of chaotic wave functions

### Eugene Bogomolny 1, Charles Schmit 1

#### Physical Review Letters 88 (2002) 114102

Nodal domains are regions where a function has definite sign. In recent paper [nlin.CD/0109029] it is conjectured that the distribution of nodal domains for quantum eigenfunctions of chaotic systems is universal. We propose a percolation-like model for description of these nodal domains which permits to calculate all interesting quantities analytically, agrees well with numerical simulations, and due to the relation to percolation theory opens the way of deeper understanding of the structure of chaotic wave functions.

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

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• ## Phase diagram and critical exponents of a Potts gauge glass

### Jesper-Lykke Jacobsen 1, Marco Picco 2

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 65 (2002) 026113

The two-dimensional q-state Potts model is subjected to a Z_q symmetric disorder that allows for the existence of a Nishimori line. At q=2, this model coincides with the +/- J random-bond Ising model. For q>2, apart from the usual pure and zero-temperature fixed points, the ferro/paramagnetic phase boundary is controlled by two critical fixed points: a weak disorder point, whose universality class is that of the ferromagnetic bond-disordered Potts model, and a strong disorder point which generalizes the usual Nishimori point. We numerically study the case q=3, tracing out the phase diagram and precisely determining the critical exponents. The universality class of the Nishimori point is inconsistent with percolation on Potts clusters.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 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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• ## Projection on higher Landau levels and non-commutative geometry

### Nicolas Macris 1, Stéphane Ouvry 2

#### Journal of Physics A 35 (2002) 4477-4484

The projection of a two dimensional planar system on the higher Landau levels of an external magnetic field is formulated in the language of the non commutative plane and leads to a new class of star products.

• 1. Institut de Physique Théorique (IPT), École Polytechnique Fédérale de Lausanne
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• ## Random walks on the braid group B_3 and magnetic translations in hyperbolic geometry

### Raphael Voituriez 1

#### Nuclear Physics B 621 (2002) 675-688

We study random walks on the three-strand braid group $B_3$, and in particular compute the drift, or average topological complexity of a random braid, as well as the probability of trivial entanglement. These results involve the study of magnetic random walks on hyperbolic graphs (hyperbolic Harper-Hofstadter problem), what enables to build a faithful representation of $B_3$ as generalized magnetic translation operators for the problem of a quantum particle on the hyperbolic plane.

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

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• ## Resonance-Assisted Tunneling

### Olivier Brodier 1, Peter Schlagheck 1, 2, Denis Ullmo 1

#### Annals of Physics 300 (2002) 88-136

We present evidence that tunneling processes in near-integrable systems are enhanced due to the manifestation of nonlinear resonances and their respective island chains in phase space. A semiclassical description of this 'resonance-assisted' mechanism is given, which is based on a local perturbative description of the dynamics in the vicinity of the resonances. As underlying picture, we obtain that the quantum state is coupled, via a succession of classically forbidden transitions across nonlinear resonances, to high excitations within the well, from where tunneling occurs with a rather large rate. The connection between this description and the complex classical structure of the underlying integrable dynamics is furthermore studied, giving ground to the general coherence of the description as well as guidelines for the identification of the dominant tunneling paths. The validity of this mechanism is demonstrated within the kicked Harper model, where good agreement between quantum and semiclassical (resonance-assisted) tunneling rates is found.

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

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• ## Scattering theory on graphs (2): the Friedel sum rule

### Christophe Texier 1, 2

#### Journal of Physics A 35 (2002) 3389-3407

We consider the Friedel sum rule in the context of the scattering theory for the Schrödinger operator $-\Dc_x^2+V(x)$ on graphs made of one-dimensional wires connected to external leads. We generalize the Smith formula for graphs. We give several examples of graphs where the state counting method given by the Friedel sum rule is not working. The reason for the failure of the Friedel sum rule to count the states is the existence of states localized in the graph and not coupled to the leads, which occurs if the spectrum is degenerate and the number of leads too small.

• 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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• ## Statistical Physics of the Glass Phase

### Marc Mézard 1

#### Physica A 306 (2002) 25

This paper gives an introduction to some of the statistical physics problems which appear in the study of structural glasses. It is a shortened and updated version of a more detailed review paper which has appeared in cond-mat/0005173.

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

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• ## Statistical properties of charged interfaces

### Sofian Teber 1

#### Journal of Physics: Condensed Matter 14 (2002) 7811-7834

We consider the equilibrium statistical properties of interfaces submitted to competing interactions; a long-range repulsive Coulomb interaction inherent to the charged interface and a short-range, anisotropic, attractive one due to either elasticity or confinement. We focus on one-dimensional interfaces such as strings. Model systems considered for applications are mainly aggregates of solitons in polyacetylene and other charge density wave systems, domain lines in uniaxial ferroelectrics and the stripe phase of oxides. At zero temperature, we find a shape instability which lead, via phase transitions, to tilted phases. Depending on the regime, elastic or confinement, the order of the zero-temperature transition changes. Thermal fluctuations lead to a pure Coulomb roughening of the string, in addition to the usual one, and to the presence of angular kinks. We suggest that such instabilities might explain the tilting of stripes in cuprate oxides. The 3D problem of the charged wall is also analyzed. The latter experiences instabilities towards various tilted phases separated by a tricritical point in the elastic regime. In the confinement regime, the increase of dimensionality favors either the melting of the wall into a Wigner crystal of its constituent charges or a strongly inclined wall which might have been observed in nickelate oxides.

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

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• ## Statistical properties of stock order books: empirical results and models

### Jean-Philippe Bouchaud 1, 2, Marc Mézard 2, 3, Marc Potters 2

#### Quantitative Finance 2 (2002) 251-256

We investigate several statistical properties of the order book of three liquid stocks of the Paris Bourse. The results are to a large degree independent of the stock studied. The most interesting features concern (i) the statistics of incoming limit order prices, which follows a power-law around the current price with a diverging mean; and (ii) the humped shape of the average order book, which can be quantitatively reproduced using a zero intelligence' numerical model, and qualitatively predicted using a simple approximation

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

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• ## Temperature chaos in a replica symmetry broken spin glass model – A hierarchical model with temperature chaos –

### Munetaka Sasaki 1, Olivier C. Martin 1, 2

#### Europhysics Letters (EPL) 66 (2002) 316

Temperature chaos is an extreme sensitivity of the equilibrium state to a change of temperature. It arises in several disordered systems that are described by the so called scaling theory of spin glasses, while it seems to be absent in mean field models. We consider a model spin glass on a tree and show that although it has mean field behavior with replica symmetry breaking, it manifestly has strong'' temperature chaos. We also show why chaos appears only very slowly with system size.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Service de physique de l'état condensé (SPEC), CNRS : URA2464 – CEA : DSM/IRAMIS

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• ## The Combinatorics of Alternating Tangles: from theory to computerized enumeration

### Jesper-Lykke Jacobsen 1, Paul Zinn-Justin 1

#### NATO Science series II: Mathematics, physics and chemistry 73 (2002) 33-45

We study the enumeration of alternating links and tangles, considered up to topological (flype) equivalences. A weight $n$ is given to each connected component, and in particular the limit $n\to 0$ yields information about (alternating) knots. Using a finite renormalization scheme for an associated matrix model, we first reduce the task to that of enumerating planar tetravalent diagrams with two types of vertices (self-intersections and tangencies), where now the subtle issue of topological equivalences has been eliminated. The number of such diagrams with $p$ vertices scales as $12^p$ for $p\to\infty$. We next show how to efficiently enumerate these diagrams (in time $\sim 2.7^p$) by using a transfer matrix method. We give results for various generating functions up to 22 crossings. We then comment on their large-order asymptotic behavior.

• 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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• ## The Local and the Occupation Time of a Particle Diffusing in a Random Medium

### Satya N. Majumdar 1, Alain Comtet 2, 3

#### Physical Review Letters 89 (2002) 060601

We consider a particle moving in a one dimensional potential which has a symmetric deterministic part and a quenched random part. We study analytically the probability distributions of the local time (spent by the particle around its mean value) and the occupation time (spent above its mean value) within an observation time window of size t. The random part of the potential is same as in the Sinai model, i.e., the potential itself is a random walk in space. In the absence of the random potential, these distributions have three typical asymptotic behaviors depending on whether the deterministic potential is unstable, stable or flat. These asymptotic behaviors are shown to get drastically modified when the random part of the potential is switched on leading to the loss of self-averaging and wide sample to sample fluctuations.

• 1. Laboratoire de Physique Quantique (LPQ), CNRS : UMR5626 – Université Paul Sabatier - Toulouse III
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 3. IHP, Institut Henri Poincaré

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• ## The Local Time Distribution of a Particle Diffusing on a Graph

### Alain Comtet 1, 2, Jean Desbois 1, Satya N. Majumdar 3

#### Journal of Physics A 35 (2002) L687-L694

We study the local time distribution of a Brownian particle diffusing along the links on a graph. In particular, we derive an analytic expression of its Laplace transform in terms of the Green's function on the graph. We show that the asymptotic behavior of this distribution has non-Gaussian tails characterized by a nontrivial large deviation function.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. IHP, Institut Henri Poincaré
• 3. Laboratoire de Physique Quantique (LPQ), CNRS : UMR5626 – Université Paul Sabatier - Toulouse III

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• ## The random K-satisfiability problem: from an analytic solution to an efficient algorithm

### Marc Mézard 1, Riccardo Zecchina 2

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 66 (2002) 056126

We study the problem of satisfiability of randomly chosen clauses, each with K Boolean variables. Using the cavity method at zero temperature, we find the phase diagram for the K=3 case. We show the existence of an intermediate phase in the satisfiable region, where the proliferation of metastable states is at the origin of the slowdown of search algorithms. The fundamental order parameter introduced in the cavity method, which consists of surveys of local magnetic fields in the various possible states of the system, can be computed for one given sample. These surveys can be used to invent new types of algorithms for solving hard combinatorial optimizations problems. One such algorithm is shown here for the 3-sat problem, with very good performances.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. The Abdus Salam International Centre for Theoretical Physics, Statistical Mechanics and Interdisciplinary Applications Group, the Abdus Salam International Centre for Theoretical Physics

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• ## The secondary structure of RNA under tension

### Markus Muller 1, Florent Krzakala 1, Marc Mézard 1

#### European Physical Journal E 9 (2002) 67-77

We study the force-induced unfolding of random disordered RNA or single-stranded DNA polymers. The system undergoes a second order phase transition from a collapsed globular phase at low forces to an extensive necklace phase with a macroscopic end-to-end distance at high forces. At low temperatures, the sequence inhomogeneities modify the critical behaviour. We provide numerical evidence for the universality of the critical exponents which, by extrapolation of the scaling laws to zero force, contain useful information on the ground state (f=0) properties. This provides a good method for quantitative studies of scaling exponents characterizing the collapsed globule. In order to get rid of the blurring effect of thermal fluctuations we restrict ourselves to the groundstate at fixed external force. We analyze the statistics of rearrangements, in particular below the critical force, and point out its implications for force-extension experiments on single molecules.

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

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• ## Theory of pseudogaps in charge density waves in application to photo electron or tunneling spectroscopy

### Serguei Matveenko 1, Serguei Brazovskii 2

#### Journal de Physique IV Colloque 12 (2002) 73

For a one-dimensional electron-phonon system we consider the photon absorption involving electronic excitations within the pseudogap energy range. In the framework of the adiabatic approximation for the electron - phonon interactions these processes are described by nonlinear configurations of an instanton type. We calculate the subgap absorption as it can be observed by means of photo electron or tunneling spectroscopies. In details we consider systems with gapless modes: 1D semiconductors with acoustic phonons and incommensurate charge density waves. We find that below the free particle edge the pseudogap starts with the exponential decrease of transition rates changing to a power law deeply within the pseudogap, near the absolute edge.

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

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• ## Theory of the ferroelectric phase in organic conductors: optics and physics of solitons

### Serguei Brazovskii 1

#### Journal de Physique IV Colloque 12 (2002) 149

Recently the ferroelectric anomaly (Nad, Monceau, et al) followed by the charge disproportionation (Brown, et al) have been discovered in (TMTTF)2X compounds. The corresponding theory of the combined Mott-Hubbard state describes both effects by interference of the build-in nonequivalence of bonds and the spontaneous one of sites. The state gives rise to three types of solitons: \pi solitons (holons) are observed via the activation energy \Delta in the conductivity $G$; noninteger \alpha solitons (the FE domain walls) provide the frequency dispersion of the ferroelectric response; combined spin-charge solitons determine G(T) below subsequent structural transitions of the tetramerisation. The photoconductivity gap 2\Delta is determined by creations of soliton - antisoliton pairs. The optical edge lies well below, given by the collective ferroelectric mode which coexists with the combined electron-phonon resonance and the phonon antiresonance. The charge disproportionation and the ferroelectricity can exist hiddenly even in the Se subfamily giving rise to the unexplained yet low frequency optical peak, the enhanced pseudogap and traces of phonons activation.

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

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• ## Thermodynamics of small Fermi systems: quantum statistical fluctuations

### Patricio Leboeuf 1, Alejandro Monastra 1

#### Annals of Physics 297 (2002) 127-156

We investigate the probability distribution of the quantum fluctuations of thermodynamic functions of finite, ballistic, phase-coherent Fermi gases. Depending on the chaotic or integrable nature of the underlying classical dynamics, on the thermodynamic function considered, and on temperature, we find that the probability distributions are dominated either (i) by the local fluctuations of the single-particle spectrum on the scale of the mean level spacing, or (ii) by the long-range modulations of that spectrum produced by the short periodic orbits. In case (i) the probability distributions are computed using the appropriate local universality class, uncorrelated levels for integrable systems and random matrix theory for chaotic ones. In case (ii) all the moments of the distributions can be explicitly computed in terms of periodic orbit theory, and are system-dependent, non-universal, functions. The dependence on temperature and number of particles of the fluctuations is explicitly computed in all cases, and the different relevant energy scales are displayed

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

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• ## Universality of coupled Potts models

### Vladimir S. Dotsenko 1, Jesper-Lykke Jacobsen 2, Xuan Son Nguyen 1, Raoul Santachiara 1

#### Nuclear Physics B 631 (2002) 426-446

We study systems of M Potts models coupled by their local energy density. Each model is taken to have a distinct number of states, and the permutational symmetry S_M present in the case of identical coupled models is thus broken initially. The duality transformations within the space of 2^M-1 multi-energy couplings are shown to have a particularly simple form. The selfdual manifold has dimension D_M = 2^{M-1}-1. Specialising to the case M=3, we identify a unique non-trivial critical point in the three-dimensional selfdual space. We compare its critical exponents as computed from the perturbative renormalisation group with numerical transfer matrix results. Our main objective is to provide evidence that at the critical point of three different coupled models the symmetry S_3 is restored.

• 1. Laboratoire de Physique Théorique et Hautes Energies (LPTHE), CNRS : UMR7589 – Université Paris VI - Pierre et Marie Curie – Université Paris VII - Paris Diderot
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• ## Alternative solutions to diluted p-spin models and XORSAT problems

### Marc Mézard 1, Federico Ricci-Tersenghi 2, Riccardo Zecchina 3

#### Journal of Statistical Physics 111 (2003) 505-533

We derive analytical solutions for p-spin models with finite connectivity at zero temperature. These models are the statistical mechanics equivalent of p-XORSAT problems in theoretical computer science. We give a full characterization of the phase diagram: location of the phase transitions (static and dynamic), together with a description of the clustering phenomenon taking place in configurational space. We use two alternative methods: the cavity approach and a rigorous derivation.

• 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 Center for Theoretical Physics, International Center for Theoretical Physics

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• ## Brownian Motion in wedges, last passage time and the second arc-sine law

### Alain Comtet 1, 2, Jean Desbois 1

#### Journal of Physics A 36 (2003) L255-L262

We consider a planar Brownian motion starting from $O$ at time $t=0$ and stopped at $t=1$ and a set $F= \{OI_i ; i=1,2,..., n\}$ of $n$ semi-infinite straight lines emanating from $O$. Denoting by $g$ the last time when $F$ is reached by the Brownian motion, we compute the probability law of $g$. In particular, we show that, for a symmetric $F$ and even $n$ values, this law can be expressed as a sum of $\arcsin$ or $(\arcsin)^2$ functions. The original result of Levy is recovered as the special case $n=2$. A relation with the problem of reaction-diffusion of a set of three particles in one dimension is discussed.

• 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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• ## Charge and current distribution in graphs

### Christophe Texier 1, 2, Pascal Degiovanni 3

#### Journal of Physics A 36 (2003) 12425-12452

We consider graphs made of one-dimensional wires connected at vertices, and on which may live a scalar potential. We are interested in a scattering situation where such a network is connected to infinite leads. We study the correlations of the charge in such graphs out of equilibrium, as well as the distribution of the currents in the wires, inside the graph. These quantities are related to the scattering matrix of the graph. We discuss the case where the graph is weakly connected to the wires.

• 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
• 3. Laboratoire de Physique de l'ENS Lyon (Phys-ENS), CNRS : UMR5672 – École Normale Supérieure - Lyon

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• ## Dense loops, supersymmetry, and Goldstone phases in two dimensions

### Jesper-Lykke Jacobsen 1, Nicholas Read 2, Hubert Saleur 3

#### Physical Review Letters 90 (2003) 090601

Loop models in two dimensions can be related to O(N) models. The low-temperature dense-loops phase of such a model, or of its reformulation using a supergroup as symmetry, can have a Goldstone broken-symmetry phase for N<2. We argue that this phase is generic for -2< N <2 when crossings of loops are allowed, and distinct from the model of non-crossing dense loops first studied by Nienhuis [Phys. Rev. Lett. 49, 1062 (1982)]. Our arguments are supported by our numerical results, and by a lattice model solved exactly by Martins et al. [Phys. Rev. Lett. 81, 504 (1998)].

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

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• ## Energy exponents and corrections to scaling in Ising spin glasses

### Jean-Philippe Bouchaud 1, Florent Krzakala 2, 3, Olivier C. Martin 1, 2

#### Physical Review B 68 (2003) 224404

We study the probability distribution P(E) of the ground state energy E in various Ising spin glasses. In most models, P(E) seems to become Gaussian with a variance growing as the system's volume V. Exceptions include the Sherrington-Kirkpatrick model (where the variance grows more slowly, perhaps as the square root of the volume), and mean field diluted spin glasses having +/-J couplings. We also find that the corrections to the extensive part of the disorder averaged energy grow as a power of the system size; for finite dimensional lattices, this exponent is equal, within numerical precision, to the domain-wall exponent theta_DW. We also show how a systematic expansion of theta_DW in powers of exp(-d) can be obtained for Migdal-Kadanoff lattices. Some physical arguments are given to rationalize our findings.

