Title: Finite-Range Coulomb Gas Models of Banded Random Matrices and Quantum Kicked Rotors,
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 {\alpha}, the
appropriate FRCG model has the effective range d = (b^2)/N = ({\alpha}^2)/N,
for large N matrix dimensionality. As d increases, there is a transition from
Poisson to classical random matrix statistics.