Time-dependent random-matrix Hamiltonians: Quantum interference effects

Mikhail Skvortsov

Landau Institute for Theoretical Physics, Chernogolovka, Russia

It is well established that the energy level statistics in disordered mesoscopic samples is universal and can be described by random matrices of an appropriate symmetry. The random matrix theory studied in great detail provides complete information about the spectral statistics. However, much less is known about time-dependent random-matrix Hamiltonians, which appear in studying, e.g., a quantum dot subject to a time-dependent gate voltage.

We review recent progress in studying dynamics of time-dependent random-matrix Hamiltonians. In a semiclassical limit, the energy absorption rate can be calculated with the help of the Kubo formula. Quantum phenomena modify this result. We show that there are two type of interference effects. The first effect is controlled by the velocity of the perturbation and is responsible for the transition between Kubo and Landau-Zener regimes of dissipation. The second effect is operative for time-reentrant perturbations when dynamic localization in the energy space may take place. We demonstrate that these effects can be described on the same footing within the Keldysh sigma-model formalism.