Quantum Dissipation due to the Interaction with Chaotic Degrees of Freedom and the Correspondence Principle

Both in atomic and in mesoscopic physics it is interesting to consider the energy time dependence of a parametrically driven chaotic system. We assume an Hamiltonian $H(Q,P;x(t\left)\right)$ where $x\left(t\right)=Vt$. The velocity $V$ is slow in the classical sense but not necessarily in the quantum-mechanical sense. The crossover (in time) from ballistic to diffusive energy spreading is studied. Dissipation is the associated irreversible growth of the average energy. It is found that a dimensionless velocity $v_{\mathrm{PR}}$ determines the nature of the dynamics, and controls the route towards quantal-classical correspondence. A perturbative regime and a nonperturbative semiclassical regime are distinguished.