Relativistic quantum transport coefficients for second-order viscous hydrodynamics

TL;DR

This paper derives relativistic quantum transport coefficients for second-order viscous hydrodynamics using various statistical distributions and approximation methods, comparing their accuracy against exact solutions in a simplified expansion scenario.

Contribution

It provides a detailed comparison of transport coefficients derived via Grad's 14-moment and Chapman-Enskog methods for different quantum statistics, highlighting improved accuracy of Chapman-Enskog.

Findings

Chapman-Enskog method yields better agreement with exact solutions.

Transport coefficients depend on quantum statistics and approximation method.

Results improve modeling of relativistic viscous fluids.

Abstract

We express the transport coefficients appearing in the second-order evolution equations for bulk viscous pressure and shear stress tensor using Bose-Einstein, Boltzmann, and Fermi-Dirac statistics for the equilibrium distribution function and Grad's 14-moment approximation as well as the method of Chapman-Enskog expansion for the non-equilibrium part. Specializing to the case of transversally homogeneous and boost-invariant longitudinal expansion of the viscous medium, we compare the results obtained using the above methods with those obtained from the exact solution of the massive 0+1d relativistic Boltzmann equation in the relaxation-time approximation. We show that compared to the 14-moment approximation, the hydrodynamic transport coefficients obtained by employing the Chapman-Enskog method leads to better agreement with the exact solution of the relativistic Boltzmann equation.