Dyson's Brownian motion and universal dynamics of quantum systems
Abstract
We establish a correspondence between the evolution of the distribution of eigenvalues of a N×N matrix subject to a random Gaussian perturbing matrix, and a Fokker-Planck equation postulated by Dyson. Within this model, we prove the equivalence conjectured by Altshuler and co-workers between the space-time correlations of the Sutherland-Calogero-Moser system in the thermodynamic limit and a set of two-variable correlations for disordered quantum systems calculated by them. Multiple variable correlation functions are, however, shown to be inequivalent for the two cases.
- Publication:
-
Physical Review Letters
- Pub Date:
- September 1993
- DOI:
- 10.1103/PhysRevLett.71.2106
- arXiv:
- arXiv:cond-mat/9306029
- Bibcode:
- 1993PhRvL..71.2106N
- Keywords:
-
- 71.25.-s;
- 05.45.+b;
- 73.20.Dx;
- Condensed Matter
- E-Print:
- 10 pages, revtex