Quantum Separation of Variables and Multi-component Dyson Brownian Motion
Igor Loutsenko
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 Q1 and Q2 , such that βQ1 Q2 = 1 on the line or circle, where β is an inverse temperature of the gas.
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