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 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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Cited by in corpus (8)

• Distribution of the ratio of two consecutive level spacings in orthogonal to unitary crossover ensembles
• Particles confined in arbitrary potentials with a class of finite-ranged interactions
• Finite-Range Coulomb Gas Models II: Applications to Quantum Kicked Rotors and Banded Random Matrices
• Finite-Range Coulomb Gas Models I: Some Analytical Results
• Spectral form factor and energy correlations in banded random matrices
• Efficient circular Dyson Brownian motion algorithm
• Anomalous energy correlations and spectral form factor in the nonergodic phase of the $\beta$-ensemble
• Enhancement in Breaking of Time-reversal Invariance in the Quantum Kicked Rotor