Value statistics of chaotic Wigner function

Abstract

We study Wigner function value statistics of classically chaotic quantum maps on compact 2D phase space. We show that the Wigner function statistics of a random state is a Gaussian, with the mean value becoming negligible compared to the width in the semi-classical limit. Using numerical example of quantized sawtooth map we demonstrate that the relaxation of time-dependent Wigner function statistics, starting from a coherent initial state, takes place on a logarithmically short log (hbar) time scale.

5 pages, 4 figures (4 .eps files); for the proceedings of the 5th International Summer School/Conference in Maribor 2002: Let's Face Chaos through Nonlinear Dynamics