• 1. Service de physique de l'état condensé (SPEC), CNRS : URA2464 – CEA : DSM/IRAMIS
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 3. Dipartimento di Fisica, INFM – SMC – Università degli studi di Roma I - La Sapienza

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• ## Ferroelectric Mott-Hubbard phase in organic conductors

### Serguei Brazovskii 1, Pierre Monceau 2, F. Ya Nad 3

#### Synthetic Metals 137 (2003) 1331-1333

We present key issues of related phenomenons of the Ferroelectricity and the Charge Disproportionation in organic metals. In (TMTTF_2X the dielectric susceptibility demonstrates clear cases of the ferroelectric and anti-ferroelectric phase transitions. Both the susceptibility and the conductivity prove independence and occasional coexistence of 'structurless' ferroelectric transitions and usual 'anionic' ones. Their sequence gives access to physics of three types of solitons emerging upon cooling via several steps of symmetry breaking. The theory invokes a concept of the Combined Mott-Hubbard State which focuses upon weak processes of electronic Umklapp scattering coming from both the build-in nonequivalence of bonds and the spontaneous one of sites. We propose that the charge ordering in its form of the ferroelectricity exists hiddenly even in the Se subfamily (TMTSF)_2X, giving rise to the unexplained yet low frequency optical peak and the enhanced pseudogap.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Centre de Recherches sur les Très Basses Températures (CRTBT), CNRS : UPR5001 – Université Joseph Fourier - Grenoble I – Institut National Polytechnique de Grenoble (INPG)

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• ## Local excitations of a spin glass in a magnetic field

### Julien Lamarcq 1, Jean-Philippe Bouchaud 1, Olivier C. Martin 2

#### Physical Review B 68 (2003) 012404

We study the minimum energy clusters (MEC) above the ground state for the 3-d Edwards-Anderson Ising spin glass in a magnetic field. For fields B below 0.4, we find that the field has almost no effect on the excitations that we can probe, of volume V <= 64. As found previously for B=0, their energies decrease with V, and their magnetization remains very small (even slightly negative). For larger fields, both the MEC energy and magnetization grow with V, as expected in a paramagnetic phase. However, all results appear to scale as BV (instead of the B sqrt(V) expected from droplet arguments), suggesting that the spin glass phase is destroyed by any small field. Finally, the geometry of the MEC is completely insensitive to the field, giving further credence that they are lattice animals, in the presence or the absence of a field.

• 1. Service de physique de l'état condensé (SPEC), CNRS : URA2464 – CEA : DSM/IRAMIS
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• ## Local Friedel sum rule on graphs

### Christophe Texier 1, 2, Markus Buttiker 3

#### Physical Review B 67 (2003) 245410

We consider graphs made of one-dimensional wires connected at vertices and on which may live a scalar potential. We are interested in a scattering situation where the graph is connected to infinite leads. We investigate relations between the scattering matrix and the continuous part of the local density of states, the injectivities, emissivities and partial local density of states. Those latter quantities can be obtained by attaching an extra lead at the point of interest and by investigating the transport in the limit of zero transmission into the additional lead. In addition to the continuous part related to the scattering states, the spectrum of graphs may present a discrete part related to states that remain uncoupled to the external leads. The theory is illustrated with the help of a few simple examples.

• 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
• 3. Département de Physique Théorique, University of Geneva

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• ## Mesoscopic Fluctuations in Quantum Dots in the Kondo Regime

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

#### Physical Review B 68 (2003) 161305

Properties of the Kondo effect in quantum dots depend sensitively on the coupling parameters and so on the realization of the quantum dot -- the Kondo temperature itself becomes a mesoscopic quantity. Assuming chaotic dynamics in the dot, we use random matrix theory to calculate the distribution of both the Kondo temperature and the conductance in the Coulomb blockade regime. We study two experimentally relevant cases: leads with single channels and leads with many channels. In the single-channel case, the distribution of the conductance is very wide as $T_K$ fluctuates on a logarithmic scale. As the number of channels increases, there is a slow crossover to a self-averaging regime.

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

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• ## Metastable configurations on the Bethe lattice

### Andrea Pagnani 1, Giorgio Parisi 2, Mathieu Ratieville 1, 2

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 67 (2003) 026116

We present a general analytic method to compute the number of metastable configurations as a function of the energy for a system of interacting Ising spins on the Bethe lattice. Our approach is based on the cavity method. We apply it to the case of ferromagnetic interactions, and also to the binary and Gaussian spin glasses. Most of our results are obtained within the replica symmetric ansatz, but we illustrate how replica symmetry breaking can be performed.

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

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• ## Near optimal configurations in mean field disordered systems

### Andrea Pagnani 1, Giorgio Parisi 2, Mathieu Ratieville 1, 2

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 68 (2003) 046706

We present a general technique to compute how the energy of a configuration varies as a function of its overlap with the ground state in the case of optimization problems. Our approach is based on a generalization of the cavity method to a system interacting with its ground state. With this technique we study the random matching problem as well as the mean field diluted spin glass. As a byproduct of this approach we calculate the de Almeida-Thouless transition line of the spin glass on a fixed connectivity random graph.

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

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• ## On Breaking Time Reversal in a Simple, Smooth, Chaotic System

### Steven Tomsovic 1, Denis Ullmo 2, 3, Tatsuro Nagano 1

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 67 (2003) 067201

Within random matrix theory, the statistics of the eigensolutions depend fundamentally on the presence (or absence) of time reversal symmetry. Accepting the Bohigas-Giannoni-Schmit conjecture, this statement extends to quantum systems with chaotic classical analogs. For practical reasons, much of the supporting numerical studies of symmetry breaking have been done with billiards or maps, and little with simple, smooth systems. There are two main difficulties in attempting to break time reversal invariance in a continuous time system with a smooth potential. The first is avoiding false symmetry breaking. The second is locating a parameter regime in which the symmetry breaking is strong enough to transition the fluctuation properties fully toward the broken symmetry case, and yet remain weak enough so as not to regularize the dynamics sufficiently that the system is no longer chaotic. We give an example of a system of two-coupled quartic oscillators whose energy level statistics closely match those of the Gaussian unitary ensemble, and which possesses only a minor proportion of regular motion in its phase space.

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

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• ## On some integrals over the U(N) unitary group and their large N limit

### Paul Zinn-Justin 1, Jean-Bernard Zuber 2

#### Journal of Physics A 36 (2003) 3173-3194

The integral over the U(N) unitary group $I=\int DU \exp\Tr A U B U^\dagger$ is reexamined. Various approaches and extensions are first reviewed. The second half of the paper deals with more recent developments: relation with integrable Toda lattice hierarchy, diagrammatic expansion and combinatorics, and on what they teach us on the large $N$ limit of $\log I$.

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

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• ## On the formal equivalence of the TAP and thermodynamic methods in the SK model

### Andrea Cavagna 1, Irene Giardina 1, Giorgio Parisi 1, Marc Mézard 2

#### Journal of Physics A 36 (2003) 1175-1194

We revisit two classic Thouless-Anderson-Palmer (TAP) studies of the Sherrington-Kirkpatrick model [Bray A J and Moore M A 1980 J. Phys. C 13, L469; De Dominicis C and Young A P, 1983 J. Phys. A 16, 2063]. By using the Becchi-Rouet-Stora-Tyutin (BRST) supersymmetry, we prove the general equivalence of TAP and replica partition functions, and show that the annealed calculation of the TAP complexity is formally identical to the quenched thermodynamic calculation of the free energy at one step level of replica symmetry breaking. The complexity we obtain by means of the BRST symmetry turns out to be considerably smaller than the previous non-symmetric value.

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

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• ## Order-parameter fluctuations in Ising spin glasses at low temperatures

### Matteo Palassini 1, Marta Sales 2, Felix Ritort 3

#### Physical Review B 68 (2003) 224430

We present a numerical study of the order-parameter fluctuations for Ising spin glasses in three and four dimensions at very low temperatures and without an external field. Accurate measurements of two previously introduced parameters, A and G, show that the order parameter is not self-averaging, consistent with a zero-temperature thermal exponent value \theta' \simeq 0, and confirm the validity of the relation G=1/3 in the thermodynamic limit in the whole low-temperature phase, as predicted by stochastic stability arguments.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Chemical and Biological Engineering Department, Northwestern University
• 3. Departament de Física Fonamental, Facultat de Física, Universitat de Barcelona

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• ## Pseudogaps due to sound modes: from incommensurate charge density waves to semiconducting wires

### Serguei Brasovskii 1, Sergey I. Matveenko 1, 2

#### JETP Letters 96 (2003) 555

We consider pseudogap effects for electrons interacting with gapless modes. We study both generic 1D semiconductors with acoustic phonons and incommensurate charge density waves. We calculate the subgap absorption as it can be observed by means of the photo electron or tunneling spectroscopy. Within the formalism of functional integration and the adiabatic approximation, the probabilities are described by nonlinear configurations of an instanton type. Particularities of both cases are determined by the topological nature of stationary excited states (acoustic polarons or amplitude solitons) and by presence of gapless phonons which change the usual dynamics to the regime of the quantum dissipation. Below the free particle edge the pseudogap starts with the exponential (stretched exponential for gapful phonons) decrease of transition rates. Deeply within the pseudogap they are dominated by a power law, in contrast with nearly exponential law for gapful modes.

• 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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• ## Quantum dot ground state energies and spin polarizations: soft versus hard chaos

### Denis Ullmo 1, 2, Tatsuro Nagano 3, Steven Tomsovic 3

#### Physical Review Letters 90 (2003) 176801

We consider how the nature of the dynamics affects ground state properties of ballistic quantum dots. We find that mesoscopic Stoner fluctuations'', that arise from the residual screened Coulomb interaction, are very sensitive to the degree of chaos. It leads to ground state energies and spin-polarizations whose fluctuations strongly increase as a system becomes less chaotic. The crucial features are illustrated with a model that depends on a parameter that tunes the dynamics from nearly integrable to mostly chaotic.

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

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• ## Quantum thermodynamic fluctuations of a chaotic Fermi-gas model

### Patricio Leboeuf 1, Alejandro Monastra 2

#### Nuclear Physics A 724 (2003) 69-84

We investigate the thermodynamics of a Fermi gas whose single-particle energy levels are given by the complex zeros of the Riemann zeta function. This is a model for a gas, and in particular for an atomic nucleus, with an underlying fully chaotic classical dynamics. The probability distributions of the quantum fluctuations of the grand potential and entropy of the gas are computed as a function of temperature and compared, with good agreement, with general predictions obtained from random matrix theory and periodic orbit theory (based on prime numbers). In each case the universal and non--universal regimes are identified.

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

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• ## Spectral properties of distance matrices

### Eugène Bogomolny 1, Oriol Bohigas 1, Charles Schmit 1

#### Journal of Physics A 36 (2003) 3595-3616

Distance matrices are matrices whose elements are the relative distances between points located on a certain manifold. In all cases considered here all their eigenvalues except one are non-positive. When the points are uncorrelated and randomly distributed we investigate the average density of their eigenvalues and the structure of their eigenfunctions. The spectrum exhibits delocalized and strongly localized states which possess different power-law average behaviour. The exponents depend only on the dimensionality of the manifold.

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

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• ## Statistical Physics of RNA-folding

### Markus Muller 1

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 67 (2003) 021914

We discuss the physics of RNA as described by its secondary structure. We examine the static properties of a homogeneous RNA-model that includes pairing and base stacking energies as well as entropic costs for internal loops. For large enough costs the model exhibits a thermal denaturation transition which we analyze in terms of the radius of gyration. We point out an inconsistency in the standard approach to RNA secondary structure prediction for large molecules. Under an external force a second order phase transition between a globular and an extended phase takes place. A Harris-type criterion shows that sequence disorder does not affect the correlation length exponent while the other critical exponents are modified in the glass phase. However, at high temperatures, on a coarse-grained level, disordered RNA is well described by a homogeneous model. The characteristics of force-extension curves are discussed as a function of the energy parameters. We show that the force transition is always second order. A re-entrance phenomenon relevant for real disordered RNA is predicted.

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

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• ## Temperature Chaos, Rejuvenation and Memory in Migdal-Kadanoff Spin Glasses

### Munetaka Sasaki 1, Olivier C. Martin 2

#### Physical Review Letters 91 (2003) 097201

We use simulations within the Migdal-Kadanoff real space renormalization approach to probe the scales relevant for rejuvenation and memory in spin glasses. One of the central questions concerns the role of temperature chaos. First we investigate scaling laws of equilibrium temperature chaos, finding super-exponential decay of correlations but no chaos for the total free energy. Then we perform out of equilibrium simulations that follow experimental protocols. We find that: (1) rejuvenation arises at a length scale smaller than the overlap length'' l(T,T'); (2) memory survives even if equilibration goes out to length scales much larger than l(T,T').

• 1. Institute for Solid State Physics (ISSP), University of Tokyo
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• ## The asymmetric ABAB matrix model

### Paul Zinn-Justin 1

#### Europhysics Letters (EPL) 64 (2003) 737-742

In this letter, it is pointed out that the two matrix model defined by the action S=(1/2)(tr A^2+tr B^2)-(alpha_A/4) tr A^4-(alpha_B/4) tr B^4-(beta/2) tr(AB)^2 can be solved in the large N limit using a generalization of the solution of Kazakov and Zinn-Justin (who considered the symmetric case alpha_A=alpha_B). This model could have useful applications to 3D Lorentzian gravity.

• 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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• ## The cavity method at zero temperature

### Marc Mézard 1, Giorgio Parisi 2

#### Journal of Statistical Physics 111 (2003) 1-34

In this note we explain the use of the cavity method directly at zero temperature, in the case of the spin glass on a Bethe lattice. The computation is done explicitly in the formalism equivalent to 'one step replica symmetry breaking'; we compute the energy of the global ground state, as well as the complexity of equilibrium states at a given energy. Full results are presented for a Bethe lattice with connectivity equal to three.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Dipartimento di Fisica, Sezione INFN, SMC and UdRm1 of INFM, Università degli studi di Roma I - La Sapienza

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• ## The General O(n) Quartic Matrix Model and its application to Counting Tangles and Links

### Paul Zinn-Justin 1

#### Communications in Mathematical Physics 238 (2003) 287-304

The counting of alternating tangles in terms of their crossing number, number of external legs and connected components is presented here in a unified framework using quantum field-theoretic methods applied to a matrix model of colored links. The overcounting related to topological equivalence of diagrams is removed by means of a renormalization scheme of the matrix model; the corresponding renormalization equations'' are derived. Some particular cases are studied in detail and solved exactly.

• 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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• ## The Impact of Discoveries of Ferroelectricity and Charge Disproportionation in Organic Conductors

### Serguei Brazovskii 1

#### Synthetic Metals 133-134 (2003) 301-303

Discoveries of the Ferroelectric anomaly (Nad, Monceau, et al) and of the related charge disproportionation (Brown et al) call for a revaluation of the phase diagram of the (TMTTF)2X compounds and return the attention to the interplay of electronic and structural properties. We shall describe a concept of the Combined Mott-Hubbard state as the source for the ferroelectricity. We shall demonstrate the existence of two types of spinless solitons: pi- solitons, the holons, are observed via the activated conductivity; the noninteger alpha- solitons are responsible for the depolarization of the FE order. We propose that the (anti) ferroelectricity does exists hiddenly even in the Se subfamily, giving rise to the unexplained yet optical peak. We remind then the abandoned theory by the author and Yakovenko for the universal phase diagram which we contrast with the recent one.

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

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• ## The LLL Anyon equation of state in the antiscreening regime

### Stefan Mashkevich 1, Stéphane Ouvry 2

#### Physics Letters A 310 (2003) 85-94

The thermodynamics of the anyon model projected on the lowest Landau level (LLL) of an external magnetic field is addressed in the anti-screening regime, where the flux tubes carried by the anyons are parallel to the magnetic field. It is claimed that the LLL-anyon equation of state, which is known in the screening regime, can be analytically continued in the statistical parameter across the Fermi point to the antiscreening regime up to the vicinity (whose width tends to zero when the magnetic field becomes infinite) of the Bose point. There, an unphysical discontinuity arises due to the dropping of the non-LLL eigenstates which join the LLL, making the LLL approximation no longer valid. However, taking into account the effect of the non-LLL states at the Bose point would only smoothen the discontinuity and not alter the physics which is captured by the LLL projection: Close to the Bose point, the critical filling factor either goes to infinity (usual bosons) in the screening situation, or to 1/2 in the anti-screening situation, the difference between the flux tubes orientation being relevant even when they carry an infinitesimal fraction of the flux quantum. An exclusion statistics interpretation is adduced, which explains this situation in semiclassical terms. It is further shown how the exact solutions of the 3-anyon problem support this scenario as far as the third cluster coefficient is concerned.

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

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• ## Topological correlations in trivial knots: new arguments in support of the crumpled polymer globule

### Oleg A. Vasilyev 1, Sergei K. Nechaev 1, 2

#### Theoretical and Mathematical Physics 134 (2003) 142-159

We prove the fractal crumpled structure of collapsed unknotted polymer ring. In this state the polymer chain forms a system of densely packed folds, mutually separated in all scales. The proof is based on the numerical and analytical investigation of topological correlations in randomly generated dense knots on strips $L_{v} \times L_{h}$ of widths $L_{v}=3,5$. We have analyzed the conditional probability of the fact that a part of an unknotted chain is also almost unknotted. The complexity of dense knots and quasi--knots is characterized by the power $n$ of the Jones--Kauffman polynomial invariant. It is shown, that for long strips $L_{h} \gg L_{v}$ the knot complexity $n$ is proportional to the length of the strip $L_{h}$. At the same time, the typical complexity of the quasi--knot which is a part of trivial knot behaves as $n\sim \sqrt{L_{h}}$ and hence is significantly smaller. Obtained results show that topological state of any part of the trivial knot in a collapsed phase is almost trivial.

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

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• ## Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models III. Triangular-Lattice Chromatic Polynomial

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

#### Journal of Statistical Physics 112 (2003) 921-1017

We study the chromatic polynomial P_G(q) for m \times n triangular-lattice strips of widths m <= 12_P, 9_F (with periodic or free transverse boundary conditions, respectively) and arbitrary lengths n (with free longitudinal boundary conditions). The chromatic polynomial gives the zero-temperature limit of the partition function for the q-state Potts antiferromagnet. We compute the transfer matrix for such strips in the Fortuin--Kasteleyn representation and obtain the corresponding accumulation sets of chromatic zeros in the complex q-plane in the limit n\to\infty. We recompute the limiting curve obtained by Baxter in the thermodynamic limit m,n\to\infty and find new interesting features with possible physical consequences. Finally, we analyze the isolated limiting points and their relation with the Beraha numbers.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Departamento de Física Teórica, Facultad de Ciencias, Universidad de Zaragoza
• 3. Department of Physics, New York University

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• ## XY frustrated systems: Continuous exponents in discontinuous phase transitions

### Mathieu Tissier 1, Bertrand Delamotte 2, Dominique Mouhanna 2

#### Physical Review B 67 (2003) 134422

XY frustrated magnets exhibit an unsual critical behavior: they display scaling laws accompanied by nonuniversal critical exponents and a negative anomalous dimension. This suggests that they undergo weak first order phase transitions. We show that all perturbative approaches that have been used to investigate XY frustrated magnets fail to reproduce these features. Using a nonperturbative approach based on the concept of effective average action, we are able to account for this nonuniversal scaling and to describe qualitatively and, to some extent, quantitatively the physics of these systems.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 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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• ## A Bijection between classes of Fully Packed Loops and Plane Partitions

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

#### Electronic Journal of Combinatories 11 (2004) R64

It has recently been observed empirically that the number of FPL configurations with 3 sets of a, b and c nested arches equals the number of plane partitions in a box of size a x b x c. In this note, this result is proved by constructing explicitly the bijection between these FPL and plane partitions.

