publications

Olivier C. Martin 1, Rémi Monasson 2, Riccardo Zecchina 3 Theoretical Computer Science 265 (2001) 3-67 Recently, it has been recognized that phase transitions play an important role in the probabilistic analysis of combinatorial optimization problems. However, there are in fact many other relations that lead to close ties between computer science and statistical physics. This review aims at presenting the tools […]

Gregory Berkolaiko 1, Eugene Bogomolny 2, J.P. Keating 3, 4 Journal of Physics A 34 (2001) 335-350 We derive an exact expression for the two-point correlation function for quantum star graphs in the limit as the number of bonds tends to infinity. This turns out to be identical to the corresponding result for certain Seba billiards in the semiclassical limit. Reasons for

Oriol Bohigas 1, Patricio Leboeuf 1, Juan Mayor Sanchez 2 Foundations of Physics 31 (2001) 489-517 ew aspects of spectral fluctuations of (quantum) chaotic and diffusive systems are considered, namely autocorrelations of the spacing between consecutive levels or spacing autocovariances. They can be viewed as a discretized two point correlation function. Their behavior results from two different contributions. One corresponds to

Jean Desbois 1 European Physical Journal B 24 (2001) 261-266 The spectral determinant of the Schrödinger operator ($ – \Delta + V(x) $) on a graph is computed for general boundary conditions. ($\Delta$ is the Laplacian and $V(x)$ is some potential defined on the graph). Applications to restricted random walks on graphs are discussed. 1. Laboratoire de

Paul Zinn-Justin 1 MSRI Publications 40 (2001) 1 The study of a certain class of matrix integrals can be motivated by their interpretation as counting objects of knot theory such as alternating prime links, tangles or knots. The simplest such model is studied in detail and allows to rederive recent results of Sundberg and Thistlethwaite. The second

Eugene Bogomolny 1, Ulrich Gerland 2, Charles Schmit 1 Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 63 (2001) 036206 We consider the statistical distribution of zeros of random meromorphic functions whose poles are independent random variables. It is demonstrated that correlation functions of these zeros can be computed analytically and explicit calculations are performed for the 2-point correlation function.

Moses, D., Wang, J., Heeger, A.J., Kirova, N., Brazovskii, S. PNAS 58 (2001) 13496-13505.

Eugene Bogomolny 1, Ulrich Gerland 2, Charles Schmit 1 European Physical Journal B 19 (2001) 121-132 We propose a plasma model for spectral statistics displaying level repulsion without long-range spectral rigidity, i.e. statistics intermediate between random matrix and Poisson statistics similar to the ones found numerically at the critical point of the Anderson metal-insulator transition in disordered systems and in certain

Denis Ullmo 1, Tatsuro Nagano 2, Steven Tomsovic 2, Harold U. Baranger 3 Physical Review B 63 (2001) 125339-1-13 We develop a semiclassical density functional theory in the context of quantum dots. Coulomb blockade conductance oscillations have been measured in several experiments using nanostructured quantum dots. The statistical properties of these oscillations remain puzzling, however, particularly the statistics of spacings between conductance peaks. To

Christophe Texier 1, 2, Gilles Montambaux 2 Journal of Physics A 34 (2001) 10307-10326 We consider the scattering theory for the Schrödinger operator $-\Dc_x^2+V(x)$ on graphs made of one-dimensional wires connected to external leads. We derive two expressions for the scattering matrix on arbitrary graphs. One involves matrices that couple arcs (oriented bonds), the other involves matrices that couple vertices.