Holographic Brownian Motion in Magnetic Environments

TL;DR

This paper investigates the behavior of a heavy quark in strongly-coupled magnetic and non-commutative environments using gauge/gravity duality, revealing new features in Brownian motion and transport properties.

Contribution

It introduces a Langevin equation for non-commutative systems and analyzes the effects of magnetic fields and non-commutativity on quark dynamics and viscosity.

Findings

Fluctuations along non-commutative directions are correlated.

Viscosity is reduced compared to the commutative case.

Fluctuation-dissipation theorem remains valid with non-commutativity.

Abstract

Using the gauge/gravity correspondence, we study the dynamics of a heavy quark in two strongly-coupled systems at finite temperature: Super-Yang-Mills in the presence of a magnetic field and non-commutative Super-Yang-Mills. In the former, our results agree qualitatively with the expected behavior from weakly-coupled theories. In the latter, we propose a Langevin equation that accounts for the effects of non-commutativity and we find new interesting features. The equation resembles the structure of Brownian motion in the presence of a magnetic field and implies that the fluctuations along non-commutative directions are correlated. Moreover, our results show that the viscosity is smaller than the commutative case and that the diffusion properties of the quark are unaffected by non-commutativity. Finally, we compute the random force autocorrelator and verify that the fluctuation-dissipation theorem holds in the presence of non-commutativity.