Relaxation of coherent states and two scaling laws of characteristic times in quantum chaos

The dynamics of coherent states is investigated for generic integrable and nearly integrable quantum mappings on the plane. An entropy in terms of Husimi distribution functions is employed to describe the decoherence process and to detect two characteristic time scales of dynamical quantum chaos. Expressions for the coherence time and for the relaxation time are given in terms of classical quantities, and a quantum asymmetry parameter, both time scales satisfying power laws in . Specifically, it turns out that the coherence time can delay to infinity, thus revealing the possibility of long lasting coherent quantum states. An exact lower bound and a dynamical upper bound for the entropy are presented, as well as the time evolution of the entropy up to the relaxation time. We argue that the results should hold for generic integrable and nearly integrable quantum systems of one degree of freedom. Also, the Husimi time evolution operator is derived for confining potentials