Finite-Range Coulomb Gas Models of Banded Random Matrices and Quantum Kicked Rotors
arXiv:1710.00059 · doi:10.1103/PhysRevE.96.052211
Abstract
Dyson demonstrated an equivalence between infinite-range Coulomb gas models and classical random matrix ensembles for study of eigenvalue statistics. We introduce finite-range Coulomb gas (FRCG) models via a Brownian matrix process, and study them analytically and by Monte-Carlo simulations. These models yield new universality classes, and provide a theoretical framework for study of banded random matrices (BRM) and quantum kicked rotors (QKR). We demonstrate that, for a BRM of bandwidth b and a QKR of chaos parameter α, the appropriate FRCG model has the effective range d = (b^2)/N = (α^2)/N, for large N matrix dimensionality. As d increases, there is a transition from Poisson to classical random matrix statistics.