LPTMS Publications

Archives :

• 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

Details Citations to the Article (21)

• 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

Details Citations to the Article (20)
• 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

Details Citations to the Article (16)
• 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

Details
• 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

Details

• 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

Details Citations to the Article (16)
• 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

Details Citations to the Article (1)
• 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

Details Citations to the Article (27)
• 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

Details Citations to the Article (29)

• 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

Details
• 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

Details Citations to the Article (8)
• 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

Details
• 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

Details
• 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

Details Citations to the Article (4)

• 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

Details
• 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

Details
• 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

Details
• 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

Details Citations to the Article (14)

• 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

Details
• 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

Details Citations to the Article (106)
• 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

Details Citations to the Article (29)
• 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

Details Citations to the Article (29)
• 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

Details Citations to the Article (14)

• 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

Details
• 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

Details

• 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

Details
• 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

Details
• 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

Details
• 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

Details Citations to the Article (26)
• 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

Details Citations to the Article (49)
• 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

Details Citations to the Article (24)
• 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