Holographic Brownian Motion in Two Dimensional Rotating Fluid

The Brownian motion of a heavy quark under a rotating plasma corresponds to BTZ black hole is studied using holographic method from string theory. The position of heavy quark is represented as the end of string at the boundary of BTZ black hole and the corresponding rotating plasma is one dimensional compact space. We requires the angular velocity of the string fluctuation to be equal to the ratio between inner horizon and outer horizon, called terminal angular velocity, which is related to the zero total force condition. We show the displacement square of this solution behaves as a Brownian particle in non-relativistic limit. For relativistic case, we argue that it is more appropriate to compute the leading order of low frequency limit of random-random force correlator. The Brownian motion relates this correlator with physical observables: effective mass of the Brownian particle, friction coefficient, and temperature of the plasma.