Statistics of thermalization in Bjorken Flow

TL;DR

This study uses numerical simulations of Bjorken flow in strongly coupled ${ m f N}=4$ supersymmetric Yang-Mills theory to investigate thermalization dynamics, revealing early thermalization around proper time 0.6 and correlations with initial entropy.

Contribution

It provides the first systematic numerical analysis of thermalization in Bjorken flow within AdS/CFT, highlighting the universality and entropy dependence of early thermalization.

Findings

Early thermalization occurs around proper time 0.6 in units of inverse temperature.

The rate of hydrodynamic cooling correlates linearly with initial entropy.

Entropy production during hydrodynamics is significant despite low viscosity-to-entropy ratio.

Abstract

The apparent early thermalization of quark-gluon plasma produced at RHIC and LHC has motivated a number of studies of strongly coupled ${\mathcal N}=4$ supersymmetric Yang-Mills theory using the AdS/CFT correspondence. Here we present the results of numerical simulations of Bjorken flow aimed at establishing typical features of the dynamics. This is done by evolving a large number of far from equilibrium initial states well into the hydrodynamic regime. The results strongly suggest that early thermalization is generic in this theory, taking place at proper times around $0.6$ in units of inverse local temperature. We also find that the scale which determines the rate of hydrodynamic cooling is linearly correlated with the entropy of initial states defined by the area of the apparent horizon in the dual geometry. Our results also suggest that entropy production during the hydrodynamic stage of evolution is not negligible despite the low value of $\eta/s$.