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Finite-range Coulomb gas models of banded random matrices and quantum kicked rotors



Finite-range Coulomb gas models of banded random matrices and quantum kicked rotors



PhysicalReview.E96(5-1):052211



Dyson demonstrated an equivalence between infinite-range Coulomb gas models and classical random matrix ensembles for the 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 the study of 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 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.

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Accession: 065153260

Download citation: RISBibTeXText

PMID: 29347738

DOI: 10.1103/physreve.96.052211


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