• 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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• ## Algebraic Bethe Ansatz for the FPL^2 model

### Jesper-Lykke Jacobsen 1, Paul Zinn-Justin 1

#### Journal of Physics A 37 (2004) 7213-7225

An exact solution of the model of fully packed loops of two colors on a square lattice has recently been proposed by Dei Cont and Nienhuis using the coordinate Bethe Ansatz approach. We point out here a simpler alternative, in which the transfer matrix is directly identified as a product of R-matrices; this allows to apply the (nested) algebraic Bethe Ansatz, which leads to the same Bethe equations. We comment on some of the applications of this result.

• 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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• ## An Anisotropic Ballistic Deposition Model with Links to the Ulam Problem and the Tracy-Widom Distribution

### Satya Majumdar 1, Sergei K. Nechaev 2, 3

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 69 (2004) 011103

We compute exactly the asymptotic distribution of scaled height in a (1+1)--dimensional anisotropic ballistic deposition model by mapping it to the Ulam problem of finding the longest nondecreasing subsequence in a random sequence of integers. Using the known results for the Ulam problem, we show that the scaled height in our model has the Tracy-Widom distribution appearing in the theory of random matrices near the edges of the spectrum. Our result supports the hypothesis that various growth models in $(1+1)$ dimensions that belong to the Kardar-Parisi-Zhang universality class perhaps all share the same universal Tracy-Widom distribution for the suitably scaled height variables.

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

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• ## Classical intermittency and quantum Anderson transition

### Antonio M. Garcia-Garcia 1

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 69 (2004) 066216

We investigate the quantum properties of 1D quantum systems whose classical counterpart presents intermittency. The spectral correlations are expressed in terms of the eigenvalues of an anomalous diffusion operator by using recent semiclassical techniques. For certain values of the parameters the spectral properties of our model show similarities with those of a disordered system at the Anderson transition. In Hamiltonian systems, intermittency is closely related to the presence of cantori in the classical phase space. We suggest, based on this relation, that our findings may be relevant for the description of the spectral correlations of (non-KAM) Hamiltonians with a classical phase space filled by cantori. Finally we discuss the extension of our results to higher dimensions and their relation to Anderson models with long range hopping.

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

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• ## Conformal field theory of the Flory model of polymer melting

### Jesper Lykke Jacobsen 1, Jane' Kondev 2

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 69 (2004) 066108

We study the scaling limit of a fully packed loop model in two dimensions, where the loops are endowed with a bending rigidity. The scaling limit is described by a three-parameter family of conformal field theories, which we characterize via its Coulomb-gas representation. One choice for two of the three parameters reproduces the critical line of the exactly solvable six-vertex model, while another corresponds to the Flory model of polymer melting. Exact central charge and critical exponents are calculated for polymer melting in two dimensions. Contrary to predictions from mean-field theory we show that polymer melting, as described by the Flory model, is continuous. We test our field theoretical results against numerical transfer matrix calculations.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Physics Department, MS057, Brandeis University

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• ## Construction of the factorized steady state distribution in models of mass transport

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

#### Journal of Statistical Mechanics: Theory and Experiment 1 (2004) L10001

For a class of one-dimensional mass transport models we present a simple and direct test on the chipping functions, which define the probabilities for mass to be transferred to neighbouring sites, to determine whether the stationary distribution is factorized. In cases where the answer is affirmative, we provide an explicit method for constructing the single-site weight function. As an illustration of the power of this approach, previously known results on the Zero-range process and Asymmetric random average process are recovered in a few lines. We also construct new models, namely a generalized Zero-range process and a binomial chipping model, which have factorized steady states.

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

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• ## Cooperativity in two-state protein folding kinetics

### Thomas R. Weikl 1, 2, Matteo Palassini 1, 3, Ken A. Dill 1

#### Protein Science 13 (2004) 822-829

We present a solvable model that predicts the folding kinetics of two-state proteins from their native structures. The model is based on conditional chain entropies. It assumes that folding processes are dominated by small-loop closure events that can be inferred from native structures. For CI2, the src SH3 domain, TNfn3, and protein L, the model reproduces two-state kinetics, and it predicts well the average Phi-values for secondary structures. The barrier to folding is the formation of predominantly local structures such as helices and hairpins, which are needed to bring nonlocal pairs of amino acids into contact.

• 1. Department of Pharmaceutical Chemistry, University of California, San Francisco
• 2. Max-Planck-institut für Kolloid - und Grenzflächenforschung, Max-Planck-Institut
• 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• ## Effect of a magnetic flux on the critical behavior of a system with long range hopping

### Antonio M. Garcia-Garcia 1

#### Physical Review B 69 (2004) 245121

We study the effect of a magnetic flux in a 1D disordered wire with long range hopping. It is shown that this model is at the metal-insulator transition (MIT) for all disorder values and the spectral correlations are given by critical statistics. In the weak disorder regime a smooth transition between orthogonal and unitary symmetry is observed as the flux strength increases. By contrast, in the strong disorder regime the spectral correlations are almost flux independent. It is also conjectured that the two level correlation function for arbitrary flux is given by the dynamical density-density correlations of the Calogero-Sutherland (CS) model at finite temperature. Finally we describe the classical dynamics of the model and its relevance to quantum chaos.

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

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• ## Electron-Electron Interactions in Isolated and Realistic Quantum Dots: A Density Functional Theory Study

### Hong Jiang 1, 2, 3, Denis Ullmo 2, 4, Weitao Yang 1, Harold U. Baranger 2

#### Physical Review B 69 (2004) 235326

We use Kohn-Sham spin-density-functional theory to study the statistics of ground-state spin and the spacing between conductance peaks in the Coulomb blockade regime for both 2D isolated and realistic quantum dots. We make a systematic investigation of the effects of electron-electron interaction strength and electron number on both the peak spacing and spin distributions. A direct comparison between the distributions from isolated and realistic dots shows that, despite the difference in the boundary conditions and confining potential, the statistical properties are qualitatively the same. Strong even/odd pairing in the peak spacing distribution is observed only in the weak e-e interaction regime and vanishes for moderate interactions. The probability of high spin ground states increases for stronger e-e interaction and seems to saturate around $r_s \sim 4$. The saturated value is larger than previous theoretical predictions. Both spin and conductance peak spacing distributions show substantial variation as the electron number increases, not saturating until $N \sim 150$. To interpret our numerical results, we analyze the spin distribution in the even $N$ case using a simple two-level model.

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

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• ## Exact Maximal Height Distribution of Fluctuating Interfaces

### Satya Majumdar 1, Alain Comtet 2, 3

#### Physical Review Letters 92 (2004) 225501

We present an exact solution for the distribution P(h_m,L) of the maximal height h_m (measured with respect to the average spatial height) in the steady state of a fluctuating Edwards-Wilkinson interface in a one dimensional system of size L with both periodic and free boundary conditions. For the periodic case, we show that P(h_m,L)=L^{-1/2}f(h_m L^{-1/2}) for all L where the function f(x) is the Airy distribution function that describes the probability density of the area under a Brownian excursion over a unit interval. For the free boundary case, the same scaling holds but the scaling function is different from that of the periodic case. Numerical simulations are in excellent agreement with our analytical results. Our results provide an exactly solvable case for the distribution of extremum of a set of strongly correlated random variables.

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

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• ## Exact Potts Model Partition Functions for Strips of the Triangular Lattice

### Shu-Chiuan Chang 1, 2, Jesper-Lykke Jacobsen 3, Jesus Salas 4, 5, Robert Shrock 1

#### Journal of Statistical Physics 114 (2004) 763-823

We present exact calculations of the Potts model partition function Z(G,q,v) for arbitrary q and temperature-like variable v on n-vertex strip graphs G of the triangular lattice for a variety of transverse widths equal to L vertices and for arbitrarily great length equal to m vertices, with free longitudinal boundary conditions and free and periodic transverse boundary conditions. These have the form Z(G,q,v)=\sum_{j=1}^{N_{Z,G,\lambda}} c_{Z,G,j}(\lambda_{Z,G,j})^{m-1}. We give general formulas for N_{Z,G,j} and its specialization to v=-1 for arbitrary L. The free energy is calculated exactly for the infinite-length limit of the graphs, and the thermodynamics is discussed. It is shown how the internal energy calculated for the case of cylindrical boundary conditions is connected with critical quantities for the Potts model on the infinite triangular lattice. Considering the full generalization to arbitrary complex q and v, we determine the singular locus {\cal B}, arising as the accumulation set of partition function zeros as m\to\infty, in the q plane for fixed v and in the v plane for fixed q.

• 1. C. N. Yang Institute for Theoretical Physics, State University of New York at Stony Brook
• 2. Department of Applied Physics, Faculty of Science, Tokyo University of Science
• 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 4. Departamento de Física Teórica, Facultad de Ciencias, Universidad de Zaragoza

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• ## Factorised Steady States in Mass Transport Models

### Martin R. Evans 1, Satya Majumdar 2, 3, Royce K.P. Zia 4, 5

#### Journal of Physics A 37 (2004) L275-L280

We study a class of mass transport models where mass is transported in a preferred direction around a one-dimensional periodic lattice and is globally conserved. The model encompasses both discrete and continuous masses and parallel and random sequential dynamics and includes models such as the Zero-range process and Asymmetric random average process as special cases. We derive a necessary and sufficient condition for the steady state to factorise, which takes a rather simple form.

• 1. School of Physics, University of Edinburgh
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 3. Laboratoire de Physique Théorique - IRSAMC (LPT), CNRS : UMR5152 – Université Paul Sabatier - Toulouse III
• 4. Department of Physics and Center for Stochastic Processes in Science and Engineering, Virginia Tech
• 5. FB-Physik, Universität Duisburg-Essen

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• ## Family of generalized random matrix ensembles

### A. C. Bertuola 1, O. Bohigas 2, M. P. Pato 1

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 70 (2004) 065102

Using the Generalized Maximium Entropy Principle based on the nonextensive q entropy a new family of random matrix ensembles is generated. This family unifies previous extensions of Random Matrix Theory and gives rise to an orthogonal invariant stable Levy ensemble with new statistical properties. Some of them are analytically derived.

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

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• ## Fermi-Edge Singularities in the Mesoscopic X-Ray Edge Problem

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

#### Physical Review Letters 93 (2004) 176807

We study the x-ray edge problem for a chaotic quantum dot or nanoparticle displaying mesoscopic fluctuations. In the bulk, x-ray physics is known to produce deviations from the naively expected photoabsorption cross section in the form of a peaked or rounded edge. For a coherent system with chaotic dynamics, we find substantial changes and in particular that a photoabsorption cross section showing a rounded edge in the bulk will change to a slightly peaked edge on average as the system size is reduced to a mesoscopic (coherent) scale.

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

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• ## Fermionic field theory for trees and forests

### Sergio Caracciolo 1, Jesper-Lykke Jacobsen 2, Hubert Saleur 3, 4, Alan D. Sokal 5, Andrea Sportiello 1

#### Physical Review Letters 93 (2004) 080601

We prove a generalization of Kirchhoff's matrix-tree theorem in which a large class of combinatorial objects are represented by non-Gaussian Grassmann integrals. As a special case, we show that unrooted spanning forests, which arise as a q \to 0 limit of the Potts model, can be represented by a Grassmann theory involving a Gaussian term and a particular bilocal four-fermion term. We show that this latter model can be mapped, to all orders in perturbation theory, onto the N-vector model at N=-1 or, equivalently, onto the sigma-model taking values in the unit supersphere in R^{1|2}. It follows that, in two dimensions, this fermionic model is perturbatively asymptotically free.

• 1. Dipartimento di Fisica (Milano), Università degli studi di Milano
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 3. Service de Physique Théorique (SPhT), CNRS : URA2306 – CEA : DSM/SPHT
• 4. Department of Physics and Astronomy, University of Southern California
• 5. Department of Physics, New York University

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• ## Glass models on Bethe lattices

### Olivier Rivoire 1, Giulio Biroli 2, Olivier C. Martin 1, Marc Mézard 1

#### European Physical Journal B 37 (2004) 55-78

We consider lattice glass models'' in which each site can be occupied by at most one particle, and any particle may have at most l occupied nearest neighbors. Using the cavity method for locally tree-like lattices, we derive the phase diagram, with a particular focus on the vitreous phase and the highest packing limit. We also study the energy landscape via the configurational entropy, and discuss different equilibrium glassy phases. Finally, we show that a kinetic freezing, depending on the particular dynamical rules chosen for the model, can prevent the equilibrium glass transitions.

• 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

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• ## Glassy phases in Random Heteropolymers with correlated sequences

### Markus Muller 1, Marc Mézard 1, Andrea Montanari 2

#### Journal of Chemical Physics 120 (2004) 11233

We develop a new analytic approach for the study of lattice heteropolymers, and apply it to copolymers with correlated Markovian sequences. According to our analysis, heteropolymers present three different dense phases depending upon the temperature, the nature of the monomer interactions, and the sequence correlations: (i) a liquid phase, (ii) a soft glass'' phase, and (iii) a frozen glass'' phase. The presence of the new intermediate soft glass'' phase is predicted for instance in the case of polyampholytes with sequences that favor the alternation of monomers. Our approach is based on the cavity method, a refined Bethe Peierls approximation adapted to frustrated systems. It amounts to a mean field treatment in which the nearest neighbor correlations, which are crucial in the dense phases of heteropolymers, are handled exactly. This approach is powerful and versatile, it can be improved systematically and generalized to other polymeric systems.

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

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• ## Landau Fermi Liquid Picture of Spin Density Functional Theory: Strutinsky Approach to Quantum Dots

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

#### Physical Review B 70 (2004) 205309

We analyze the ground state energy and spin of quantum dots obtained from spin density functional theory (SDFT) calculations. First, we introduce a Strutinsky-type approximation, in which quantum interference is treated as a correction to a smooth Thomas-Fermi description. For large irregular dots, we find that the second-order Strutinsky expressions have an accuracy of about 5 percent compared to the full SDFT and capture all the qualitative features. Second, we perform a random matrix theory/random plane wave analysis of the Strutinsky SDFT expressions. The results are statistically similar to the SDFT quantum dot statistics. Finally, we note that the second-order Strutinsky approximation provides, in essence, a Landau Fermi liquid picture of spin density functional theory. For instance, the leading term in the spin channel is simply the familiar exchange constant. A direct comparison between SDFT and the perturbation theory derived universal Hamiltonian'' is thus made possible.

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

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• ## Landau theory of glassy dynamics

### Satya Majumdar 1, 2, Dibyendu Das 3, Jane' Kondev 4, Bulbul Chakraborty 4

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 70 (2004) 060501

An exact solution of a Landau model of an order-disorder transition with activated critical dynamics is presented. The model describes a funnel-shaped topography of the order parameter space in which the number of energy lowering trajectories rapidly diminishes as the ordered ground-state is approached. This leads to an asymmetry in the effective transition rates which results in a non-exponential relaxation of the order-parameter fluctuations and a Vogel-Fulcher-Tammann divergence of the relaxation times, typical of a glass transition. We argue that the Landau model provides a general framework for studying glassy dynamics in a variety of systems.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Laboratoire de Physique Théorique - IRSAMC (LPT), CNRS : UMR5152 – Université Paul Sabatier - Toulouse III
• 3. Department of Physics, Indian Institute of Technology Bombay
• 4. Martin Fisher School of Physics, Brandeis University

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• ## Large deviations in spin-glass ground-state energies

### A. Andreanov, Francesca Barbieri, Olivier C. Martin 1

#### European Physical Journal B 41 (2004) 365

The ground-state energy E_0 of a spin glass is an example of an extreme statistic. We consider the large deviations of this energy for a variety of models when the number of spins N goes to infinity. In most cases, the behavior can be understood qualitatively, in particular with the help of semi-analytical results for hierarchical lattices. Particular attention is paid to the Sherrington-Kirkpatrick model; after comparing to the Tracy-Widom distribution which follows from the spherical approximation, we find that the large deviations give rise to non-trivial scaling laws with N.

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

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• ## Long range disorder and Anderson transition in systems with chiral symmetry

### Antonio M. Garcia-Garcia 1, Kazutaka Takahashi 2

#### Nuclear Physics B 700 (2004) 361

We study the spectral properties of a chiral random banded matrix (chRBM) with elements decaying as a power-law ${{\cal H}_{ij}}\sim |i-j|^{-\alpha}$. This model is equivalent to a chiral 1D Anderson Hamiltonian with long range power-law hopping. In the weak disorder limit we obtain explicit nonperturbative analytical results for the density of states and the two-level correlation function by mapping the chRBM onto a nonlinear sigma model. We also put forward, by exploiting the relation between the chRBM at $\alpha=1$ and a generalized chiral random matrix model, an exact expression for the above correlation functions. We give compelling analytical and numerical evidence that for this value the chRBM reproduces all the features of an Anderson transition. Finally we discuss possible applications of our results to QCD.

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

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• ## Low-dimensional trapped gases

### D. Petrov 1, 2, Dimitri M. Gangardt 3, 4, Gora V. Shlyapnikov 1, 2, 3, 4

#### Journal de Physique IV Colloque 116 (2004) 5-44

Recent developments in the physics of ultracold gases provide wide possibilities for reducing the dimensionality of space for magnetically or optically trapped atoms. The goal of these lectures is to show that regimes of quantum degeneracy in two-dimensional (2D) and one-dimensional (1D) trapped gases are drastically different from those in three dimensions and to stimulate an interest in low-dimensional systems. Attention is focused on the new physics appearing in currently studied low-dimensional trapped gases and related to finite-size and finite-temperature effects.

• 1. FOM Institute, FOM Institute
• 2. National Research Centre "Kurchatov Institute" (NRC KI), University of Moscow
• 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 4. Laboratoire Kastler Brossel (LKB (Lhomond)), CNRS : UMR8552 – Université Paris VI - Pierre et Marie Curie – Ecole Normale Supérieure de Paris - ENS Paris

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• ## Matrix Integrals and the Generation and Counting of Virtual Tangles and Links

### Paul Zinn-Justin 1, Jean-Bernard Zuber 2

#### Journal of Knot Theory and Its Ramifications 13 (2004) 325-355

Virtual links are generalizations of classical links that can be represented by links embedded in a thickened'' surface $\Sigma\times I$, product of a Riemann surface of genus $h$ with an interval. In this paper, we show that virtual alternating links and tangles are naturally associated with the $1/N^2$ expansion of an integral over $N\times N$ complex matrices. We suggest that it is sufficient to count the equivalence classes of these diagrams modulo ordinary (planar) flypes. To test this hypothesis, we use an algorithm coding the corresponding Feynman diagrams by means of permutations that generates virtual diagrams up to 6 crossings and computes various invariants. Under this hypothesis, we use known results on matrix integrals to get the generating functions of virtual alternating tangles of genus 1 to 5 up to order 10 (i.e.\ 10 real crossings). The asymptotic behavior for $n$ large of the numbers of links and tangles of genus $h$ and with $n$ crossings is also computed for $h=1,2,3$ and conjectured for general $h$.

