Related papers: On "Universal" Correlations in Disordered and Chao…
Disordered systems are an important class of models in statistical mechanics, having the defining characteristic that the energy landscape is a fixed realization of a random field. Examples include various models of glasses and polymers.…
Spectral statistics and correlations are the usual way to study the presence or absence of quantum chaos in quantum systems. We present our investigation on the study of the fluctuation average and variance of certain correlation functions…
This paper presents a more complete version than hitherto published of our explanation of a transition from regular to irregular motions and more generally of the nature of a certain kind of deterministic chaos. To this end we introduced a…
We establish a new approach to calculating spectral statistics in disordered conductors, by considering how energy levels move in response to changes in the impurity potential. We use this fictitious dynamics to calculate the spectral form…
We derive a simple analytical expression for the level correlation function of an integrable system. It accounts for both the lack of correlations at smaller energy scales and for global rigidity (level number conservation) at larger…
A study of correlations in tractable multiparticle cascade models in terms of wavelets reveals many promising features. The selfsimilar construction of the wavelet basis functions and their multiscale localization properties provide a new…
The way a relativistic system approaches fluid dynamical behaviour can be understood physically through the signals that will contribute to its linear response to perturbations. What these signals are is captured in the analytic structure…
The autocorrelation function of spectral determinants is proposed as a convenient tool for the characterization of spectral statistics in general, and for the study of the intimate link between quantum chaos and random matrix theory, in…
We discuss a modification to Random Matrix Theory eigenstate statistics, that systematically takes into account the non-universal short-time behavior of chaotic systems. The method avoids diagonalization of the Hamiltonian, instead…
A class of numerical methods to determine Pollicott-Ruelle resonances in chaotic dynamical systems is proposed. This is achieved by relating some existing procedures which make use of Pade approximants and interpolating exponentials to both…
We set up and analyze a random matrix model to study energy localization and its time behavior in two chaotically coupled systems. This investigation is prompted by a recent experimental and theoretical study of Weaver and Lobkis on coupled…
Statistical properties of parametric motion in ensembles of Hermitian banded random matrices are studied. We analyze the distribution of level velocities and level curvatures as well as their correlation functions in the crossover regime…
We present an analytical description of the distribution of diagonal lines in Recurrence Plots (RPs) for white noise and chaotic systems, and find that the latter one is linked to the correlation entropy. Further we identify two scaling…
We prove that the spectrum of an individual chaotic quantum graph shows universal spectral correlations, as predicted by random--matrix theory. The stability of these correlations with regard to non--universal corrections is analyzed in…
Damped-driven systems are ubiquitous in engineering and science. Despite the diversity of physical processes observed in a broad range of applications, the underlying instabilities observed in practice have a universal characterization…
We describe an experiment dedicated to the study of the trajectories of a ball bouncing randomly on a vibrating plate. The system was originally used, considering a sinusoidal vibration, to illustrate period doubling and the route to chaos.…
We present an improved method for calculating the parallel and perpendicular velocity correlation functions directly from peculiar velocity surveys using weighted maximum-likelihood estimators. A central feature of the new method is the use…
Heat conduction in one-dimensional (1D) systems is studied based on an analytical S-matrix method, which is developed in the mesoscopic electronic transport theory and molecular dynamic (MD) simulations. It is found that heat conduction in…
We study velocity correlations induced by diffusion and dissipation in a simple dissipative dynamical system. We observe that diffusion, as a result of time reversible microscopic processes, leads to correlations with different spatial…
We examine synchronization between identical chaotic systems. A rigorous criteria is presented which, if satisfied, guarantees that the coupling produces linearly stable synchronous motion. The criteria can also be used to design couplings…