Related papers: Random matrix universality in dynamical correlatio…
In order to investigate the reliability of the classical approximation for non-perturbative real time correlation functions at finite temperature we study the two-point correlator for the anharmonic oscillator. For moderately large times…
Using molecular dynamics computer simulations we investigate the out-of-equilibrium dynamics of a Lennard-Jones system after a quench from a high temperature to one below the glass transition temperature. By studying the radial distribution…
Using the diagrammatic method, we derive a set of self-consistent equations that describe eigenvalue distributions of large correlated asymmetric random matrices. The matrix elements can have different variances and be correlated with each…
We analyze cross-correlations between price fluctuations of different stocks using methods of random matrix theory (RMT). Using two large databases, we calculate cross-correlation matrices C of returns constructed from (i) 30-min returns of…
We analyze numerically the out-of-equilibrium relaxation dynamics of a long-range Hamiltonian system of $N$ fully coupled rotators. For a particular family of initial conditions, this system is known to enter a particular regime in which…
This chapter discusses the conditions and timescales under which isolated many-body quantum systems, initially far from equilibrium, ultimately reach thermal equilibrium. We also examine quantities that, during the relaxation process,…
We derive analytical expressions for the correlation functions of the electronic conductance fluctuations of an open quantum dot under several conditions. Both the variation of energy and that of an external parameter such as an applied…
Motivated by the importance ascribed to correlations in random matrices used to model phenomena in various scientific disciplines, we report how algebraic correlations between matrix elements affect the eigenvalue statistics and spectral…
We propose a method for calculating dynamical correlation functions at finite temperature in integrable lattice models of Yang-Baxter type. The method is based on an expansion of the correlation functions as a series over matrix elements of…
The limit of small entropy production is reached in relaxing systems long after preparation, and in stationary driven systems in the limit of small driving power. Surprisingly, for extended systems this limit is not in general the…
We consider the statistics of time delay in a chaotic cavity having $M$ open channels, in the absence of time-reversal invariance. In the random matrix theory approach, we compute the average value of polynomial functions of the time delay…
We show that time-correlation functions of arbitrary order for any random variable in a statistical dynamical system can be calculated as higher-order response functions of the mean history of the variable. The response is to a ``control…
Focusing on non-ergodic macroscopic systems we reconsider the variances of time averages time-series. The total variance (direct average over all time-series) is known to be the sum of an internal variance (fluctuations within the…
Changing some of its parameters over time is a paradigmatic way of driving an otherwise isolated many-body quantum system out of equilibrium, and a vital ingredient for building quantum computers and simulators. Here, we further develop a…
We review the recent developments in the theory of normal, normal self-dual and general complex random matrices. The distribution and correlations of the eigenvalues at large scales are investigated in the large $N$ limit. The 1/N expansion…
This paper summarizes some work I've been doing on eigenvalue correlators of Random Matrix Models which show some interesting behaviour. First we consider matrix models with gaps in there spectrum or density of eigenvalues. The…
Theoretical analyses of the random energy model with only two states and its extension with a hierarchy of only two levels show that these models reproduce out-of-equilibrium phenomena observed in experiments of glassy materials; the…
We compute averages of products and ratios of characteristic polynomials associated with Orthogonal, Unitary, and Symplectic Ensembles of Random Matrix Theory. The pfaffian/determinantal formulas for these averages are obtained, and the…
We study the effects of an arbitrary external perturbation in the statistical properties of the S-matrix of quantum chaotic scattering systems in the limit of isolated resonances. We derive, using supersymmetry, an exact non-perturbative…
Many models for chaotic systems consist of joining two integrable systems with incompatible constants of motion. The quantum counterparts of such models have a propagator which factorizes into two integrable parts. Each part can be…