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
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