Statistical aspects of dissipation by Landau-Zener transitions

Considers the effect of slowly varying the parameters Xi of a finite-sized quantum mechanical system. The system is excited to higher energies by Landau-Zener transitions at avoided crossing; since this increases the energy of the system, it has the effect of dissipation of the driving motion. The rate of dissipation depends on the level spacing distribution of the system. When the spectral statistics are those of the Gaussian unitary ensemble, the rate of dissipation is proportional to Xi2, i.e. there is viscous or ohmic damping. When the spectral statistics are of those of the Gaussian orthogonal ensemble, the rate of dissipation is proportional to Xi32/.