Holographic Brownian Motion and Time Scales in Strongly Coupled Plasmas

TL;DR

This paper investigates the dynamics of a heavy quark undergoing Brownian motion in a strongly coupled plasma using holographic duality, deriving a formula for the mean-free-path time and analyzing collision behavior.

Contribution

It introduces a holographic computation of the 4-point function for Brownian motion and relates it to mean-free-path time in strongly coupled plasmas, applying it to charged black holes.

Findings

Mean-free-path time is related to the 4-point function of the random force.

Holographic regularization of IR divergence yields a general formula.

Brownian particles collide with many plasma constituents simultaneously.

Abstract

We study Brownian motion of a heavy quark in field theory plasma in the AdS/CFT setup and discuss the time scales characterizing the interaction between the Brownian particle and plasma constituents. In particular, the mean-free-path time is related to the connected 4-point function of the random force felt by the Brownian particle. By holographically computing the 4-point function and regularizing the IR divergence appearing in the computation, we write down a general formula for the mean-free-path time, and apply it to the STU black hole which corresponds to plasma charged under three U(1) R-charges. The result indicates that the Brownian particle collides with many plasma constituents simultaneously.