# LPTMS Publications

Archives :

• ## 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

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• ## 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
• 3. Darmstadt University of Technology, Darmstadt University

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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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