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

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• ## On metric structure of ultrametric spaces

### Oleg A. Vasilyev 1, Sergei K. Nechaev 1, 2

#### Journal of Physics A 37 (2004) 3783-3804

In our work we have reconsidered the old problem of diffusion at the boundary of ultrametric tree from a 'number theoretic' point of view. Namely, we use the modular functions (in particular, the Dedekind eta-function) to construct the 'continuous' analog of the Cayley tree isometrically embedded in the Poincare upper half-plane. Later we work with this continuous Cayley tree as with a standard function of a complex variable. In the frameworks of our approach the results of Ogielsky and Stein on dynamics on ultrametric spaces are reproduced semi-analytically/semi-numerically. The speculation on the new 'geometrical' interpretation of replica n->0 limit is proposed.

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

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• ## On the Asymptotic Number of Plane Curves and Alternating Knots

### Gilles Schaeffer 1, Paul Zinn-Justin 2

#### Experimental Mathematics 13 (2004) 4

We present a conjecture for the power-law exponent in the asymptotic number of types of plane curves as the number of self-intersections goes to infinity. In view of the description of prime alternating links as flype equivalence classes of plane curves, a similar conjecture is made for the asymptotic number of prime alternating knots. The rationale leading to these conjectures is given by quantum field theory. Plane curves are viewed as configurations of loops on a random planar lattices, that are in turn interpreted as a model of 2d quantum gravity with matter. The identification of the universality class of this model yields the conjecture. Since approximate counting or sampling planar curves with more than a few dozens of intersections is an open problem, direct confrontation with numerical data yields no convincing indication on the correctness of our conjectures. However, our physical approach yields a more general conjecture about connected systems of curves. We take advantage of this to design an original and feasible numerical test, based on recent perfect samplers for large planar maps. The numerical datas strongly support our identification with a conformal field theory recently described by Read and Saleur.

• 1. Laboratoire d'informatique de l'école polytechnique (LIX), CNRS : UMR7161 – Polytechnique - X
• 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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• ## Optimization and Physics: On the satisfiability of random Boolean formulae

### Marc Mézard 1

#### Annales de l'Institut Henri Poincare Physique Theorique 4 (2004) S475-S488

LECTURE GIVEN AT TH2002. Given a set of Boolean variables, and some constraints between them, is it possible to find a configuration of the variables which satisfies all constraints? This problem, which is at the heart of combinatorial optimization and computational complexity theory, is used as a guide to show the convergence between these fields and the statistical physics of disordered systems. New results on satisfiability, both on the theoretical and practical side, can be obtained thanks to the use of physics concepts and methods.

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

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• ## Periodic orbit spectrum in terms of Ruelle–Pollicott resonances

### Patricio Leboeuf 1

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 69 (2004) 026204

Fully chaotic Hamiltonian systems possess an infinite number of classical solutions which are periodic, e.g. a trajectory p'' returns to its initial conditions after some fixed time tau_p. Our aim is to investigate the spectrum tau_1, tau_2, ... of periods of the periodic orbits. An explicit formula for the density rho(tau) = sum_p delta (tau - tau_p) is derived in terms of the eigenvalues of the classical evolution operator. The density is naturally decomposed into a smooth part plus an interferent sum over oscillatory terms. The frequencies of the oscillatory terms are given by the imaginary part of the complex eigenvalues (Ruelle--Pollicott resonances). For large periods, corrections to the well--known exponential growth of the smooth part of the density are obtained. An alternative formula for rho(tau) in terms of the zeros and poles of the Ruelle zeta function is also discussed. The results are illustrated with the geodesic motion in billiards of constant negative curvature. Connections with the statistical properties of the corresponding quantum eigenvalues, random matrix theory and discrete maps are also considered. In particular, a random matrix conjecture is proposed for the eigenvalues of the classical evolution operator of chaotic billiards.

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

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• ## Persistence Exponents and the Statistics of Crossings and Occupation Times for Gaussian Stationary Processes

### George M. C. A. Ehrhardt 1, Satya Majumdar 2, 3, Alan J. Bray 1

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 69 (2004) 016106

We consider the persistence probability, the occupation-time distribution and the distribution of the number of zero crossings for discrete or (equivalently) discretely sampled Gaussian Stationary Processes (GSPs) of zero mean. We first consider the Ornstein-Uhlenbeck process, finding expressions for the mean and variance of the number of crossings and the 'partial survival\' probability. We then elaborate on the correlator expansion developed in an earlier paper [G. C. M. A. Ehrhardt and A. J. Bray, Phys. Rev. Lett. 88, 070602 (2001)] to calculate discretely sampled persistence exponents of GSPs of known correlator by means of a series expansion in the correlator. We apply this method to the processes d^n x/dt^n=\\eta(t) with n > 2, incorporating an extrapolation of the series to the limit of continuous sampling. We extend the correlator method to calculate the occupation-time and crossing-number distributions, as well as their partial-survival distributions and the means and variances of the occupation time and number of crossings. We apply these general methods to the d^n x/dt^n=\\eta(t) processes for n=1 (random walk), n=2 (random acceleration) and larger n, and to diffusion from random initial conditions in 1-3 dimensions. The results for discrete sampling are extrapolated to the continuum limit where possible.

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

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• ## Persistence in nonequilibrium surface growth

### M. Constantin 1, 2, Chandan Dasgupta 1, 3, Punyindu Chatraphorn 1, 4, Satya Majumdar 5, 6, S. Das Sarma 1

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 69 (2004) 061608

Persistence probabilities of the interface height in (1+1)- and (2+1)-dimensional atomistic, solid-on-solid, stochastic models of surface growth are studied using kinetic Monte Carlo simulations, with emphasis on models that belong to the molecular beam epitaxy (MBE) universality class. Both the initial transient and the long-time steady-state regimes are investigated. We show that for growth models in the MBE universality class, the nonlinearity of the underlying dynamical equation is clearly reflected in the difference between the measured values of the positive and negative persistence exponents in both transient and steady-state regimes. For the MBE universality class, the positive and negative persistence exponents in the steady-state are found to be $\theta^S_{+} = 0.66 \pm 0.02$ and $\theta^S_{-} = 0.78 \pm 0.02$, respectively, in (1+1) dimensions, and $\theta^S_{+} = 0.76 \pm 0.02$ and $\theta^S_{-} =0.85 \pm 0.02$, respectively, in (2+1) dimensions. The noise reduction technique is applied on some of the (1+1)-dimensional models in order to obtain accurate values of the persistence exponents. We show analytically that a relation between the steady-state persistence exponent and the dynamic growth exponent, found earlier to be valid for linear models, should be satisfied by the smaller of the two steady-state persistence exponents in the nonlinear models. Our numerical results for the persistence exponents are consistent with this prediction. We also find that the steady-state persistence exponents can be obtained from simulations over times that are much shorter than that required for the interface to reach the steady state. The dependence of the persistence probability on the system size and the sampling time is shown to be described by a simple scaling form.

• 1. Condensed Matter Theory Center, Department of Physics, University of Maryland at College Park
• 2. Materials Research Science and Engineering Center, Department of Physics, University of Maryland at College Park
• 3. Department of Physics, Indian Institute od Science
• 4. Department of Physics, Faculty of Science, Chulalongkorn University
• 5. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 6. Laboratoire de Physique Théorique - IRSAMC (LPT), CNRS : UMR5152 – Université Paul Sabatier - Toulouse III

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• ## Pinning and Sliding of Driven Elastic Systems: from Domain Walls to Charge Density Waves

### Serguei Brazovskii 1, Thomas Nattermann 1

#### Advances In Physics 53 (2004) 177-252

The review is devoted to the theory of collective and it local pinning effects in various disordered non-linear driven systems. Although the emphasis is put on charge and spin density waves and magnetic domain walls, the theory has also applications to flux lines and lattices thereof, dislocation lines, adsorbed mono-layers and related systems. In the first part we focus on the theory of the collective pinning which includes the equilibrium properties of elastic systems with frozen-in disorder as well as the features close to the dynamic depinning transition enforced by an external driving force and at finite temperatures. Thermal fluctuations smear out this transition and allow for a creep motion of the elastic objects even at small forces. An ac-driving force also destroys the sharp transition which is replaced by a velocity hysteresis. The second part is devoted to the local pinning picture and its applications. Inclusion of plastic deformations results in a rich cross-over behavior of the force-velocity relation as well as of the frequency dependence of the dynamic response. The local pinning recovers and exploits new elements of the energy landscape such as termination points of metastable branches or irreversibility of other ones related to generation of topological defects in the course of sliding. It also gives access to the quantum creep described as a tunneling between retarded and advanced configurations.

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

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• ## Quantum Mechanics of a Particle with Two Magnetic Impurities

### Stefan Mashkevich 1, Jan Myrheim 2, Stéphane Ouvry 3

#### Physics Letters A 330 (2004) 41-47

A two-dimensional quantum mechanical system consisting of a particle coupled to two magnetic impurities of different strengths, in a harmonic potential, is considered. Topological boundary conditions at impurity locations imply that the wave functions are linear combinations of two-dimensional harmonics. A number of low-lying states are computed numerically, and the qualitative features of the spectrum are analyzed.

• 1. Physics Department, Taras Shevchenko Kiev National University
• 2. Department of Physics, The Norwegian University of Science and Technology
• 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• ## Spectral statistics of a quantum interval-exchange map

### E. Bogomolny 1, C. Schmit 1

#### Physical Review Letters 93 (2004) 254102

Curious spectral properties of an ensemble of random unitary matrices appearing in the quantization of a map p -> p+alpha, q -> q+f(p+alpha) in [Giraud et al. nlin.CD/0403033] are investigated. When alpha=m/n with integer co-prime m,n and matrix dimension N -> infinity is such that mN = 1 or -1 mod n, local spectral statistics of this ensemble tends to the semi-Poisson distribution [Bogomolny et al. Eur. Phys. J. B 19, 121 (2001)] with arbitrary integer or half-integer level repulsion at small distances: R(s)-> s^{beta} when s -> 0 and beta=n-1 or n/2-1 depending on time-reversal symmetry of the map.

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

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• ## Summary for Theory of the Ferroelectric Phase in Organic Conductors in Relation to Experiments

### Serguei Brazovskii 1

#### Journal de Physique IV Colloque 114 (2004) 9

Mysterious high temperature structureless transitions in (TMTTF)2X compounds have been discovered in mid 80's (Coulon, Lawersanne,vet al), but left unexplained and abandoned, together with other warnings from structural effects (Moret, Pouget, et al), with dramatic consequences for the whole field. Recently their nature has been identified as the ferroelectricity (Nad, Monceau, et al) and, more generally, the charge disproportionation (Brown, et al). New phenomena unify an unusual variety of concepts: ferroelectricity of good conductors, structural instability towards Mott- Hubbard state, Wigner crystallization in a dense electronic system, ordered 4kF density wave, richness of physics of solitons, interplay of structural and electronic symmetries. The ferroelectric state gives rise to several types of solitons carrying electronic charge, a noninteger charge, spin or both spin and charge in special cases. They are clearly observed via conductivity, electric and magnetic susceptibilities. Solitons are challenging for optics where they already seem to determine the pseudogap in absorption. Various features also appear, or are expected, from collective electronic and coupled electron-phonon modes. REFERENCES: cond-mat/0012237 cond-mat/0304076 cond-mat/0304483 cond-mat/0306006

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

Details
• ## Survival in equilibrium step fluctuations

### C. Dasgupta 1, M. Constantin 1, 2, S. Das Sarma 1, Satya N. Majumdar 3

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 69 (2004) 022101

We report the results of analytic and numerical investigations of the time scale of survival or non-zero-crossing probability $S(t)$ in equilibrium step fluctuations described by Langevin equations appropriate for attachment/detachment and edge-diffusion limited kinetics. An exact relation between long-time behaviors of the survival probability and the autocorrelation function is established and numerically verified. $S(t)$ is shown to exhibit simple scaling behavior as a function of system size and sampling time. Our theoretical results are in agreement with those obtained from an analysis of experimental dynamical STM data on step fluctuations on Al/Si(111) and Ag(111) surfaces.

• 1. Condensed Matter Theory Center, Department of Physics, University of Maryland at College Park
• 2. Materials Research Science and Engineering Center, Department of Physics, University of Maryland at College Park
• 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• ## The Phase Diagram of Random Heteropolymers

### Andrea Montanari 1, Markus Muller 2, Marc Mézard 2

#### Physical Review Letters 92 (2004) 185509

We propose a new analytic approach to study the phase diagram of random heteropolymers, based on the cavity method. For copolymers we analyze the nature and phenomenology of the glass transition as a function of sequence correlations. Depending on these correlations, we find that two different scenarios for the glass transition can occur. We show that, beside the much studied possibility of an abrupt freezing transition at low temperature, the system can exhibit, upon cooling, a first transition to a soft glass phase with fully broken replica symmetry and a continuously growing degree of freezing as the temperature is lowered.

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

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• ## The traveling salesman problem, conformal invariance, and dense polymers

### Jesper-Lykke Jacobsen 1, Nicholas Read 2, Hubert Saleur 3, 4

#### Physical Review Letters 93 (2004) 038701

We propose that the statistics of the optimal tour in the planar random Euclidean traveling salesman problem is conformally invariant on large scales. This is exhibited in power-law behavior of the probabilities for the tour to zigzag repeatedly between two regions, and in subleading corrections to the length of the tour. The universality class should be the same as for dense polymers and minimal spanning trees. The conjectures for the length of the tour on a cylinder are tested numerically.

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

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• ## Universal correlations of trapped one-dimensional impenetrable bosons

### Dimitri M. Gangardt 1, 2

#### Journal of Physics A 37 (2004) 9335-9356

We calculate the asymptotic behaviour of the one body density matrix of one-dimensional impenetrable bosons in finite size geometries. Our approach is based on a modification of the Replica Method from the theory of disordered systems. We obtain explicit expressions for oscillating terms, similar to fermionic Friedel oscillations. These terms are universal and originate from the strong short-range correlations between bosons in one dimension.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Laboratoire Kastler Brossel (LKB (Lhomond)), CNRS : UMR8552 – Université Paris VI - Pierre et Marie Curie – Ecole Normale Supérieure de Paris - ENS Paris

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• ## Weakly bound dimers of fermionic atoms

### D. Petrov 1, 2, Christophe Salomon 3, Gora V. Shlyapnikov 1, 2, 3

#### Physical Review Letters 93 (2004) 090404

We discuss the behavior of weakly bound bosonic dimers formed in a cold Fermi gas at a large positive scattering length $a$ for the interspecies interaction. We find the exact solution for the dimer-dimer elastic scattering and obtain a strong decrease of their collisional relaxation and decay with increasing $a$. The large ratio of the elastic to inelastic rate is promising for achieving Bose-Einstein condensation of the dimers and cooling the condensed gas to very low temperatures.

• 1. FOM Institute for Atomic and Molecular Physics, Institut for Atomic and Molecular Physics
• 2. National Research Centre "Kurchatov Institute" (NRC KI), University of Moscow
• 3. Laboratoire Kastler Brossel (LKB (Lhomond)), CNRS : UMR8552 – Université Paris VI - Pierre et Marie Curie – Ecole Normale Supérieure de Paris - ENS Paris

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• ## Hydrodynamics within the Electric Double Layer on slipping surfaces

### Laurent Joly 1 Christophe Ybert 1 Emmanuel Trizac 2 Lyderic Bocquet 1

#### Physical Review Letters, American Physical Society, 2004, 93 (25), pp.257805. 〈10.1103/PhysRevLett.93.257805〉

We show, using extensive Molecular Dynamics simulations, that the dynamics of the electric double layer (EDL) is very much dependent on the wettability of the charged surface on which the EDL develops. For a wetting surface, the dynamics, characterized by the so-called Zeta potential, is mainly controlled by the electric properties of the surface, and our work provides a clear interpretation for the traditionally introduced immobile Stern layer. In contrast, the immobile layer disappears for non-wetting surfaces and the Zeta potential deduced from electrokinetic effects is considerably amplified by the existence of a slippage at the solid substrate.

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

Details

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

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

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

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

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

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

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

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

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

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

Details

• ## Brownian Functionals in Physics and Computer Science

### Satya N. Majumdar 1

#### Current Science 89 (2005) 2076

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

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

Details
• ## Cavity Approach to the Random Solid State

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

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

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

• 1. Physics Department (UIUC), University of Illinois at Urbana Champaign
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 3. Institute for Scientific Interchange, Institute for Scientific Interchange

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• ## Cluster Algorithms for Quantum Impurity Models and Mesoscopic Kondo Physics

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

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

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

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

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• ## Clustering of solutions in the random satisfiability problem

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

### A. Minguzzi 1, D. M. Gangardt 1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Unite mixte de service de l'institut Henri Poincaré (UMSIHP), CNRS : UMS839 – Université Paris VI - Pierre et Marie Curie
• 3. Laboratoire de Physique des Solides (LPS), CNRS : UMR8502 – Université Paris XI - Paris Sud

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• ## Geometry of Gaussian signals

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

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

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

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

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• ## Granular gases: dynamics and collective effects

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

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

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

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

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

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

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

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

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

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• ## Interacting classical dimers on the square lattice

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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• ## Landscape of solutions in constraint satisfaction problems

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

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

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

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

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

### Patricio Leboeuf 1

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

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

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

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• ## Lossy data compression with random gates

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

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

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

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

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

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

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

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

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

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• ## Mesoscopic Kondo Problem

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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• ## Persistence of Randomly Coupled Fluctuating Interfaces

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

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

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

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

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

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

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

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

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

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

### N. Bilas 1, N. Pavloff 1

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

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

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

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

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

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

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

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

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• ## Quantum oscillations in mesoscopic rings and anomalous diffusion

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

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

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

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

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

### Stephane Ouvry 1

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

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

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

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• ## Random multi-index matching problems

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

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

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

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

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• ## Regularity and chaos in the nuclear masses

### P. Leboeuf 1

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

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

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

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

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

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

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

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

Details Citations to the Article (102)
• ## Scrambling and Gate Effects in Realistic Quantum Dots

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

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

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

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

Details Citations to the Article (3)

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

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

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

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

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

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

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

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

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

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

Details Citations to the Article (10)
• ## Spin waves in a one-dimensional spinor Bose gas

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

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

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

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

Details Citations to the Article (40)
• ## Statistical mechanics of combinatorial optimization problems with site disorder

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

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

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

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

Details Citations to the Article (5)
• ## Statistics of randomly branched polymers in a semi-space

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

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

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

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

Details Citations to the Article (1)
• ## Statistics of Wave Functions in Disordered Systems with Applications to Coulomb Blockade Peak Spacing

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

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

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

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

Details Citations to the Article (4)

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

### G. Orso 1, G. V. Shlyapnikov 2, 3

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

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

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

Details Citations to the Article (20)

Details
• ## Survey propagation: an algorithm for satisfiability

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

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

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

• 1. Scuola Internazionale Superiore di Studi Avanzati / International School for Advanced Studies (SISSA / ISAS), Scuola Internazionale Superiore di Studi Avanzati/International School for Advanced Studies (SISSA/ISAS)
• 2. ICTP, the Abdus Salam International Centre for Theoretical Physics
• 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

Details
• ## Survey-propagation decimation through distributed local computations

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

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

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

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

Details Citations to the Article (9)

Details
• ## The cavity method for large deviations

### Olivier Rivoire 1

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

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

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

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

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

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

We study the phenomenon of real space condensation in the steady state of a class of one dimensional mass transport models. We derive the criterion for the occurrence of a condensation transition and analyse the precise nature of the shape and the size of the condensate in the condensed phase. We find two distinct condensate regimes: one where the condensate is gaussian distributed and the particle number fluctuations scale normally as $L^{1/2}$ where $L$ is the system size, and a second regime where the particle number fluctuations become anomalously large and the condensate peak is non-gaussian. We interpret these results within the framework of sums of random variables.

