Eur. Phys. J. D 11, 3-12 (2000)
https://doi.org/10.1007/s100530070099

Dissipative chaotic quantum maps: Expectation values, correlation functions and the invariant state

FB7, Universität-GHS Essen, 45117 Essen, Germany

Received: 7 October 1999
Published online: 15 July 2000

Abstract

I investigate the propagator of the Wigner function for a dissipative chaotic quantum map. I show that a small amount of dissipation reduces the propagator of sufficiently smooth Wigner functions to its classical counterpart, the Frobenius-Perron operator, if . Several consequences arise: the Wigner transform of the invariant density matrix is a smeared out version of the classical strange attractor; time dependent expectation values and correlation functions of observables can be evaluated via hybrid quantum-classical formulae in which the quantum character enters only via the initial Wigner function. If a classical phase-space distribution is chosen for the latter or if the map is iterated sufficiently many times the formulae become entirely classical, and powerful classical trace formulae apply.