Finite-range Coulomb gas models. II. Applications to quantum kicked rotors and banded random matrices

In part I of this two-stage exposition [Pandey, Kumar, and Puri, preceding paper, Phys. Rev. E 101, 022217 (2020)10.1103/PhysRevE.101.022217], we introduced finite-range Coulomb gas (FRCG) models, and developed an integral-equation framework for their study. We obtained exact analytical results for d=0,1,2, where d denotes the range of eigenvalue interaction. We found that the integral-equation framework was not analytically tractable for higher values of d. In this paper, we develop a Monte Carlo (MC) technique to study FRCG models. Our MC simulations provide a solution of FRCG models for arbitrary d. We show that, as d increases, there is a transition from Poisson to Wigner-Dyson classical random matrix statistics. Thus FRCG models provide a route for transition from Poisson to Wigner-Dyson statistics. The analytical formulation obtained in part I, and MC techniques developed in this paper, are used to study banded random matrices (BRMs) and quantum kicked rotors (QKRs). We demonstrate that, for a BRM of bandwidth b and a QKR of chaos parameter α, the appropriate FRCG model has range d=b^{2}/N=α^{2}/N, for N→∞. Here, N is the dimensionality of the matrix in the BRM, and the evolution operator matrix in the QKR.