Far-from-equilibrium attractors in kinetic theory for a mixture of quark and gluon fluids

TL;DR

This paper presents an exact solution to a kinetic theory model of quark-gluon fluids, revealing the existence of far-from-equilibrium attractors that influence the system's evolution before hydrodynamics becomes applicable.

Contribution

It introduces a novel exact solution to the RTA-Boltzmann equation for coupled quark and gluon fluids, including chemical non-equilibrium and different collision rates, and identifies early-time attractors for distribution moments.

Findings

Existence of early and late-time attractors for distribution moments.

Attractors emerge before hydrodynamic regime is reached.

Analysis of shear viscosity, entropy density, and entropy production.

Abstract

We exactly solve an RTA-Boltzmann equation that describes the dynamics of coupled massless quark and gluon fluids undergoing transversally homogeneous longitudinal boost-invariant expansion. We include a fugacity parameter that allows quarks to be out of chemical equilibrium and we account for the different collision rates of quarks and gluons, which are related by Casimir scaling. Based on these assumptions, we numerically determine the evolution of a large set of moments of the quark and gluon distribution functions and reconstruct their entire distribution functions. We find that both late and early-time attractors exist for all moments of the distribution functions containing more than one power of the squared longitudinal momentum. These attractors emerge long before the system reaches the regime where hydrodynamic approximations apply. In addition, we discuss how the shear viscous corrections and entropy density of the fluid mixture evolve and consider the properties of their respective attractors. Finally, the entropy production is also investigated for different initial values of momentum anisotropy and quark abundance.