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