Quantization of the Kicked Rotator With Dissipation

Abstract

The effect of dissipation on a quantum system exhibiting chaos in its classical limit is studied by coupling the kicked quantum rotator to a reservoir with angular momentum exchange. A master equation is derived which maps the density matrix from one kick to the subsequent one. The limits of h→0 and of vanishing dissipation reproduce the classical kicked damped rotator and the kicked quantum rotator, respectively. In the semi-classical limit the quantum map reduces to a classical map with quantum mechanically determined classical noise terms. For sufficiently small dissipation quantum mechanical interference effects render the Wigner distribution negative in some parts of phase space and prevent its interpretation in classical terms.