Weak and strong coupling limits of the Boltzmann equation in the relaxation-time approximation

TL;DR

This paper investigates how different momentum-dependent relaxation times in the Boltzmann equation affect transport coefficients, revealing connections to weak and strong coupling regimes and comparing with Grad's 14-moment method.

Contribution

It introduces a power law parametrization of relaxation time in the Boltzmann equation and analyzes its impact on transport coefficients and off-equilibrium corrections.

Findings

Linear ansatz corresponds to weak coupling regime.

Quadratic ansatz corresponds to strong coupling regime.

Off-equilibrium corrections match Grad's 14-moment method for massless particles.

Abstract

We consider a momentum dependent relaxation time for the Boltzmann equation in the relaxation time approximation. We employ a power law parametrization for the momentum dependence of the relaxation time, and calculate the shear and bulk viscosity, as well as, the charge and heat conductivity. We show, that for the two popular parametrizations, referred to as the linear and quadratic ansatz, one can obtain transport coefficients which corresponds to the weak and strong coupling regimes, respectively. We also show that, for a system of massless particles with vanishing chemical potential, the off-equilibrium corrections to the phase-space distribution function calculated with the quadratic ansatz are identical with those of the Grad's 14-moment method.