Diffusion in an Expanding Plasma using AdS/CFT

TL;DR

This paper investigates the diffusion behavior of a heavy quark in an expanding strongly coupled plasma using AdS/CFT, revealing time-dependent diffusion constants and noise correlations.

Contribution

It introduces a novel approach to model heavy quark diffusion in an expanding plasma via AdS/CFT, incorporating time-dependent effects and Langevin dynamics.

Findings

Diffusion constant D(τ) approaches an adiabatic limit proportional to 1/T(τ).

Noise correlation scales as 1/T(τ), indicating temperature-dependent decoherence.

Energy loss exhibits Langevin-like behavior for MD>1.

Abstract

We consider the diffusion of a non-relativistic heavy quark of fixed mass M, in a one-dimensionally expanding and strongly coupled plasma using the AdS/CFT duality. The Green's function constructed around a static string embedded in a background with a moving horizon, is identified with the noise correlation function in a Langevin approach. The (electric) noise decorrelation is of order 1/T(\tau) while the velocity de-correlation is of order MD(\tau)/T(\tau). For MD>1, the diffusion regime is segregated and the energy loss is Langevin-like. The time dependent diffusion constant D(\tau) asymptotes its adiabatic limit 2/\pi\sqrt{\lambda} T(\tau) when \tau/\tau_0=(1/3\eta_0\tau_0)^3 where \eta_0 is the drag coefficient at the initial proper time \tau_0.