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

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

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

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

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

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

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

### Stefano Ciliberti 1, Marc Mezard 1

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

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

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

Details Citations to the Article (3)

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

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

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

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

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

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

### Serguei Brazovskii 1, 2

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

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

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

Details

Details
• ## Spatial correlation functions in $3-d$ Ising spin glasses – Archive ouverte HAL

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

#### Cirano de Dominicis, Irene Giardina, Enzo Marinari, Olivier C. Martin, Francesco Zuliani. Spatial correlation functions in $3-d$ Ising spin glasses. Physical Review B: Condensed Matter and Materials Physics, American Physical Society, 2005, 72, pp.014443. ⟨hal-00008767⟩

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

• 1. SPhT - Service de Physique Théorique
• 2. CNR ISC, Via dei Taurini 19, 00185 Roma, Italy and Dipartimento di Fisica
• 3. INFN - Istituto Nazionale di Fisica Nucleare [Sezione di Roma 1]
• 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

Details
• ## Archive ouverte HAL – Spatial correlation functions in $3-d$ Ising spin glasses

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

#### Cirano de Dominicis, Irene Giardina, Enzo Marinari, Olivier C. Martin, Francesco Zuliani. Spatial correlation functions in $3-d$ Ising spin glasses. Physical Review B: Condensed Matter and Materials Physics, American Physical Society, 2005, 72, pp.014443. ⟨hal-00008767⟩

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

• 1. SPhT - Service de Physique Théorique
• 2. CNR ISC, Via dei Taurini 19, 00185 Roma, Italy and Dipartimento di Fisica
• 3. INFN - Istituto Nazionale di Fisica Nucleare [Sezione di Roma 1]
• 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

Details

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

### Nicolas Bilas 1, Nicolas Pavloff 1

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

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

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

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

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

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

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

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

Details
• ## Artificial square ice and related dipolar nanoarrays

### Gunnar Moller 1, R. Moessner 2

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

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

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

Details Citations to the Article (46)
• ## Average ground-state energy of finite Fermi systems

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

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

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

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

Details Citations to the Article (11)
• ## Bosonization, Pairing, and Superconductivity of the Fermionic Tonks-Girardeau Gas

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

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

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

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

Details Citations to the Article (19)

Details
• ## Canonical Analysis of Condensation in Factorised Steady State

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

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

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

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

Details Citations to the Article (37)
• ## Casimir interaction between a plate and a cylinder

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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• ## Constraint Satisfaction by Survey Propagation

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

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

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

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

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• ## Correlation-induced inhomogeneity in circular quantum dots

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

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

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

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

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• ## Coulombian Disorder in Periodic Systems

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

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

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

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

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• ## Dimensional reduction on a sphere

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

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

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

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

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• ## Dynamics below the depinning threshold

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

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

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

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

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

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

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

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

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

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• ## Energy fluctuations in vibrated and driven granular gases

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

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

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

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

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

### G. Tellez 1, E. Trizac 2, 3

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

### Serguei Brazovskii 1, 2

#### x, France (2006)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Details
• ## Interaction driven real-space condensation

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

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

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

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

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• ## Large Deviations of Extreme Eigenvalues of Random Matrices

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

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

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

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

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

### Patricio Leboeuf 1, Jérôme Roccia 1

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

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

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

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

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

#### Complexus 3 (2006) 58

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

### Ying Jiang 1, Thorsten Emig 1, 2

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

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

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

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

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

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

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

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

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• ## Photon density of states for deformed surfaces

### Thorsten Emig 1, 2

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

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

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

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

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

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

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

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

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

### Paul Zinn-Justin 1

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

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

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

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

### S. Sumedha 1, 2, Deepak Dhar 1

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

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

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

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• ## Randomly incomplete spectra and intermediate statistics

### O. Bohigas 1, M. P. Pato 1, 2

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

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

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

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• ## Reconstruction on trees and spin glass transition

### Marc Mezard 1, Andrea Montanari 2

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

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

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

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• ## Secondary Structures in Long Compact Polymers

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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• ## Spectral statistics in an open parametric billiard system

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

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

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

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

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• ## Spectroscopy of the Kondo Problem in a Box

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

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

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

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

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

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

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

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

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

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

### Thierry Mora 1, Olivier Rivoire 2

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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• ## The number of matchings in random graphs

### Lenka Zdeborová 1, Marc Mézard 1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

### Jesper Lykke Jacobsen, Jesus Salas 1

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

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

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

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

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

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

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

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

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

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

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

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

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Unite mixte de service de l'institut Henri Poincaré (UMSIHP), CNRS : UMS839 – Université Paris VI - Pierre et Marie Curie
• 3. Michigan Center for Theoretical Physics and Department of chemical Engineering, University of Michigan-Ann Arbor

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

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

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

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

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

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

### Paolo Visco 1

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

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

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

Details Citations to the Article (32)
• ## Electrokinetic Effects on Slipping Surfaces

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

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

• 1. DAEP - Département Aérodynamique Energétique et Propulsion
• 2. LPMCN - Laboratoire de Physique de la Matière Condensée et Nanostructures
• 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
• ## Liquid friction on charged surfaces: From hydrodynamic slippage to electrokinetics

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

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

• 1. DAEP - Département Aérodynamique Energétique et Propulsion
• 2. LPMCN - Laboratoire de Physique de la Matière Condensée et Nanostructures
• 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
• ## Exact stationary state of a run-and-tumble particle with three internal states in a harmonic trap – Archive ouverte HAL

### Urna Basu 1 Satya N. Majumdar 2 Alberto Rosso 2 Sanjib Sabhapandit 3 Gregory Schehr 2

#### Urna Basu, Satya N. Majumdar, Alberto Rosso, Sanjib Sabhapandit, Gregory Schehr. Exact stationary state of a run-and-tumble particle with three internal states in a harmonic trap. Journal of Physics A: Mathematical and General (1975 - 2006), IOP Publishing, 2020, ⟨10.10083⟩. ⟨hal-02512239⟩

We study the motion of a one-dimensional run-and-tumble particle with three discrete internal states in the presence of a harmonic trap of stiffness $\mu.$ The three internal states, corresponding to positive, negative and zero velocities respectively, evolve following a jump process with rate $\gamma$. We compute the stationary position distribution exactly for arbitrary values of $\mu$ and $\gamma$ which turns out to have a finite support on the real line. We show that the distribution undergoes a shape-transition as $\beta=\gamma/\mu$ is changed. For $\beta<1,$ the distribution has a double-concave shape and shows algebraic divergences with an exponent $(\beta-1)$ both at the origin and at the boundaries. For $\beta>1,$ the position distribution becomes convex, vanishing at the boundaries and with a single, finite, peak at the origin. We also show that for the special case $\beta=1,$ the distribution shows a logarithmic divergence near the origin while saturating to a constant value at the boundaries.

• 1. Theoretical Condensed Matter Physics Division
• 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
• 3. Raman Research Institute

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• ## Archive ouverte HAL – Exact stationary state of a run-and-tumble particle with three internal states in a harmonic trap

### Urna Basu 1 Satya N. Majumdar 2 Alberto Rosso 2 Sanjib Sabhapandit 3 Gregory Schehr 2

#### Urna Basu, Satya N. Majumdar, Alberto Rosso, Sanjib Sabhapandit, Gregory Schehr. Exact stationary state of a run-and-tumble particle with three internal states in a harmonic trap. Journal of Physics A: Mathematical and General (1975 - 2006), IOP Publishing, 2020, ⟨10.10083⟩. ⟨hal-02512239⟩

We study the motion of a one-dimensional run-and-tumble particle with three discrete internal states in the presence of a harmonic trap of stiffness $\mu.$ The three internal states, corresponding to positive, negative and zero velocities respectively, evolve following a jump process with rate $\gamma$. We compute the stationary position distribution exactly for arbitrary values of $\mu$ and $\gamma$ which turns out to have a finite support on the real line. We show that the distribution undergoes a shape-transition as $\beta=\gamma/\mu$ is changed. For $\beta<1,$ the distribution has a double-concave shape and shows algebraic divergences with an exponent $(\beta-1)$ both at the origin and at the boundaries. For $\beta>1,$ the position distribution becomes convex, vanishing at the boundaries and with a single, finite, peak at the origin. We also show that for the special case $\beta=1,$ the distribution shows a logarithmic divergence near the origin while saturating to a constant value at the boundaries.

• 1. Theoretical Condensed Matter Physics Division
• 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
• 3. Raman Research Institute

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• ## A Toy Model of the Rat Race

### D. ben-Avraham 1, Satya N. Majumdar 2, S. Redner 3

#### Journal of Statistical Mechanics: Theory and Experiment (2007) L04002

We introduce a toy model of the 'rat race' in which individuals try to better themselves relative to the rest of the population. An individual is characterized by a real-valued fitness and each advances at a constant rate by an amount that depends on its standing in the population. The leader advances to remain ahead of its nearest neighbor, while all others advance by an amount that is set by the distance to the leader. A rich dynamics occurs as a function of the mean jump size of the trailing particles. For small jumps, the leader maintains its position, while for large jumps, there are long periods of stasis that are punctuated by episodes of explosive advancement and many lead changes. Intermediate to these two regimes, agents reach a common fitness and evolution grinds to a halt.

• 1. Department of Physics [Potsdam NY], Clarkson University
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 3. Center for Polymer Studies (CPS), Boston University

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• ## Al’tshuler-Aronov correction to the conductivity of a large metallic square network

### Christophe Texier 1, Gilles Montambaux 2

#### Physical Review B 76 (2007) 094202

We consider the correction $\Delta\sigma_\mathrm{ee}$ due to electron-electron interaction to the conductivity of a weakly disordered metal (Al'tshuler-Aronov correction). The correction is related to the spectral determinant of the Laplace operator. The case of a large square metallic network is considered. The variation of $\Delta\sigma_\mathrm{ee}(L_T)$ as a function of the thermal length $L_T$ is found very similar to the variation of the weak localization $\Delta\sigma_\mathrm{WL}(L_\phi)$ as a function of the phase coherence length. Our result for $\Delta\sigma_\mathrm{ee}$ interpolates between the known 1d and 2d results, but the interaction parameter entering the expression of $\Delta\sigma_\mathrm{ee}$ keeps a 1d behaviour. Quite surprisingly, the result is very close to the 2d logarithmic behaviour already for $L_T\sim{a}/2$, where $a$ is the lattice parameter.

• 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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• ## BCS-BEC crossover in a random external potential

### G. Orso 1

#### Physical Review Letters 99 (2007) 250402

We investigate the ground state properties of a disordered superfluid Fermi gas across the BCS-BEC (Bose Einstein condensate) crossover. We show that, for weak disorder, both the depletion of the condensate fraction of pairs and the normal fluid density exhibit a nonmonotonic behavior as a function of the interaction parameter $1/k_Fa$, reaching their minimum value near unitarity. We find that, moving away from the weak coupling BCS regime, Anderson's theorem ceases to apply and the superfluid order parameter is more and more affected by the random potential.

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

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• ## Boltzmann equation for dissipative gases in homogeneous states with nonlinear friction

### E. Trizac 1, A. Barrat 2, M. H. Ernst 3

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 76 (2007) 031305

Combining analytical and numerical methods, we study within the framework of the homogeneous non-linear Boltzmann equation, a broad class of models relevant for the dynamics of dissipative fluids, including granular gases. We use the new method presented in a previous paper [J. Stat. Phys. 124, 549 (2006)] and extend our results to a different heating mechanism, namely a deterministic non-linear friction force. We derive analytically the high energy tail of the velocity distribution and compare the theoretical predictions with high precision numerical simulations. Stretched exponential forms are obtained when the non-equilibrium steady state is stable. We derive sub-leading corrections and emphasize their relevance. In marginal stability cases, power-law behaviors arise, with exponents obtained as the roots of transcendental equations. We also consider some simple BGK (Bhatnagar, Gross, Krook) models, driven by similar heating devices, to test the robustness of our 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
• 3. Instituut voor Theoretische Fysica, Universiteit Utrecht

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• ## Casimir force driven ratchets

### Thorsten Emig 1

#### Physical Review Letters 98 (2007) 160801

We explore the non-linear dynamics of two parallel periodically patterned metal surfaces that are coupled by the zero-point fluctuations of the electromagnetic field between them. The resulting Casimir force generates for asymmetric patterns with a time-periodically driven surface-to-surface distance a ratchet effect, allowing for directed lateral motion of the surfaces in sizeable parameter ranges. It is crucial to take into account inertia effects and hence chaotic dynamics which are described by Langevin dynamics. Multiple velocity reversals occur as a function of driving, mean surface distance, and effective damping. These transport properties are shown to be stable against weak ambient noise.

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

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• ## Casimir forces between arbitrary compact objects

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

#### Physical Review Letters 99 (2007) 170403

We develop an exact method for computing the Casimir energy between arbitrary compact objects, either dielectrics or perfect conductors. The energy is obtained as an interaction between multipoles, generated by quantum 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 an example, we obtain this series for two dielectric spheres and the full interaction at all separations for perfectly conducting spheres.

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

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• ## Combinatorial point for higher spin loop models

### Paul Zinn-Justin 1

#### Communications in Mathematical Physics 272 (2007) 661-682

Integrable loop models associated with higher representations (spin k/2) of U_q(sl(2)) are investigated at the point q=-e^{i\pi/(k+2)}. The ground state eigenvalue and eigenvectors are described. Introducing inhomogeneities into the models allows to derive a sum rule for the ground state entries.

• 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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• ## Crystalline phase of strongly interacting Fermi mixtures

### D. S. Petrov 1, 2, G. E. Astrakharchik 3, D. J. Papoular 1, C. Salomon 4, G. V. Shlyapnikov 1, 5

#### Physical Review Letters 99 (2007) 130407

We show that the system of weakly bound molecules of heavy and light fermionic atoms is characterized by a long-range intermolecular repulsion and can undergo a gas-crystal quantum transition if the mass ratio exceeds a critical value. For the critical mass ratio above 100 obtained in our calculations, this crystalline order can be observed as a superlattice in an optical lattice for heavy atoms with a small filling factor. We also find that this novel system is sufficiently stable with respect to molecular relaxation into deep bound states and to the process of trimer formation.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. National Research Centre "Kurchatov Institute" (NRC KI), University of Moscow
• 3. Departament de Fisica i Enginyeria Nuclear, Campus Nord B4-B5, Universitat Politécnica de Catalunya
• 4. Laboratoire Kastler Brossel (LKB (Lhomond)), CNRS : UMR8552 – Université Paris VI - Pierre et Marie Curie – Ecole Normale Supérieure de Paris - ENS Paris
• 5. Van der Waals-Zeeman Institute, University of Amsterdam

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• ## Density of near-extreme events

### Sanjib Sabhapandit 1, Satya N. Majumdar 1

#### Physical Review Letters 98 (2007) 140201

We provide a quantitative analysis of the phenomenon of crowding of near-extreme events by computing exactly the density of states (DOS) near the maximum of a set of independent and identically distributed random variables. We show that the mean DOS converges to three different limiting forms depending on whether the tail of the distribution of the random variables decays slower than, faster than, or as a pure exponential function. We argue that some of these results would remain valid even for certain {\em correlated} cases and verify it for power-law correlated stationary Gaussian sequences. Satisfactory agreement is found between the near-maximum crowding in the summer temperature reconstruction data of western Siberia and the theoretical prediction.

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

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• ## Dimensional crossover in quantum networks: from macroscopic to mesoscopic Physics

### Félicien Schopfer 1, François Mallet 1, D. Mailly 2, C. Texier 3, 4, G. Montambaux 4, Christopher Bauerle 1, Laurent Saminadayar 1, 5, 6

#### Physical Review Letters 98 (2007) 026807

We report on magnetoconductance measurements of metallic networks of various sizes ranging from 10 to $10^{6}$ plaquettes, with anisotropic aspect ratio. Both Altshuler-Aronov-Spivak (AAS) $h/2e$ periodic oscillations and Aharonov-Bohm (AB) $h/e$ periodic oscillations are observed for all networks. For large samples, the amplitude of both oscillations results from the incoherent superposition of contributions of phase coherent regions. When the transverse size becomes smaller than the phase coherent length $L_\phi$, one enters a new regime which is phase coherent (mesoscopic) along one direction and macroscopic along the other, leading to a new size dependence of the quantum oscillations.

• 1. Institut Néel (NEEL), CNRS : UPR2940 – Université Joseph Fourier - Grenoble I – Institut National Polytechnique de Grenoble (INPG)
• 2. Laboratoire de photonique et de nanostructures (LPN), CNRS : UPR20
• 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 4. Laboratoire de Physique des Solides (LPS), CNRS : UMR8502 – Université Paris XI - Paris Sud
• 5. Université Joseph Fourier (Grenoble 1 UJF), Université Joseph Fourier - Grenoble I
• 6. Institut Universitaire de France (IUF), Ministère de l'Enseignement Supérieur et de la Recherche Scientifique

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• ## Directional emission of stadium-shaped micro-lasers

### Mélanie Lebental 1, 2, Jean-Sébastien Lauret 1, Joseph Zyss 1, C. Schmit 2, E. Bogomolny 2

#### Physical Review A: Atomic, Molecular and Optical Physics 75 (2007) 033806

The far-field emission of two dimensional (2D) stadium-shaped dielectric cavities is investigated. Micro-lasers with such shape present a highly directional emission. We provide experimental evidence of the dependance of the emission directionality on the shape of the stadium, in good agreement with ray numerical simulations. We develop a simple geometrical optics model which permits to explain analytically main observed features. Wave numerical calculations confirm the results.

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

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• ## Effect of connecting wires on the decoherence due to electron-electron interaction in a metallic ring

### Christophe Texier 1

#### Physical Review B 76 (2007) 153312

We consider the weak localization in a ring connected to reservoirs through leads of finite length and submitted to a magnetic field. The effect of decoherence due to electron-electron interaction on the harmonics of AAS oscillations is studied, and more specifically the effect of the leads. Two results are obtained for short and long leads regimes. The scale at which the crossover occurs is discussed. The long leads regime is shown to be more realistic experimentally.

