LPTMS Publications

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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