Holographic Brownian Motion in Two Dimensional Rotating Fluid

TL;DR

This paper investigates holographic Brownian motion of a heavy quark in a rotating plasma modeled by BTZ black hole, analyzing both non-relativistic and relativistic regimes to connect string fluctuations with plasma properties.

Contribution

It introduces a holographic approach to study Brownian motion in rotating plasma, including the concept of terminal angular velocity and low-frequency force correlator analysis.

Findings

Displacement squared behaves as in non-relativistic Brownian motion.

Relativistic case analyzed via low-frequency force correlator.

Connects string fluctuation dynamics with plasma temperature and friction.

Abstract

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.