Quantum Separation of Variables and Multi-component Dyson Brownian Motion
arXiv:cond-mat/0408364
Abstract
A new type of Coulomb gas is defined, consisting of arbitrary numbers of point charges of two species executing Brownian motions under the influence of their mutual electrostatic repulsion. Being a generalization of a model of identical particles introduced by Dyson as a dynamical system describing non-equilibrium state of various random matrix ensembles, our system gives an exact mathematical description of the Brownian motion of charges of magnitudes and , such that on the line or circle, where is an inverse temperature of the gas.
The paper has been withdrawn by the author