Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5374992 | Chemical Physics | 2010 | 6 Pages |
Abstract
We consider Brownian random walks of infinitely large matrices using the tools of free random variables calculus. We establish relations between stochastic evolution of hermitian and unitary ensembles. We point out that matrix-valued diffusion equation develops non-linear terms, responsible for such phenomena as shock-waves. We comment the connection between unitary matrix diffusion and two-dimensional Yang-Mills theory. Finally, we speculate on application of string model techniques to the problem of quantum transport, where infinite products of pseudounitary matrices play the major role.
Keywords
Related Topics
Physical Sciences and Engineering
Chemistry
Physical and Theoretical Chemistry
Authors
Ewa Gudowska-Nowak, Romuald Janik, Jerzy Jurkiewicz, Maciej A. Nowak, Waldemar Wieczorek,