Stochastic trailing string and Langevin dynamics from AdS/CFT

TL;DR

This paper derives Langevin equations for a relativistic heavy quark in strongly-coupled plasma using AdS/CFT, revealing non-thermal fluctuations originating from the string world-sheet horizon and providing estimates for drag and momentum broadening.

Contribution

It introduces a novel derivation of Langevin dynamics from gauge/string duality, highlighting the non-thermal origin of fluctuations and offering physical insights into quark-medium interactions.

Findings

Stochasticity originates at the string world-sheet horizon.

Fluctuations are non-thermal and do not obey Einstein relation.

Provides estimates for drag force and momentum broadening coefficients.

Abstract

Using the gauge/string duality, we derive a set of Langevin equations describing the dynamics of a relativistic heavy quark moving with constant average speed through the strongly-coupled N=4 SYM plasma at finite temperature. We show that the stochasticity arises at the string world-sheet horizon, and thus is causally disconnected from the black hole horizon in the space-time metric. This hints at the non-thermal nature of the fluctuations, as further supported by the fact that the noise term and the drag force in the Langevin equations do not obey the Einstein relation. We propose a physical picture for the dynamics of the heavy quark in which dissipation and fluctuations are interpreted as medium-induced radiation and the associated quantum-mechanical fluctuations. This picture provides the right parametric estimates for the drag force and the (longitudinal and transverse) momentum broadening coefficients.