A random-matrix model for the non-perturbative response of a complex quantum system.

M Wilkinson, Elizabeth Austin

Research output: Contribution to journalArticlepeer-review

Abstract

We consider the dynamics of a complex quantum system subjected to a time-dependent perturbation, using a random matrix approach. The dynamics are described by a diffusion constant characterizing the spread of the probability distribution for the energy of a particle which was initially in an eigenstate.

We discuss a system of stochastic differential equations which are a model for the Schrodinger equation written in an adiabatic basis. We examine the dependence of the diffusion constant D on the rate of change of the perturbation parameter, X. Our analysis indicates that D alpha X(2), in agreement with the Kubo formula, up to a critical velocity X*; for faster perturbations, the rate of diffusion is lower than that predicted from the Kubo formula. These predictions are confirmed in numerical experiments on a banded random matrix model. The implications of this result are discussed.

Original languageEnglish
Pages (from-to)2277-2296
Number of pages20
JournalJournal of Physics A: Mathematical and General
VolumeA28
Issue number8
DOIs
Publication statusPublished - 21 Apr 1995

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