Holographic Brownian motion at finite density

TL;DR

This paper investigates the behavior of a heavy charged particle undergoing Brownian motion at finite density and near-zero temperature using holographic duality, focusing on the dynamics near extremal Reissner-Nordström black holes.

Contribution

It provides an analytical computation of the retarded Green's function for small frequencies in a holographic setup at finite density and near-zero temperature.

Findings

Derived the functional form of the retarded Green's function.

Analyzed dissipative behavior at low temperatures.

Connected holographic models to Brownian motion dynamics.

Abstract

Brownian motion of a heavy charged particle at zero and small (but finite) temperature is studied in presence of finite density. We are primarily interested in the dynamics at (near) zero temperature which is holographically described by motion of a fundamental string in an (near-) extremal Reissner-Nordstr$\ddot{\text{o}}$m black hole. We analytically compute the functional form of retarded Green's function for small frequencies and extract the dissipative behavior at and near zero temperature.