Related papers: The spectrum of coupled random matrices
In the framework of a random matrix description of chaotic quantum scattering the positions of $S-$matrix poles are given by complex eigenvalues $Z_i$ of an effective non-Hermitian random-matrix Hamiltonian. We put forward a conjecture on…
We investigate bicomplex Hamiltonian systems in the framework of an analogous version of the Schrodinger equation. Since in such a setting three different types of conjugates of bicomplex numbers appear, each is found to define in a natural…
The physical aspects of partially coherent radiation interacting with deterministic non-Hermitian periodic materials remain largely unexplored in the statistical optics literature. Here, we consider the scattering of partially coherent…
We analyze complete spectra of the lattice Dirac operator in SU(2) gauge theory and demonstrate that the distribution of low-lying eigenvalues is described by random matrix theory. We present possible practical applications of this…
We present a robust analysis of the spectral fluctuations exhibited by the light meson spectrum. This analysis provides information about the degree of chaos in light mesons and may be useful to get some insight on the underlying…
Statistical properties of eigenvectors in non-Hermitian random matrix ensembles are discussed, with an emphasis on correlations between left and right eigenvectors. Two approaches are described. One is an exact calculation for Ginibre's…
The discrete autonomous/non-autonomous Toda equations and the discrete Lotka-Volterra system are important integrable discrete systems in fields such as mathematical physics, mathematical biology and statistical physics. They also have…
A simple non-Hermitean random matrix (RM) model is used to study the Glasgow method of finite-density lattice QCD. The zeros of the RM partition function are evaluated through an averaging procedure, involving the zeros of the RM…
The typicality approach and the Hilbert space averaging method as its technical manifestation are important concepts of quantum statistical mechanics. Extensively used for expectation values we extend them in this paper to transition…
We discuss spectral correlations in coarse-grained chaotic two-dimensional CFTs with large central charge. We study a partition function describing the dense part of the spectrum of primary states in a way that disentangles the chaotic…
The spectral properties of a multilevel atomic system interacting with multiple electromagnetic fields, a modified inverted-Y system, have been theoretically investigated. In this study, a numerical matrix propagation method has been…
We briefly review the random matrix theory for large N by N matrices viewed as free random variables in a context of stochastic diffusion. We establish a surprising link between the spectral properties of matrix-valued multiplicative…
It is known that hermitean random matrix ensembles can be identified with symmetric coset spaces of Lie groups, or else with tangent spaces of the same. This results in a classification of random matrix ensembles as well as applications in…
We propose to analyse the statistical properties of a sequence of vectors using the spectrum of the associated Gram matrix. Such sequences arise e.g. by the repeated action of a deterministic kicked quantum dynamics on an initial condition…
A symmetric doubly stochastic matrix A is said to be determined by its spectra if the only symmetric doubly stochastic matrices that are similar to A are of the form $P^TAP$ for some permutation matrix P. The problem of characterizing such…
In this short note we collect together known results on the use of Random Matrix Theory in lattice statistical mechanics. The purpose here is two fold. Firstly the RMT analysis provides an intrinsic characterization of integrability, and…
Parity-Time (PT) symmetric quantum mechanics is a complex extension of conventional Hermitian quantum mechanics in which physical observables possess a real eigenvalue spectrum. However, an experimental demonstration of the true quantum…
PT-symmetric systems can have a real spectrum even when their Hamiltonian is non-hermitian, but develop a complex spectrum when the degree of non-hermiticity increases. Here we utilize random-matrix theory to show that this spontaneous…
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…
We consider symmetric and Hermitian random matrices whose entries are independent and symmetric random variables with an arbitrary variance pattern. Under a novel Short-to-Long Mixing condition, which is sharp in the sense that it precludes…