A BROWNIAN-MOTION MODEL FOR THE PARAMETER DEPENDENCE OF MATRIX-ELEMENTS

We introduce a Brownian motion model for the parametric evolution of e igenstates of a complex quantum system, modelled by a random matrix. T he model is analogous to Dyson's model for the evolution of the eigenv alues. We use this approach to analyse correlation functions describin g the parameter dependence of diagonal and off-diagonal matrix element s of a generic operator. In the case of diagonal matrix elements, we c ompare our results with a semiclassical approach, which relates sums o f matrix elements to periodic classical orbits. For systems with a cha otic classical limit, the semiclassical correlation function agrees ex actly with the random matrix theory.