Exact solutions of the (0+1)-dimensional kinetic equation in the relaxation time approximation

TL;DR

This paper derives exact solutions for a (0+1)-dimensional kinetic equation with massive particles, highlighting the importance of quantum statistics and shear-bulk coupling effects in hydrodynamic descriptions.

Contribution

It provides the first exact solutions including quantum statistics for the kinetic equation in this context, emphasizing the limitations of traditional hydrodynamics.

Findings

Classical statistics neglect shear-bulk coupling

Quantum statistics significantly affect bulk viscosity effects

Exact solutions improve understanding of kinetic-hydrodynamic correspondence

Abstract

We present exact solutions of the (0+1)-dimensional kinetic equation for a massive gas in the relaxation time approximation. At first, we analyse the case of classical statistics and argue that the traditional second-order hydrodynamics misses the shear-bulk coupling. In the next step, we include Bose-Einstein and Fermi-Dirac statistics in the calculations and show that they are important for description of the effects connected with bulk viscosity.