Driven chaotic mesoscopic systems, dissipation and decoherence

Driven quantum systems, described by Hamiltonian H(Q,P,x(t)) where x(t) is a time dependent parameter, are of interest in mesoscopic physics (quantum dots), as well as in nuclear, atomic and molecular physics. Such systems tend to absorb energy. This irreversible effect is known as dissipation. More generally, x may be a dynamical variable, where the total Hamiltonian is Ho(x,p) +H(Q, P; x). In such case the interaction of (x,p) with the environmental degrees of freedom (Q, P) leads to dephasing as well as to dissipation. It should be emphasized that even few (Q, P) degrees of freedom can serve as a miniature heat bath, provided they have chaotic dynamics. We shall introduce a general framework for the analysis of dissipation and dephasing, and we shall clarify the tight connection to recent studies of quantum irreversibility (also referred to as "Loschmidt echo" or as the "fidelity" of quantum computation). Specific model systems that will be presented are: particle in a box driven by moving a wall, and particle in a box/ring driven by electro-motive-force. These two examples are related to studies of nuclear friction and mesoscopic conductance. Specific issues to be discussed are the limitations of kinetic theory, the capabilities of linear response theory, and the manifestation of non-perturbative quantum-mechanical effects. In particular we shall explain that random matrix theory and the semiclassical theory lead to different non-perturbative limits.