Far-from-equilibrium dynamics of a strongly coupled non-Abelian plasma with non-zero charge density or external magnetic field

John F Fuini,Laurence G Yaffe

doi:10.1007/jhep07(2015)116

John F Fuini, Laurence G Yaffe

Open Access

https://doi.org/10.1007/jhep07(2015)116

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Abstract

Using holography, we study the evolution of a spatially homogeneous, far from equilibrium, strongly coupled $$ \mathcal{N}=4 $$ supersymmetric Yang-Mills plasma with a non-zero charge density or a background magnetic field. This gauge theory problem corresponds, in the dual gravity description, to an initial value problem in Einstein-Maxwell theory with homogeneous but anisotropic initial conditions. We explore the dependence of the equilibration process on different aspects of the initial departure from equilibrium and, while controlling for these dependencies, examine how the equilibration dynamics are affected by the presence of a non-vanishing charge density or an external magnetic field. The equilibration dynamics are remarkably insensitive to the addition of even large chemical potentials or magnetic fields; the equilibration time is set primarily by the form of the initial departure from equilibrium. For initial deviations from equilibrium which are well localized in scale, we formulate a simple model for equilibration times which agrees quite well with our results.

Highlights

In this paper, we extend previous work on the dynamics of homogeneous but anisotropic N = 4 SYM plasma [7,8,9]
We explore the dependence of the equilibration process on different aspects of the initial departure from equilibrium and, while controlling for these dependencies, examine how the equilibration dynamics are affected by the presence of a non-vanishing charge density or an external magnetic field
The above results show that to a good level of accuracy: 1. the pressure anisotropy response is a linear functional of the initial anisotropy pulse profile; 2. the time course of the response, measured in units set by the energy density,27 is insensitive to the charge density or background magnetic field when the pulse profile and the energy density are held fixed; 3. the time course of the response, measured in units set by the equilibrium temperature, is insensitive to the charge density or background magnetic field when the pulse profile and equilibrium temperature are held fixed

Summary

Introduction

We examine the influence on the equilibration dynamics of a non-zero global U(1) charge density, or a background magnetic field Inclusion of these effects is motivated by the physics of relativistic heavy ion collisions [19,20,21]. When studying states with a non-zero charge density (but no background magnetic field) appropriate numerical methods for asymptotically AdS Einstein-Maxwell theory are immediate generalizations of methods which have previously been found to work well for pure gravity. The inclusion of a background magnetic field induces a trace anomaly in the dual quantum field theory which, in the gravitational description, manifests in the appearance of logarithmic terms in the near-boundary behavior of fields Such non-analytic terms degrade the performance of spectral methods, on which we rely, and necessitate careful attention to numerical issues.

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