Related papers: Quantum chaotic systems: a random-matrix approach
Theory of Random Matrix Ensembles have proven to be a useful tool in the study of the statistical distribution of energy or transmission levels of a wide variety of physical systems. We give an overview of certain q-generalizations of the…
The main purpose of these lectures is to discuss briefly recent methods of calculation of statistical properties of quantum eigenvalues for chaotic systems based on semi-classical trace formulas. Under the assumption that periodic orbit…
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…
Correspondence in quantum chaotic systems is lost in short time scales. Introducing some noise we study the spectrum of the resulting coarse grained propagaor of density matrices. Some differen methods to compute the spectrum are reviewed.…
Random matrix theory (RMT) universality is the defining property of quantum mechanical chaotic systems, and can be probed by observables like the spectral form factor (SFF). In this paper, we describe systematic deviations from RMT…
While the notion of quantum chaos is tied to random matrix spectral correlations, also eigenstate properties in chaotic systems are often assumed to be described by random matrix theory. Analytic insights into eigenstate correlations can be…
Models of disorder with a direction (constant imaginary vector-potential) are considered. These non-Hermitian models can appear as a result of computation for models of statistical physics using transfer matrix technique or describe…
We analyze an approach aiming at determining statistical properties of spectra of time-periodic quantum chaotic system based on the parameter dynamics of their quasienergies. In particular we show that application of the methods of…
We use semiclassical methods to evaluate the spectral two-point correlation function of quantum chaotic systems with discrete geometrical symmetries. The energy spectra of these systems can be divided into subspectra that are associated to…
A method of resummation of infinite series of perturbation theory diagrams is applied for studying the properties of random band matrices. The topological classification of Feynman diagrams, which was actively used in last years for matrix…
The concept of concurrence is researched to characterize the dynamical behavior of the bipartite systems. The quantum kicked top model has great significance in the qubit systems and the chaotic properties of the entanglement. The…
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…
Random matrix theory allows one to deduce the eigenvalue spectrum of a large matrix given only statistical information about its elements. Such results provide insight into what factors contribute to the stability of complex dynamical…
The entanglement spectrum, i.e., the full distribution of Schmidt eigenvalues of the reduced density matrix, contains more information than the conventional entanglement entropy and has been studied recently in several many-particle…
The group symmetries inherent in quantum channels often make them tractable and applicable to various problems in quantum information theory. In this paper, we introduce natural probability distributions for covariant quantum channels.…
We formulate gaussian and circular random-matrix models representing a coupled system consisting of an absorbing and an amplifying resonator, which are mutually related by a generalized time-reversal symmetry. Motivated by optical…
We present experimental and theoretical results for the fluctuation properties in the incomplete spectra of quantum systems with symplectic symmetry and a chaotic dynamics in the classical limit. To obtain theoretical predictions, we extend…
Entanglement plays an important role in quantum communication, algorithms, and error correction. Schmidt coefficients are correlated to the eigenvalues of the reduced density matrix. These eigenvalues are used in Von Neumann entropy to…
We use random matrix theory to study the spectrum of random geometric graphs, a fundamental model of spatial networks. Considering ensembles of random geometric graphs we look at short range correlations in the level spacings of the…
Correlation functions involving products and ratios of half-integer powers of characteristic polynomials of random matrices from the Gaussian Orthogonal Ensemble (GOE) frequently arise in applications of Random Matrix Theory (RMT) to…