Quantum Separation of Variables and Multi-component Dyson Brownian Motion

Details Quantum Separation of Variables and Multi-component Dyson Brownian Motion Quantum Separation of Variables and Multi-component Dyson Brownian Motion

2004-08-16

arxiv.org/abs/cond-mat/0408364v2

Physics

Condensed Matter

Other Condensed Matter

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Scientific paper

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 $ \beta Q_1 Q_2 = 1 $ on the line or circle, where $\beta$ is an inverse temperature of the gas.

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