DYSON BROWNIAN-MOTION AND UNIVERSAL DYNAMICS OF QUANTUM-SYSTEMS

We establish a correspondence between the evolution of the distributio n of eigenvalues of a N x N matrix subject to a random Gaussian pertur bing matrix, and a Fokker-Planck equation postulated by Dyson. Within this model, we prove the equivalence conjectured by Altshuler and co-w orkers between the space-time correlations of the Sutherland-Calogero- Moser system in the thermodynamic limit and a set of two-variable corr elations for disordered quantum systems calculated by them. Multiple v ariable correlation functions are, however, shown to be inequivalent f or the two cases.