Abstract
We use the identity of the canonical distribution for Dyson's Coulomb gas on the unit circle for inverse temperatures β= 1, 2, and 4 with the joint distribution of eigenphases for the three circular ensembles of unitary random matrices (orthogonal, unitary, and symplectic, respectively), to investigate their statistical spectral properties by Monte Carlo simulation of the Coulomb gas. We extend the study to intermediate temperatures, and test a conjecture for the β-dependence of the nearest-neighbor spacing distribution. We propose to use this conjecture to determine the “true” degree of eigenvalue repulsion β for spectra of quantum dynamics with completely chaotic classical limit, which cannot be described by random matrix theory because of dynamic localization.
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