A RANDOM-MATRIX MODEL FOR THE NONPERTURBATIVE RESPONSE OF A COMPLEX QUANTUM SYSTEM

We consider the dynamics of a complex quantum system subjected to a ti me-dependent perturbation, using a random matrix approach. The dynamic s are described by a diffusion constant characterizing the spread of t he probability distribution for the energy of a particle which was ini tially in an eigenstate. We discuss a system of stochastic differentia l equations which are a model for the Schrodinger equation written in an adiabatic basis. We examine the dependence of the diffusion constan t D on the rate of change of the perturbation parameter, X. Our analys is indicates that D alpha X(2), in agreement with the Kubo formula, up to a critical velocity X; for faster perturbations, the rate of diff usion is lower than that predicted from the Kubo formula. These predic tions are confirmed in numerical experiments on a banded random matrix model. The implications of this result are discussed.