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

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• ## Equilibrium and dynamics of a trapped superfluid Fermi gas with unequal masses

### G. Orso 1, L. P. Pitaevskii 2, 3, S. Stringari 2

#### Physical Review A: Atomic, Molecular and Optical Physics 77 (2007) 033611

Interacting Fermi gases with equal populations but unequal masses are investigated at zero temperature using local density approximation and the hydrodynamic theory of superfluids in the presence of harmonic trapping. We derive the conditions of energetic stability of the superfluid configuration with respect to phase separation and the frequencies of the collective oscillations in terms of the mass ratio and the trapping frequencies of the two components. We discuss the behavior of the gas after the trapping potential of a single component is switched off and show that, near a Feshbach resonance, the released component can still remain trapped due to many-body interaction effects. Explicit predictions are presented for a mixture of $^6$Li and $^{40}$K with resonant interaction.

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

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• ## Exact results for the Spectra of Bosons and Fermions with Contact Interaction

### Stefan Mashkevich 1, Sergey I. Matveenko 2, Stéphane Ouvry 3

#### Nuclear Physics B 763 (2007) 431-444

An N-body bosonic model with delta-contact interactions projected on the lowest Landau level is considered. For a given number of particles in a given angular momentum sector, any energy level can be obtained exactly by means of diagonalizing a finite matrix: they are roots of algebraic equations. A complete solution of the three-body problem is presented, some general properties of the N-body spectrum are pointed out, and a number of novel exact analytic eigenstates are obtained. The FQHE N-fermion model with Laplacian-delta interactions is also considered along the same lines of analysis. New exact eigenstates are proposed, along with the Slater determinant, whose eigenvalues are shown to be related to Catalan numbers.

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

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• ## Fermi Edge Singularities in the Mesoscopic Regime: II. Photo-absorption Spectra

### M. Hentschel 1, 2, D. Ullmo 2, 3, H. U. Baranger 2

#### Physical Review B 76 (2007) 245419

We study Fermi edge singularities in photo-absorption spectra of generic mesoscopic systems such as quantum dots or nanoparticles. We predict deviations from macroscopic-metallic behavior and propose experimental setups for the observation of these effects. The theory is based on the model of a localized, or rank one, perturbation caused by the (core) hole left behind after the photo-excitation of an electron into the conduction band. The photo-absorption spectra result from the competition between two many-body responses, Anderson's orthogonality catastrophe and the Mahan-Nozieres-DeDominicis contribution. Both mechanisms depend on the system size through the number of particles and, more importantly, fluctuations produced by the coherence characteristic of mesoscopic samples. The latter lead to a modification of the dipole matrix element and trigger one of our key results: a rounded K-edge typically found in metals will turn into a (slightly) peaked edge on average in the mesoscopic regime. We consider in detail the effect of the 'bound state' produced by the core hole.

• 1. Max Planck Institute for Physics of Complex Systems, Max-Planck-Institut
• 2. Duke Physics, Duke University
• 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• ## Finite-size effects on the dynamics of the zero-range process

### Shamik Gupta 1, Mustansir Barma 1, Satya N. Majumdar 2

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 76 (2007) 060101

We study finite-size effects on the dynamics of a one-dimensional zero-range process which shows a phase transition from a low-density disordered phase to a high-density condensed phase. The current fluctuations in the steady state show striking differences in the two phases. In the disordered phase, the variance of the integrated current shows damped oscillations in time due to the motion of fluctuations around the ring as a dissipating kinematic wave. In the condensed phase, this wave cannot propagate through the condensate, and the dynamics is dominated by the long-time relocation of the condensate from site to site.

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

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• ## Fractional Laplacian in Bounded Domains

### A. Zoia 1, A. Rosso 2, 3, M. Kardar 3

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 76 (2007) 021116

The fractional Laplacian operator, $-(-\triangle)^{\frac{\alpha}{2}}$, appears in a wide class of physical systems, including Lévy flights and stochastic interfaces. In this paper, we provide a discretized version of this operator which is well suited to deal with boundary conditions on a finite interval. The implementation of boundary conditions is justified by appealing to two physical models, namely hopping particles and elastic springs. The eigenvalues and eigenfunctions in a bounded domain are then obtained numerically for different boundary conditions. Some analytical results concerning the structure of the eigenvalues spectrum are also obtained.

• 1. Department of Nuclear Engineering,, Polytechnic of Milan
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 3. Department of Physics Massachusetts Institute of Technology, Massachusetts Institute of Technology

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• ## General flux to a trap in one and three dimensions

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

#### Journal of Physics: Condensed Matter 19 (2007) 065102

The problem of the flux to a spherical trap in one and three dimensions, for diffusing particles undergoing discrete-time jumps with a given radial probability distribution, is solved in general, verifying the Smoluchowski-like solution in which the effective trap radius is reduced by an amount proportional to the jump length. This reduction in the effective trap radius corresponds to the Milne extrapolation length.

• 1. Michigan Center for Theoretical Physics and Department of chemical Engineering, University of Michigan-Ann Arbor
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 3. Unite mixte de service de l'institut Henri Poincaré (UMSIHP), CNRS : UMS839 – Université Paris VI - Pierre et Marie Curie

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• ## Gibbs States and the Set of Solutions of Random Constraint Satisfaction Problems

### Florent Krzakala 1, Andrea Montanari 2, Federico Ricci-Tersenghi, Guilhem Semerjian 2, Lenka Zdeborova 3

#### Proceeding of the national academy of sciences 104, 25 (2007) 10318

An instance of a random constraint satisfaction problem defines a random subset S (the set of solutions) of a large product space (the set of assignments). We consider two prototypical problem ensembles (random k-satisfiability and q-coloring of random regular graphs), and study the uniform measure with support on S. As the number of constraints per variable increases, this measure first decomposes into an exponential number of pure states ('clusters'), and subsequently condensates over the largest such states. Above the condensation point, the mass carried by the n largest states follows a Poisson-Dirichlet process. For typical large instances, the two transitions are sharp. We determine for the first time their precise location. Further, we provide a formal definition of each phase transition in terms of different notions of correlation between distinct variables in the problem. The degree of correlation naturally affects the performances of many search/sampling algorithms. Empirical evidence suggests that local Monte Carlo Markov Chain strategies are effective up to the clustering phase transition, and belief propagation up to the condensation point. Finally, refined message passing techniques (such as survey propagation) may beat also this threshold.

• 1. Laboratoire de Physico-Chimie Théorique (LPCT), CNRS : UMR7083 – ESPCI ParisTech
• 2. Laboratoire de Physique Théorique de l'ENS (LPTENS), CNRS : UMR8549 – Université Paris VI - Pierre et Marie Curie – Ecole Normale Supérieure de Paris - ENS Paris
• 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• ## Incipient Wigner Localization in Circular Quantum Dots

### Amit Ghosal 1, 2, A.D. Guclu 1, 3, C.J. Umrigar 3, Denis Ullmo 1, 4, Harold U. Baranger 1

#### Physical Review B 76 (2007) 085341

We study the development of electron-electron correlations in circular quantum dots as the density is decreased. We consider a wide range of both electron number, N<=20, and electron gas parameter, r_s<18, using the diffusion quantum Monte Carlo technique. Features associated with correlation appear to develop very differently in quantum dots than in bulk. The main reason is that translational symmetry is necessarily broken in a dot, leading to density modulation and inhomogeneity. Electron-electron interactions act to enhance this modulation ultimately leading to localization. This process appears to be completely smooth and occurs over a wide range of density. Thus there is a broad regime of incipient'' Wigner crystallization in these quantum dots. Our specific conclusions are: (i) The density develops sharp rings while the pair density shows both radial and angular inhomogeneity. (ii) The spin of the ground state is consistent with Hund's (first) rule throughout our entire range of r_s for all 4

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

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• ## Inferring periodic orbits from spectra of simple shaped micro-lasers

### Mélanie Lebental 1, 2, Nadia Djellali 1, Carole Arnaud 1, Jean-Sébastien Lauret 1, Joseph Zyss 1, R. Dubertrand 2, C. Schmit 2, E. Bogomolny 2

#### Physical Review A: Atomic, Molecular and Optical Physics 76 (2007) 023830

Dielectric micro-cavities are widely used as laser resonators and characterizations of their spectra are of interest for various applications. We experimentally investigate micro-lasers of simple shapes (Fabry-Perot, square, pentagon, and disk). Their lasing spectra consist mainly of almost equidistant peaks and the distance between peaks reveals the length of a quantized periodic orbit. To measure this length with a good precision, it is necessary to take into account different sources of refractive index dispersion. Our experimental and numerical results agree with the superscar model describing the formation of long-lived states in polygonal cavities. The limitations of the two-dimensional approximation are briefly discussed in connection with micro-disks.

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

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• ## Integer Partitions and Exclusion Statistics

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

#### Journal of Physics A General Physics 40 (2007) 11255-11269

We provide a combinatorial description of exclusion statistics in terms of minimal difference $p$ partitions. We compute the probability distribution of the number of parts in a random minimal $p$ partition. It is shown that the bosonic point $p=0$ is a repulsive fixed point for which the limiting distribution has a Gumbel form. For all positive $p$ the distribution is shown to be Gaussian.

• 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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• ## Integer partitions and exclusion statistics: Limit shapes and the largest part of Young diagrams

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

#### Journal of statistical mechanics-theory and experiment (2007) P10001

We compute the limit shapes of the Young diagrams of the minimal difference $p$ partitions and provide a simple physical interpretation for the limit shapes. We also calculate the asymptotic distribution of the largest part of the Young diagram and show that the scaled distribution has a Gumbel form for all $p$. This Gumbel statistics for the largest part remains unchanged even for general partitions of the form $E=\sum_i n_i i^{1/\nu}$ with $\nu>0$ where $n_i$ is the number of times the part $i$ appears.

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

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• ## Large Deviations of the Maximum Eigenvalue in Wishart Random Matrices

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

#### Journal of Physics A: Mathematical and General 40 (2007) 4317-4337

We compute analytically the probability of large fluctuations to the left of the mean of the largest eigenvalue in the Wishart (Laguerre) ensemble of positive definite random matrices. We show that the probability that all the eigenvalues of a (N x N) Wishart matrix W=X^T X (where X is a rectangular M x N matrix with independent Gaussian entries) are smaller than the mean value <\lambda>=N/c decreases for large N as $\sim \exp[-\frac{\beta}{2}N^2 \Phi_{-}(\frac{2}{\sqrt{c}}+1;c)]$, where \beta=1,2 correspond respectively to real and complex Wishart matrices, c=N/M < 1 and \Phi_{-}(x;c) is a large deviation function that we compute explicitly. The result for the Anti-Wishart case (M < N) simply follows by exchanging M and N. We also analytically determine the average spectral density of an ensemble of constrained Wishart matrices whose eigenvalues are forced to be smaller than a fixed barrier. The numerical simulations are in excellent agreement with the analytical predictions.

• 1. School of Information Systems, Computing & Mathematics, Brunel University
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• ## Level Density of a Bose Gas and Extreme Value Statistics

### A. Comtet 1, 2, P. Leboeuf 1, Satya N. Majumdar 1

#### Physical Review Letters 98 (2007) 070404

We establish a connection between the level density of a gas of non-interacting bosons and the theory of extreme value statistics. Depending on the exponent that characterizes the growth of the underlying single-particle spectrum, we show that at a given excitation energy the limiting distribution function for the number of excited particles follows the three universal distribution laws of extreme value statistics, namely Gumbel, Weibull and Fréchet. Implications of this result, as well as general properties of the level density at different energies, are discussed.

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

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• ## Longest increasing subsequence as expectation of a simple nonlinear stochastic PDE with a low noise intensity

### E. Katzav 1, S. Nechaev 2, O. Vasilyev 3, 4

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 75 (2007) 061113

We report some new observation concerning the statistics of Longest Increasing Subsequences (LIS). We show that the expectation of LIS, its variance, and apparently the full distribution function appears in statistical analysis of some simple nonlinear stochastic partial differential equation (SPDE) in the limit of very low noise intensity.

• 1. 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
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 3. Max-Planck-Institut für Metallforschung, Max-Planck-Institut
• 4. Institut für Theoretische und Angewandte Physik, Universität Stuttgart

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• ## Loop model with mixed boundary conditions, qKZ equation and alternating sign matrices

### Paul Zinn-Justin 1

#### Journal of Statistical Mechanics: Theory and Experiment (2007) P01007

The integrable loop model with mixed boundary conditions based on the 1-boundary extended Temperley--Lieb algebra with loop weight 1 is considered. The corresponding qKZ equation is introduced and its minimal degree solution described. As a result, the sum of the properly normalized components of the ground state in size L is computed and shown to be equal to the number of Horizontally and Vertically Symmetric Alternating Sign Matrices of size 2L+3. A refined counting is also considered.

• 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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• ## Magnetic exponents of two-dimensional Ising spin glasses

### F. Liers 1, O. C. Martin 2

#### Physical Review B 76 (2007) 060405

The magnetic critical properties of two-dimensional Ising spin glasses are controversial. Using exact ground state determination, we extract the properties of clusters flipped when increasing continuously a uniform field. We show that these clusters have many holes but otherwise have statistical properties similar to those of zero-field droplets. A detailed analysis gives for the magnetization exponent delta = 1.30 +/- 0.02 using lattice sizes up to 80x80; this is compatible with the droplet model prediction delta = 1.282. The reason for previous disagreements stems from the need to analyze both singular and analytic contributions in the low-field regime.

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

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• ## Many-body effects in the mesoscopic x-ray edge problem

### Martina Hentschel 1, Georg Roeder 1, Denis Ullmo 2

#### Progress of Theoretical Physics Supplement 166 (2007) 143-151

Many-body phenomena, a key interest in the investigation of bulk solid state systems, are studied here in the context of the x-ray edge problem for mesoscopic systems. We investigate the many-body effects associated with the sudden perturbation following the x-ray excitation of a core electron into the conduction band. For small systems with dimensions at the nanoscale we find considerable deviations from the well-understood metallic case where Anderson orthogonality catastrophe and the Mahan-Nozieres-DeDominicis response cause characteristic deviations of the photoabsorption cross section from the naive expectation. Whereas the K-edge is typically rounded in metallic systems, we find a slightly peaked K-edge in generic mesoscopic systems with chaotic-coherent electron dynamics. Thus the behavior of the photoabsorption cross section at threshold depends on the system size and is different for the metallic and the mesoscopic case.

• 1. Max Planck Institute for Physics of Complex Systems, Max-Planck-Institut
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• ## Mosaic length and finite interaction-range effects in a one dimensional random energy model

### Silvio Franz 1, Giorgio Parisi 2, 3, 4, Federico Ricci-Tersenghi 2

#### Journal of Physics A: Mathematical and General 41 (2007) 324011

In this paper we study finite interaction range corrections to the mosaic picture of the glass transition as emerges from the study of the Kac limit of large interaction range for disordered models. To this aim we consider point to set correlation functions, or overlaps, in a one dimensional random energy model as a function of the range of interaction. In the Kac limit, the mosaic length defines a sharp first order transition separating a high overlap phase from a low overlap one. Correspondingly we find that overlap curves as a function of the window size and different finite interaction ranges cross roughly at the mosaic lenght. Nonetheless we find very slow convergence to the Kac limit and we discuss why this could be a problem for measuring the mosaic lenght in realistic models.

• 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. Dipartimento di Fisica, SMC, INFM, and INFN, Università degli studi di Roma I - La Sapienza
• 4. Dipartimento di Fisica, Sezione INFN, SMC and UdRm1 of INFM, Università degli studi di Roma I - La Sapienza

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• ## Network of inherent structures in spin glasses: scaling and scale-free distributions

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

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 76 (2007) 051107

The local minima (inherent structures) of a system and their associated transition links give rise to a network. Here we consider the topological and distance properties of such a network in the context of spin glasses. We use steepest descent dynamics, determining for each disorder sample the transition links appearing within a given barrier height. We find that differences between linked inherent structures are typically associated with local clusters of spins; we interpret this within a framework based on droplets in which the characteristic length scale'' grows with the barrier height. We also consider the network connectivity and the degrees of its nodes. Interestingly, when the spin glass is of the mean-field type, the degree distribution of the network of inherent structures exhibits a non-trivial scale-free behavior.

• 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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• ## Non-Abelian states with negative flux: a new series of quantum Hall states

### Thierry Jolicoeur 1

#### Physical Review Letters 99 (2007) 036805

By applying the idea of parafermionic clustering to composite bosons with positive as well as negative flux, a new series of trial wavefunctions to describe fractional quantum Hall states is proposed. These non-Abelian states compete at filling factors k/(3k +/- 2) with other ground states like stripes or composite fermion states. These two series contain all the states recently discovered by Pan et al. [Phys. Rev. Lett. 90, 016801 (2003)] including the even denominator cases. Exact diagonalization studies on the sphere and torus point to their possible relevance for filling factors 3/7, 3/11, and 3/8.

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

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• ## Numerical Calculation of the Functional renormalization group fixed-point functions at the depinning transition

### Alberto Rosso 1, Pierre Le Doussal 2, Kay Joerg Wiese 2

#### Physical Review B 75 (2007) 22020a

We compute numerically the sequence of successive pinned configurations of an elastic line pulled quasi-statically by a spring in a random bond (RB) and random field (RF) potential. Measuring the fluctuations of the center of mass of the line allows to obtain the functional renormalization group (FRG) functions at the depinning transition. The universal form of the second cumulant Delta(u) is found to have a linear cusp at the origin, to be identical for RB and RF, different from the statics, and in good agreement with 2-loop FRG. The cusp is due to avalanches, which we visualize. Avalanches also produce a cusp in the third cumulant, whose universal form is obtained, as predicted by FRG.

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

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• ## On the distribution of surface extrema in several one- and two-dimensional random landscapes

### Florent Hivert 1, S. Nechaev 2, 3, G. Oshanin 4, 5, 6, O. Vasilyev 4, 7

#### Journal of Statistical Physics 126 (2007) 243-279

We study here a standard next-nearest-neighbor (NNN) model of ballistic growth on one- and two-dimensional substrates focusing our analysis on the probability distribution function $P(M,L)$ of the number $M$ of maximal points (i.e., local peaks'') of growing surfaces. Our analysis is based on two central results: (i) the proof (presented here) of the fact that uniform one--dimensional ballistic growth process in the steady state can be mapped onto ''rise-and-descent'' sequences in the ensemble of random permutation matrices; and (ii) the fact, established in Ref. \cite{ov}, that different characteristics of rise-and-descent'' patterns in random permutations can be interpreted in terms of a certain continuous--space Hammersley--type process. For one--dimensional system we compute $P(M,L)$ exactly and also present explicit results for the correlation function characterizing the enveloping surface. For surfaces grown on 2d substrates, we pursue similar approach considering the ensemble of permutation matrices with long--ranged correlations. Determining exactly the first three cumulants of the corresponding distribution function, we define it in the scaling limit using an expansion in the Edgeworth series, and show that it converges to a Gaussian function as $L \to \infty$.

