Dissipative chaotic quantum maps: Expectation values, correlation functions and the invariant state
FB7, Universität-GHS Essen, 45117 Essen, Germany
Published online: 15 July 2000
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.
PACS: 03.65.Sq – Semiclassical theories and applications / 05.45.Mt – Semiclassical chaos ("quantum chaos")
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2000