Homogeneous isotropization and equilibration of a strongly coupled plasma with a critical point

TL;DR

This paper uses holography to study how a strongly coupled plasma with a critical point isotropizes and thermalizes, revealing how relaxation times depend on proximity to the critical point and initial conditions.

Contribution

It provides new insights into the late-time isotropization and thermalization processes of a strongly coupled plasma near a critical point using holographic methods.

Findings

Isotropization time varies with chemical potential near the critical point.

Thermalization time always increases with chemical potential.

Late-time dynamics are robust across different initial conditions.

Abstract

We use holography to investigate the process of homogeneous isotropization and thermalization in a strongly coupled $\mathcal{N} = 4$ Super Yang-Mills plasma charged under a $U(1)$ subgroup of the global $SU(4)$ R-symmetry which features a critical point in its phase diagram. Isotropization dynamics at late times is affected by the critical point in agreement with the behavior of the characteristic relaxation time extracted from the analysis of the lowest non-hydrodynamic quasinormal mode in the $SO(3)$ quintuplet (external scalar) channel of the theory. In particular, the isotropization time may decrease or increase as the chemical potential increases depending on whether one is far or close enough to the critical point, respectively. On the other hand, the thermalization time associated with the equilibration of the scalar condensate, which happens only after the system has relaxed to a (nearly) isotropic state, is found to always increase with chemical potential in agreement with the characteristic relaxation time associated to the lowest non-hydrodynamic quasinormal mode in the $SO(3)$ singlet (dilaton) channel. These conclusions about the late dynamics of the system are robust in the sense that they hold for different initial conditions seeding the time evolution of the far-from-equilibrium plasma.