Driven Systems (1996-2000)

Consider a driven which is described by a time-dependent Hamiltonian H(Q,P;X(t)). Such system absorbs energy.  This irreversible effect is known as dissipation. The driving also induces currents. Our aim is to develop a general theory for the energy absorption and for the induced transport. Our interest is not in open but rather in closed systems (no leads), hence quantum chaos considerations become essential. The ohmic nature of dissipation and the associated fluctuation-dissipation relation are studied within the framework of quantum mechanics. It turns out that there are three regimes in the theory: the adiabatic regime; the linear-response (Kubo) regime; and the non-perturbative regime. The mesoscopic Drude formula for electrical conductance, and the wall formula for nuclear friction, can be regarded as special cases of the general formulation of the dissipation problem. The research involves numerical studies. Of particular interest is the analysis of either "network" or "billiard" systems. An important issue is to understand the clash between random matrix theory and semiclassical methods.