• 1. Laboratoire d'Informatique, de Traitement de l'Information et des Systèmes (LITIS), Institut National des Sciences Appliquées (INSA) - Rouen – Université du Havre – Université de Rouen : EA4108
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 3. P. N. Lebedev Physical Institute, Russian Academy of Science
• 4. Laboratoire de Physique Théorique de la Matière Condensée (LPTMC), CNRS : UMR7600 – Université Paris VI - Pierre et Marie Curie
• 5. Max-Planck-Institut fur Metallforschung, Max-Planck-Institut
• 6. Institut fur Theoretische und Angewandte Physik, Universität Stuttgart
• 7. Center for Molecular Modelling, Materia Nova, Université de Mons-Hainaut

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• ## On the Feasibility of Portfolio Optimization under Expected Shortfall

### Stéfano Ciliberti 1, Imre Kondor 2, Marc Mézard 1

#### Quantitative Finance 7 (2007) 389-396

We address the problem of portfolio optimization under the simplest coherent risk measure, i.e. the expected shortfall. As it is well known, one can map this problem into a linear programming setting. For some values of the external parameters, when the available time series is too short, the portfolio optimization is ill posed because it leads to unbounded positions, infinitely short on some assets and infinitely long on some others. As first observed by Kondor and coworkers, this phenomenon is actually a phase transition. We investigate the nature of this transition by means of a replica approach.

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

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• ## On the ground–state energy of finite Fermi systems

### Jérôme Roccia 1, Patricio Leboeuf 1

#### Physical Review C 76 (2007) 014301

We study the ground--state shell correction energy of a fermionic gas in a mean--field approximation. Considering the particular case of 3D harmonic trapping potentials, we show the rich variety of different behaviors (erratic, regular, supershells) that appear when the number--theoretic properties of the frequency ratios are varied. For self--bound systems, where the shape of the trapping potential is determined by energy minimization, we obtain accurate analytic formulas for the deformation and the shell correction energy as a function of the particle number $N$. Special attention is devoted to the average of the shell correction energy. We explain why in self--bound systems it is a decreasing (and negative) function of $N$.

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

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• ## On the Inelastic Collapse of a Ball Bouncing on a Randomly Vibrating Platform

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

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 76 (2007) 031130

We study analytically the dynamics of a ball bouncing inelastically on a randomly vibrating platform, as a simple toy model of inelastic collapse. Of principal interest are the distributions of the number of flights n_f till the collapse and the total time \tau_c elapsed before the collapse. In the strictly elastic case, both distributions have power law tails characterised by exponents which are universal, i.e., independent of the details of the platform noise distribution. In the inelastic case, both distributions have exponential tails: P(n_f) ~ exp[-\theta_1 n_f] and P(\tau_c) ~ exp[-\theta_2 \tau_c]. The decay exponents \theta_1 and \theta_2 depend continuously on the coefficient of restitution and are nonuniversal; however as one approches the elastic limit, they vanish in a universal manner that we compute exactly. An explicit expression for \theta_1 is provided for a particular case of the platform noise distribution.

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

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• ## On the macroion virial contribution to the osmotic pressure in charge-stabilized colloidal suspensions

### E. Trizac 1, 2, L. Belloni 3, J. Dobnikar 4, 5, H. H. von Grunberg 4, R. Castaneda-Priego 6

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 75 (2007) 011401

Our interest goes to the different virial contributions to the equation of state of charged colloidal suspensions. Neglect of surface effects in the computation of the colloidal virial term leads to spurious and paradoxical results. This pitfall is one of the several facets of the danger of a naive implementation of the so called One Component Model, where the micro-ionic degrees of freedom are integrated out to only keep in the description the mesoscopic (colloidal) degrees of freedom. On the other hand, due incorporation of wall induced forces dissolves the paradox brought forth in the naive approach, provides a consistent description, and confirms that for salt-free systems, the colloidal contribution to the pressure is dominated by the micro-ionic one. Much emphasis is put on the no salt case but the situation with added electrolyte is also discussed.

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

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• ## Parafermionic states in rotating Bose-Einstein condensates

### Nicolas Regnault 1, Thierry Jolicoeur 1, 2

#### Physical Review B 76 (2007) 235324

We investigate possible parafermionic states in rapidly rotating ultracold bosonic atomic gases at lowest Landau level filling factor nu=k/2. We study how the system size and interactions act upon the overlap between the true ground state and a candidate Read-Rezayi state. We also consider the quasihole states which are expected to display non-Abelian statistics. We numerically evaluate the degeneracy of these states and show agreement with a formula given by E. Ardonne. We compute the overlaps between low-lying exact eigenstates and quasihole candidate wavefunctions. We discuss the validity of the parafermion description as a function of the filling factor.

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

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• ## Persistence of a Rouse polymer chain under transverse shear flow

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

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 75 (2007) 061122

We consider a single Rouse polymer chain in two dimensions in presence of a transverse shear flow along the $x$ direction and calculate the persistence probability $P_0(t)$ that the $x$ coordinate of a bead in the bulk of the chain does not return to its initial position up to time $t$. We show that the persistence decays at late times as a power law, $P_0(t)\sim t^{-\theta}$ with a nontrivial exponent $\theta$. The analytical estimate of $\theta=0.359...$ obtained using an independent interval approximation is in excellent agreement with the numerical value $\theta\approx 0.360\pm 0.001$.

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

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• ## Phase diagram of the chromatic polynomial on a torus

### Jesper Lykke Jacobsen 1, 2, Jesus Salas 3

#### Nuclear Physics B - Proceedings Supplements 783 (2007) 238-296

We study the zero-temperature partition function of the Potts antiferromagnet (i.e., the chromatic polynomial) on a torus using a transfer-matrix approach. We consider square- and triangular-lattice strips with fixed width L, arbitrary length N, and fully periodic boundary conditions. On the mathematical side, we obtain exact expressions for the chromatic polynomial of widths L=5,6,7 for the square and triangular lattices. On the physical side, we obtain the exact phase diagrams'' for these strips of width L and infinite length, and from these results we extract useful information about the infinite-volume phase diagram of this model: in particular, the number and position of the different phases.

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

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• ## Phase Transitions in the Coloring of Random Graphs

### Lenka Zdeborová 1, Florent Krzakala 2

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 76 (2007) 031131

We consider the problem of coloring the vertices of a large sparse random graph with a given number of colors so that no adjacent vertices have the same color. Using the cavity method, we present a detailed and systematic analytical study of the space of proper colorings (solutions). We show that for a fixed number of colors and as the average vertex degree (number of constraints) increases, the set of solutions undergoes several phase transitions similar to those observed in the mean field theory of glasses. First, at the clustering transition, the entropically dominant part of the phase space decomposes into an exponential number of pure states so that beyond this transition a uniform sampling of solutions becomes hard. Afterward, the space of solutions condenses over a finite number of the largest states and consequently the total entropy of solutions becomes smaller than the annealed one. Another transition takes place when in all the entropically dominant states a finite fraction of nodes freezes so that each of these nodes is allowed a single color in all the solutions inside the state. Eventually, above the coloring threshold, no more solutions are available. We compute all the critical connectivities for Erdos-Renyi and regular random graphs and determine their asymptotic values for large number of colors. Finally, we discuss the algorithmic consequences of our findings. We argue that the onset of computational hardness is not associated with the clustering transition and we suggest instead that the freezing transition might be the relevant phenomenon. We also discuss the performance of a simple local Walk-COL algorithm and of the belief propagation algorithm in the light of our results.

• 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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• ## Polynomial solutions of qKZ equation and ground state of XXZ spin chain at Delta = -1/2

### A. V. Razumov 1, Yu. G. Stroganov 1, Paul Zinn-Justin 2

#### Journal of Physics A Mathematical and Theoretical 40 (2007) 11827-11847

Integral formulae for polynomial solutions of the quantum Knizhnik-Zamolodchikov equations associated with the R-matrix of the six-vertex model are considered. It is proved that when the deformation parameter q is equal to e^{+- 2 pi i/3} and the number of vertical lines of the lattice is odd, the solution under consideration is an eigenvector of the inhomogeneous transfer matrix of the six-vertex model. In the homogeneous limit it is a ground state eigenvector of the antiferromagnetic XXZ spin chain with the anisotropy parameter Delta equal to -1/2 and odd number of sites. The obtained integral representations for the components of this eigenvector allow to prove some conjectures on its properties formulated earlier. A new statement relating the ground state components of XXZ spin chains and Temperley-Lieb loop models is formulated and proved.

• 1. Division of Theoretical Physics, Institut for High Energy Physics
• 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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• ## Population size effects in evolutionary dynamics on neutral networks and toy landscapes

### Olivier C Martin 1, 2, Luca Peliti 3, S. Sumedha 1

#### Journal of Statistical Mechanics: Theory and Experiment (2007) P05011

We study the dynamics of a population subject to selective pressures, evolving either on RNA neutral networks or in toy fitness landscapes. We discuss the spread and the neutrality of the population in the steady state. Different limits arise depending on whether selection or random drift are dominant. In the presence of strong drift we show that observables depend mainly on $M \mu$, $M$ being the population size and $\mu$ the mutation rate, while corrections to this scaling go as 1/M: such corrections can be quite large in the presence of selection if there are barriers in the fitness landscape. Also we find that the convergence to the large $M \mu$ limit is linear in $1/M \mu$. Finally we introduce a protocol that minimizes drift; then observables scale like 1/M rather than $1/(M\mu)$, allowing one to determine the large $M$ limit faster when $\mu$ is small; furthermore the genotypic diversity increases from $O(\ln M)$ to $O(M)$.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Génétique Végétale (GV), CNRS : UMR8120 – Institut national de la recherche agronomique (INRA) : UMR0320 – Université Paris XI - Paris Sud – Institut National Agronomique Paris-Grignon
• 3. Dipartimento di Scienze Fisiche, Università degli studi di Napoli Federico II

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• ## Preferential interaction coefficient for nucleic acids and other cylindrical poly-ions

### E. Trizac 1, 2, G. Tellez 3

#### Macromolecules 40 (2007) 1305-1310

The thermodynamics of nucleic acid processes is heavily affected by the electric double-layer of micro-ions around the polyions. We focus here on the Coulombic contribution to the salt-polyelectrolyte preferential interaction (Donnan) coefficient and we report extremely accurate analytical expressions valid in the range of low salt concentration (when polyion radius is smaller than the Debye length). The analysis is performed at Poisson-Boltzmann level, in cylindrical geometry, with emphasis on highly charged poly-ions (beyond counter-ion condensation''). The results hold for any electrolyte of the form $z_-$:$z_+$. We also obtain a remarkably accurate expression for the electric potential in the vicinity of the poly-ion.

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

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• ## Quantum Knizhnik-Zamolodchikov equation: reflecting boundary conditions and combinatorics

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

#### Journal of statistical mechanics-theory and experiment (2007) P12009

We consider the level 1 solution of quantum Knizhnik-Zamolodchikov equation with reflecting boundary conditions which is relevant to the Temperley--Lieb model of loops on a strip. By use of integral formulae we prove conjectures relating it to the weighted enumeration of Cyclically Symmetric Transpose Complement Plane Partitions and related combinatorial objects.

• 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 patterns generated by random permutations of natural numbers

### G. Oshanin 1, 2, R. Voituriez 1, S. Nechaev 3, O. Vasilyev 2, Florent Hivert 4

#### The European Physical Journal Special Topics 143 (2007) 143-157

We survey recent results on some one- and two-dimensional patterns generated by random permutations of natural numbers. In the first part, we discuss properties of random walks, evolving on a one-dimensional regular lattice in discrete time $n$, whose moves to the right or to the left are induced by the rise-and-descent sequence associated with a given random permutation. We determine exactly the probability of finding the trajectory of such a permutation-generated random walk at site $X$ at time $n$, obtain the probability measure of different excursions and define the asymptotic distribution of the number of 'U-turns' of the trajectories - permutation 'peaks' and 'through'. In the second part, we focus on some statistical properties of surfaces obtained by randomly placing natural numbers $1,2,3, >...,L$ on sites of a 1d or 2d square lattices containing $L$ sites. We calculate the distribution function of the number of local 'peaks' - sites the number at which is larger than the numbers appearing at nearest-neighboring sites - and discuss some surprising collective behavior emerging in this model.

• 1. Laboratoire de Physique Théorique de la Matière Condensée (LPTMC), CNRS : UMR7600 – Université Paris VI - Pierre et Marie Curie
• 2. Department of Inhomogeneous Condensed Matter Theory, Max-Planck-Institut
• 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 4. Laboratoire d'Informatique, de Traitement de l'Information et des Systèmes (LITIS), Institut National des Sciences Appliquées (INSA) - Rouen – Université du Havre – Université de Rouen : EA4108

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• ## Relation between directed polymers in random media and random bond dimer models

### Ying Jiang 1, Thorsten Emig 2

#### Physical Review B 75 (2007) 134413

We reassess the relation between classical lattice dimer models and the continuum elastic description of a lattice of fluctuating polymers. In the absence of randomness we determine the density and line tension of the polymers in terms of the bond weights of hard-core dimers on the square and the hexagonal lattice. For the latter, we demonstrate the equivalence of the canonical ensemble for the dimer model and the grand-canonical description for polymers by performing explicitly the continuum limit. Using this equivalence for the random bond dimer model on a square lattice, we resolve a previously observed discrepancy between numerical results for the random dimer model and a replica approach for polymers in random media. Further potential applications of the equivalence are briefly discussed.

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

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• ## Risk Minimization through Portfolio Replication

### Stefano Ciliberti 1, 2, Marc Mezard 1

#### European Physical Journal B 57, 2 (2007) 175-180

We use a replica approach to deal with portfolio optimization problems. A given risk measure is minimized using empirical estimates of asset values correlations. We study the phase transition which happens when the time series is too short with respect to the size of the portfolio. We also study the noise sensitivity of portfolio allocation when this transition is approached. We consider explicitely the cases where the absolute deviation and the conditional value-at-risk are chosen as a risk measure. We show how the replica method can study a wide range of risk measures, and deal with various types of time series correlations, including realistic ones with volatility clustering.

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

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• ## Role of conformational entropy in force-induced bio-polymer unfolding

### Sanjay Kumar 1, Iwan Jensen 2, Jesper L. Jacobsen 3, Anthony J. Guttmann 2

#### Physical Review Letters 98 (2007) 128101

A statistical mechanical description of flexible and semi-flexible polymer chains in a poor solvent is developed in the constant force and constant distance ensembles. We predict the existence of many intermediate states at low temperatures stabilized by the force. A unified response to pulling and compressing forces has been obtained in the constant distance ensemble. We show the signature of a cross-over length which increases linearly with the chain length. Below this cross-over length, the critical force of unfolding decreases with temperature, while above, it increases with temperature. For stiff chains, we report for the first time 'saw-tooth' like behavior in the force-extension curves which has been seen earlier in the case of protein unfolding.

• 1. Department of Physics, Banaras Hindu University
• 2. ARC Centre of Excellence for Mathematics and Statistics of Complex Systems, Department of Mathematics and Statistics, The University of Melbourne
• 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• ## SLE description of the nodal lines of random wave functions

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

#### Journal of Physics A: Mathematical and General 40 (2007) 381-395

The nodal lines of random wave functions are investigated. We demonstrate numerically that they are well approximated by the so-called SLE_6 curves which describe the continuum limit of the percolation cluster boundaries. This result gives an additional support to the recent conjecture that the nodal domains of random (and chaotic) wave functions in the semi classical limit are adequately described by the critical percolation theory. It is also shown that using the dipolar variant of SLE reduces significantly finite size effects.

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

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• ## Soliton-soliton scattering in dipolar Bose-Einstein condensates

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

#### Physical Review A: Atomic, Molecular and Optical Physics 76 (2007) 013606

We analyze the scattering of bright solitons in dipolar Bose-Einstein condensates placed in unconnected layers. Whereas for short-range interactions unconnected layers are independent, a remarkable consequence of the dipole interaction is the appearance of novel nonlocal interlayer effects. In particular, we show that the interlayer interaction leads to an effective molecular potential between disconnected solitons, inducing a complex scattering physics between them, which includes inelastic fusion into soliton-molecules, and strong symmetric and asymmetric inelastic resonances. In addition, a fundamentally new 2D scattering scenario in matter-wave solitons is possible, in which inelastic spiraling occurs, resembling phenomena in photorrefractive materials. Finally, we consider the scattering of unconnected 1D solitons and discuss the feasibility in current on going experiments.

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

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• ## Statistical Mechanics of the Hyper Vertex Cover Problem

### M. Mézard 1, M. Tarzia 1

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 76 (2007) 041124

We introduce and study a new optimization problem called Hyper Vertex Cover. This problem is a generalization of the standard vertex cover to hypergraphs: one seeks a configuration of particles with minimal density such that every hyperedge of the hypergraph contains at least one particle. It can also be used in important practical tasks, such as the Group Testing procedures where one wants to detect defective items in a large group by pool testing. Using a Statistical Mechanics approach based on the cavity method, we study the phase diagram of the HVC problem, in the case of random regualr hypergraphs. Depending on the values of the variables and tests degrees different situations can occur: The HVC problem can be either in a replica symmetric phase, or in a one-step replica symmetry breaking one. In these two cases, we give explicit results on the minimal density of particles, and the structure of the phase space. These problems are thus in some sense simpler than the original vertex cover problem, where the need for a full replica symmetry breaking has prevented the derivation of exact results so far. Finally, we show that decimation procedures based on the belief propagation and the survey propagation algorithms provide very efficient strategies to solve large individual instances of the hyper vertex cover problem.

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

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• ## Statistical properties of single-file diffusion front

### Sanjib Sabhapandit 1

#### Journal of Statistical Mechanics: Theory and Experiment (2007) L05002

Statistical properties of the front of a semi-infinite system of single-file diffusion (one dimensional system where particles cannot pass each other, but in-between collisions each one independently follow diffusive motion) are investigated. Exact as well as asymptotic results are provided for the probability density function of (a) the front-position, (b) the maximum of the front-positions, and (c) the first-passage time to a given position. The asymptotic laws for the front-position and the maximum front-position are found to be governed by the Fisher-Tippett-Gumbel extreme value statistics. The asymptotic properties of the first-passage time is dominated by a stretched-exponential tail in the distribution. The farness of the front with the rest of the system is investigated by considering (i) the gap from the front to the closest particle, and (ii) the density profile with respect to the front-position, and analytical results are provided for late time behaviors.

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

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• ## Superfluidity versus Anderson localization in a dilute Bose gas

### T. Paul 1, P. Schlagheck 2, P. Leboeuf 1, N. Pavloff 1

#### Physical Review Letters 98 (2007) 210602

We consider the motion of a quasi one dimensional beam of Bose-Einstein condensed particles in a disordered region of finite extent. Interaction effects lead to the appearance of two distinct regions of stationary flow. One is subsonic and corresponds to superfluid motion. The other one is supersonic, dissipative and shows Anderson localization. We compute analytically the interaction-dependent localization length. We also explain the disappearance of the supersonic stationary flow for large disordered samples.

