Spectral statistics in semiclassical random-matrix ensembles.

Abstract

A novel random-matrix ensemble is introduced which mimics the global structure inherent in the Hamiltonian matrices of autonomous, ergodic systems. Changes in its parameters induce a transition between a Poisson and a Wigner distribution for the level spacings, {ital P}({ital s}). The intermediate distributions are uniquely determined by a single scaling variable. Semiclassical constraints force the ensemble to be in a regime with Wigner {ital P}({ital s}) for systems with more than two freedoms.