Exponential Approach to the Hydrodynamic Attractor in Yang-Mills Kinetic Theory

TL;DR

This paper investigates how the hydrodynamic attractor in Yang-Mills kinetic theory approaches equilibrium, revealing an exponential decay governed by the shear viscosity to entropy density ratio, using principal component analysis.

Contribution

It introduces a principal component analysis approach to characterize the hydrodynamic attractor and its approach in Yang-Mills kinetic theory with new insights into decay rates.

Findings

Late time approach is exponential across couplings.

The decay rate depends simply on shear viscosity to entropy density ratio.

A single principal component determines the energy scale of the attractor.

Abstract

We use principal component analysis to study the hydrodynamic attractor in Yang-Mills kinetic theory undergoing the Bjorken expansion with Color Glass Condensate initial conditions. The late time hydrodynamic attractor is characterized by a single principal component determining the overall energy scale. How it is reached is governed by the disappearance of single subleading principal component characterizing deviations of the pressure anisotropy, the screening mass and the scattering rate. We find that for wide range of couplings the approach to the hydrodynamic attractor at late times is well described by an exponential. Its decay rate dependence on the coupling turns out to translate into a simple dependence on the shear viscosity to entropy density ratio.