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

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• ## Tagged Particle Correlations in the Asymmetric Simple Exclusion Process: Finite Size Effects

### Shamik Gupta 1, Satya N. Majumdar 2, Claude Godrèche 3, Mustansir Barma 1

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 76 (2007) 021112

We study finite size effects in the variance of the displacement of a tagged particle in the stationary state of the Asymmetric Simple Exclusion Process (ASEP) on a ring of size $L$. The process involves hard core particles undergoing stochastic driven dynamics on a lattice. The variance of the displacement of the tagged particle, averaged with respect to an initial stationary ensemble and stochastic evolution, grows linearly with time at both small and very large times. We find that at intermediate times, it shows oscillations with a well defined size-dependent period. These oscillations arise from sliding density fluctuations (SDF) in the stationary state with respect to the drift of the tagged particle, the density fluctuations being transported through the system by kinematic waves. In the general context of driven diffusive systems, both the Edwards-Wilkinson (EW) and the Kardar-Parisi-Zhang (KPZ) fixed points are unstable with respect to the SDF fixed point, a flow towards which is generated on adding a gradient term to the EW and the KPZ time-evolution equation. We also study tagged particle correlations for a fixed initial configuration, drawn from the stationary ensemble, following earlier work by van Beijeren. We find that the time dependence of this correlation is determined by the dissipation of the density fluctuations. We show that an exactly solvable linearized model captures the essential qualitative features seen in the finite size effects of the tagged particle correlations in the ASEP. Moreover, this linearized model also provides an exact coarse-grained description of two other microscopic models.

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

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• ## The first-passage area for drifted Brownian motion and the moments of the Airy distribution

### Michael J. Kearney 1, Satya N. Majumdar 2, Richard J. Martin 3

#### Journal of Physics A Mathematical and Theoretical 40 (2007) F863

An exact expression for the distribution of the area swept out by a drifted Brownian motion till its first-passage time is derived. A study of the asymptotic behaviour confirms earlier conjectures and clarifies their range of validity. The analysis also leads to a simple closed-form solution for the moments of the Airy distribution.

• 1. Faculty of Engineering and Physical Sciences, University of Surrey
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 3. Quantitative Credit Strategy Group, Credit suisse

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• ## The Phase Diagram of 1-in-3 Satisfiability Problem

### Jack Raymond 1, Andrea Sportiello 2, Lenka Zdeborová 3

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 76 (2007) 011101

We study the typical case properties of the 1-in-3 satisfiability problem, the boolean satisfaction problem where a clause is satisfied by exactly one literal, in an enlarged random ensemble parametrized by average connectivity and probability of negation of a variable in a clause. Random 1-in-3 Satisfiability and Exact 3-Cover are special cases of this ensemble. We interpolate between these cases from a region where satisfiability can be typically decided for all connectivities in polynomial time to a region where deciding satisfiability is hard, in some interval of connectivities. We derive several rigorous results in the first region, and develop the one-step--replica-symmetry-breaking cavity analysis in the second one. We discuss the prediction for the transition between the almost surely satisfiable and the almost surely unsatisfiable phase, and other structural properties of the phase diagram, in light of cavity method results.

• 1. NCRG, Aston University
• 2. Università degli Studi di Milano, Università degli studi di Milano
• 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• ## The renormalized jellium model for spherical and cylindrical colloids

### Salete Pianegonda 1, 2, Emmanuel Trizac 1, Yan Levin 2

#### Journal of Chemical Physics 126 (2007) 014702

Starting from a mean-field description for a dispersion of highly charged spherical or (parallel) rod-like colloids, we introduce the simplification of a homogeneous background to include the contribution of other polyions to the static field created by a tagged polyion. The charge of this background is self-consistently renormalized to coincide with the polyion effective charge, the latter quantity thereby exhibiting a non-trivial density dependence, which directly enters into the equation of state through a simple analytical expression. The good agreement observed between the pressure calculated using the renormalized jellium and Monte Carlo simulations confirms the relevance of the {renormalized} jellium model for theoretical and experimental purposes and provides an alternative to the Poisson-Boltzmann cell model since it is free of some of the intrinsic limitations of this approach.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Instituto de Física, Universidade Federal do Rio de Janeiro

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• ## The Rotor Model with spectral parameters and enumerations of Alternating Sign Matrices

### Luigi Cantini 1

#### Journal of statistical mechanics-theory and experiment (2007) P08012

In this paper we study the Rotor Model of Martins and Nienhuis. After introducing spectral parameters, a combined use of integrability, polynomiality of the ground state wave function and a mapping into the fully-packed O(1)-model allows us to determine the sum rule and a family of maximally nested components for different boundary conditions. We see in this way the appearance of 3-enumerations of Alternating Sign Matrices.

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

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• ## Universal Extremal Statistics in a Freely Expanding Jepsen Gas

### Ioana Bena 1, Satya N. Majumdar 2

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 75 (2007) 051103

We study the extremal dynamics emerging in an out-of-equilibrium one-dimensional Jepsen gas of $(N+1)$ hard-point particles. The particles undergo binary elastic collisions, but move ballistically in-between collisions. The gas is initally uniformly distributed in a box $[-L,0]$ with the 'leader' (or the rightmost particle) at X=0, and a random positive velocity, independently drawn from a distribution $\phi(V)$, is assigned to each particle. The gas expands freely at subsequent times. We compute analytically the distribution of the leader's velocity at time $t$, and also the mean and the variance of the number of collisions that are undergone by the leader up to time $t$. We show that in the thermodynamic limit and at fixed time $t\gg 1$ (the so-called 'growing regime'), when interactions are strongly manifest, the velocity distribution exhibits universal scaling behavior of only three possible varieties, depending on the tail of $\phi(V)$. The associated scaling functions are novel and different from the usual extreme-value distributions of uncorrelated random variables. In this growing regime the mean and the variance of the number of collisions of the leader up to time $t$ increase logarithmically with $t$, with universal prefactors that are computed exactly. The implications of our results in the context of biological evolution modeling are pointed out.

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

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• ## Universal width distributions in non-Markovian Gaussian processes

### Raoul Santachiara 1, 2, Alberto Rosso 3, Werner Krauth 4

#### Journal of Statistical Mechanics: Theory and Experiment (2007) P02009

We study the influence of boundary conditions on self-affine random functions u(t) in the interval t/L \in [0,1], with independent Gaussian Fourier modes of variance ~ 1/q^{\alpha}. We consider the probability distribution of the mean square width of u(t) taken over the whole interval or in a window t/L \in [x, x+\delta]. Its characteristic function can be expressed in terms of the spectrum of an infinite matrix. This distribution strongly depends on the boundary conditions of u(t) for finite \delta, but we show that it is universal (independent of boundary conditions) in the small-window limit. We compute it directly for all values of \alpha, using, for \alpha<3, an asymptotic expansion formula that we derive. For \alpha > 3, the limiting width distribution is independent of \alpha. It corresponds to an infinite matrix with a single non-zero eigenvalue. We give the exact expression for the width distribution in this case. Our analysis facilitates the estimation of the roughness exponent from experimental data, in cases where the standard extrapolation method cannot be used

• 1. Laboratoire de Physique Théorique (LPTH), CNRS : UMR7085 – Université Louis Pasteur - Strasbourg I
• 2. Laboratoire de Physique Théorique de l'ENS (LPTENS), CNRS : UMR8549 – Université Paris VI - Pierre et Marie Curie – Ecole Normale Supérieure de Paris - ENS Paris
• 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

Details Citations to the Article (6)
• ## Archive ouverte HAL – A congruence index for testing topological similarity between trees

### Damien M VienneTatiana Giraud 1 Olivier C Martin 2, 3, 4, 5

#### Bioinformatics, Oxford University Press (OUP), 2007, 23 (23), pp.3119--3124

MOTIVATION: Phylogenetic trees are omnipresent in evolutionary biology and the comparison of trees plays a central role there. Tree congruence statistics are based on the null hypothesis that two given trees are not more congruent (topologically similar) than expected by chance. Usually, one searches for the most parsimonious evolutionary scenario relating two trees and then one tests the null hypothesis by generating a high number of random trees and comparing these to the one between the observed trees. However, this approach requires a lot of computational work (human and machine) and the results depend on the evolutionary assumptions made. RESULTS: We propose an index, I(cong), for testing the topological congruence between trees with any number of leaves, based on maximum agreement subtrees (MAST). This index is straightforward, simple to use, does not rely on parametrizing the likelihood of evolutionary events, and provides an associated confidence level. AVAILABILITY: A web site has been created that allows rapid and easy online computation of this index and of the associated P-value at http://www.ese.u-psud.fr/bases/upresa/pages/devienne/index.html

• 1. ESE - Ecologie Systématique et Evolution
• 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
• 3. GQE-Le Moulon - Génétique Quantitative et Evolution - Le Moulon (Génétique Végétale)
• 4. BIOSP - Biostatistique et Processus Spatiaux
• 5. IS2 - Statistical Inference for Industry and Health
• ## Sex-Specific Crossover Distributions and Variations in Interference Level along Arabidopsis thaliana Chromosome 4

### Jan Drouaud 1 Raphaël Mercier 1 Liudmila Chelysheva 1 Aurélie Bérard 2 Matthieu Falque 3 Olivier Martin 3, 4 Vanessa Zanni 5 Dominique Brunel 2 Christine Mezard 1

#### PLoS Genetics, Public Library of Science, 2007, 3 (6), pp.1096-1107. <10.1371/journal.pgen.0030106.eor>

In many species, sex-related differences in crossover (CO) rates have been described at chromosomal and regional levels. In this study, we determined the CO distribution along the entire Arabidopsis thaliana Chromosome 4 (18 Mb) in male and female meiosis, using high density genetic maps built on large backcross populations (44 markers, .1,300 plants). We observed dramatic differences between male and female map lengths that were calculated as 88 cM and 52 cM, respectively. This difference is remarkably parallel to that between the total synaptonemal complex lengths measured in male and female meiocytes by immunolabeling of ZYP1 (a component of the synaptonemal complex). Moreover, CO landscapes were clearly different: in particular, at both ends of the map, male CO rates were higher (up to 4-fold the mean value), whereas female CO rates were equal or even below the chromosomal average. This unique material gave us the opportunity to perform a detailed analysis of CO interference on Chromosome 4 in male and female meiosis. The number of COs per chromosome and the distances between them clearly departs from randomness. Strikingly, the interference level (measured by coincidence) varied significantly along the chromosome in male meiosis and was correlated to the physical distance between COs. The significance of this finding on the relevance of current CO interference models is discussed.

• 1. IJPB - Institut Jean-Pierre Bourgin
• 2. UR Etude du Polymorphisme des Génomes végétaux
• 3. GQE - Génétique Quantitative et Evolution (Génétique Végétale)
• 4. Laboratoire de Physique Théorique et Modèles Statistiques
• 5. UR254 - Unité de Recherche en Génétique et Amélioration des Plantes

Details
• ## A congruence index for testing topological similarity between trees

### Damien M VienneTatiana Giraud 1 Olivier C Martin 2, 3, 4, 5

#### Bioinformatics, Oxford University Press (OUP), 2007, 23 (23), pp.3119--3124

• 1. ESE - Ecologie Systématique et Evolution
• 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
• 3. GQE-Le Moulon - Génétique Quantitative et Evolution - Le Moulon (Génétique Végétale)
• 4. BIOSP - Biostatistique et Processus Spatiaux
• 5. IS2 - Statistical Inference for Industry and Health
• ## Sex-Specific Crossover Distributions and Variations in Interference Level along Arabidopsis thaliana Chromosome 4 – Archive ouverte HAL

### Jan Drouaud 1 Raphaël Mercier 1 Liudmila Chelysheva 1 Aurélie Bérard 2 Matthieu Falque 3 Olivier Martin 3, 4 Vanessa Zanni 5 Dominique Brunel 2 Christine Mezard 1

#### Jan Drouaud, Raphaël Mercier, Liudmila Chelysheva, Aurélie Bérard, Matthieu Falque, et al.. Sex-Specific Crossover Distributions and Variations in Interference Level along Arabidopsis thaliana Chromosome 4. PLoS Genetics, Public Library of Science, 2007, 3 (6), pp.1096-1107. ⟨10.1371/journal.pgen.0030106.eor⟩. ⟨hal-01203942⟩

In many species, sex-related differences in crossover (CO) rates have been described at chromosomal and regional levels. In this study, we determined the CO distribution along the entire Arabidopsis thaliana Chromosome 4 (18 Mb) in male and female meiosis, using high density genetic maps built on large backcross populations (44 markers, .1,300 plants). We observed dramatic differences between male and female map lengths that were calculated as 88 cM and 52 cM, respectively. This difference is remarkably parallel to that between the total synaptonemal complex lengths measured in male and female meiocytes by immunolabeling of ZYP1 (a component of the synaptonemal complex). Moreover, CO landscapes were clearly different: in particular, at both ends of the map, male CO rates were higher (up to 4-fold the mean value), whereas female CO rates were equal or even below the chromosomal average. This unique material gave us the opportunity to perform a detailed analysis of CO interference on Chromosome 4 in male and female meiosis. The number of COs per chromosome and the distances between them clearly departs from randomness. Strikingly, the interference level (measured by coincidence) varied significantly along the chromosome in male meiosis and was correlated to the physical distance between COs. The significance of this finding on the relevance of current CO interference models is discussed.

• 1. IJPB - Institut Jean-Pierre Bourgin
• 2. UR Etude du Polymorphisme des Génomes végétaux
• 3. GQE-Le Moulon - Génétique Quantitative et Evolution - Le Moulon (Génétique Végétale)
• 4. Laboratoire de Physique Théorique et Modèles Statistiques
• 5. UR254 - Unité de Recherche en Génétique et Amélioration des Plantes

Details
• ## Robustness Can Evolve Gradually in Complex Regulatory Gene Networks with Varying Topology – Archive ouverte HAL

### S. Ciliberti 1 O. Martin 1, 2 A. Wagner 3

#### S. Ciliberti, O. Martin, A. Wagner. Robustness Can Evolve Gradually in Complex Regulatory Gene Networks with Varying Topology. PLoS Computational Biology, Public Library of Science, 2007, 3 (2) (2), pp.e15. ⟨10.1371/journal.pcbi.0030015⟩. ⟨hal-00143879⟩

The topology of cellular circuits (the who-interacts-with-whom) is key to understand their robustness to both mutations and noise. The reason is that many biochemical parameters driving circuit behavior vary extensively and are thus not fine-tuned. Existing work in this area asks to what extent the function of any one given circuit is robust. But is high robustness truly remarkable, or would it be expected for many circuits of similar topology? And how can high robustness come about through gradual Darwinian evolution that changes circuit topology gradually, one interaction at a time? We here ask these questions for a model of transcriptional regulation networks, in which we explore millions of different network topologies. Robustness to mutations and noise are correlated in these networks. They show a skewed distribution, with a very small number of networks being vastly more robust than the rest. All networks that attain a given gene expression state can be organized into a graph whose nodes are networks that differ in their topology. Remarkably, this graph is connected and can be easily traversed by gradual changes of network topologies. Thus, robustness is an evolvable property. This connectedness and evolvability of robust networks may be a general organizational principle of biological networks. In addition, it exists also for RNA and protein structures, and may thus be a general organizational principle of all biological systems.

• 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
• 2. GQE-Le Moulon - Génétique Quantitative et Evolution - Le Moulon (Génétique Végétale)
• 3. Department of Biochemistry

Details
• ## Archive ouverte HAL – Sex-Specific Crossover Distributions and Variations in Interference Level along Arabidopsis thaliana Chromosome 4

### Jan Drouaud 1 Raphaël Mercier 1 Liudmila Chelysheva 1 Aurélie Bérard 2 Matthieu Falque 3 Olivier Martin 3, 4 Vanessa Zanni 5 Dominique Brunel 2 Christine Mezard 1

#### Jan Drouaud, Raphaël Mercier, Liudmila Chelysheva, Aurélie Bérard, Matthieu Falque, et al.. Sex-Specific Crossover Distributions and Variations in Interference Level along Arabidopsis thaliana Chromosome 4. PLoS Genetics, Public Library of Science, 2007, 3 (6), pp.1096-1107. ⟨10.1371/journal.pgen.0030106.eor⟩. ⟨hal-01203942⟩

In many species, sex-related differences in crossover (CO) rates have been described at chromosomal and regional levels. In this study, we determined the CO distribution along the entire Arabidopsis thaliana Chromosome 4 (18 Mb) in male and female meiosis, using high density genetic maps built on large backcross populations (44 markers, .1,300 plants). We observed dramatic differences between male and female map lengths that were calculated as 88 cM and 52 cM, respectively. This difference is remarkably parallel to that between the total synaptonemal complex lengths measured in male and female meiocytes by immunolabeling of ZYP1 (a component of the synaptonemal complex). Moreover, CO landscapes were clearly different: in particular, at both ends of the map, male CO rates were higher (up to 4-fold the mean value), whereas female CO rates were equal or even below the chromosomal average. This unique material gave us the opportunity to perform a detailed analysis of CO interference on Chromosome 4 in male and female meiosis. The number of COs per chromosome and the distances between them clearly departs from randomness. Strikingly, the interference level (measured by coincidence) varied significantly along the chromosome in male meiosis and was correlated to the physical distance between COs. The significance of this finding on the relevance of current CO interference models is discussed.

• 1. IJPB - Institut Jean-Pierre Bourgin
• 2. UR Etude du Polymorphisme des Génomes végétaux
• 3. GQE-Le Moulon - Génétique Quantitative et Evolution - Le Moulon (Génétique Végétale)
• 4. Laboratoire de Physique Théorique et Modèles Statistiques
• 5. UR254 - Unité de Recherche en Génétique et Amélioration des Plantes

Details
• ## Archive ouverte HAL – Robustness Can Evolve Gradually in Complex Regulatory Gene Networks with Varying Topology

### S. Ciliberti 1 O. Martin 1, 2 A. Wagner 3

#### S. Ciliberti, O. Martin, A. Wagner. Robustness Can Evolve Gradually in Complex Regulatory Gene Networks with Varying Topology. PLoS Computational Biology, Public Library of Science, 2007, 3 (2) (2), pp.e15. ⟨10.1371/journal.pcbi.0030015⟩. ⟨hal-00143879⟩

The topology of cellular circuits (the who-interacts-with-whom) is key to understand their robustness to both mutations and noise. The reason is that many biochemical parameters driving circuit behavior vary extensively and are thus not fine-tuned. Existing work in this area asks to what extent the function of any one given circuit is robust. But is high robustness truly remarkable, or would it be expected for many circuits of similar topology? And how can high robustness come about through gradual Darwinian evolution that changes circuit topology gradually, one interaction at a time? We here ask these questions for a model of transcriptional regulation networks, in which we explore millions of different network topologies. Robustness to mutations and noise are correlated in these networks. They show a skewed distribution, with a very small number of networks being vastly more robust than the rest. All networks that attain a given gene expression state can be organized into a graph whose nodes are networks that differ in their topology. Remarkably, this graph is connected and can be easily traversed by gradual changes of network topologies. Thus, robustness is an evolvable property. This connectedness and evolvability of robust networks may be a general organizational principle of biological networks. In addition, it exists also for RNA and protein structures, and may thus be a general organizational principle of all biological systems.

• 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
• 2. GQE-Le Moulon - Génétique Quantitative et Evolution - Le Moulon (Génétique Végétale)
• 3. Department of Biochemistry

Details

• ## 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)

Details
• ## 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

Details
• ## 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

Details
• ## 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)

Details
• ## 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

Details Citations to the Article (7)

Details
• ## 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

Details
• ## 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

Details Citations to the Article (26)
• ## 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

Details Citations to the Article (21)
• ## 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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