Quantum Separation of Variables and Multi-component Dyson Brownian Motion

Igor Loutsenko

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arXiv · cond-mat/0408364

Quantum Separation of Variables and Multi-component Dyson Brownian Motion

Igor Loutsenko

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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 $ Q_1 $ and $ Q_2 $, such that $ βQ_1 Q_2 = 1 $ on the line or circle, where $β$ is an inverse temperature of the gas.

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cond-mat.other cond-mat.mes-hall cond-mat.stat-mech hep-th math-ph math.MP math.PR nlin.CD nlin.SI

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Igor Loutsenko. 2005-03-22. Quantum Separation of Variables and Multi-component Dyson Brownian Motion. https://arxiv.org/abs/cond-mat/0408364

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