Exact solution of the (0+1)-dimensional Boltzmann equation for massive Bose-Einstein and Fermi-Dirac gases

TL;DR

This paper derives an exact solution to the (0+1)-dimensional Boltzmann equation for massive quantum gases, showing quantum statistics have minimal impact on thermodynamics and shear viscosity but are significant for bulk viscosity.

Contribution

It provides the first exact solution for the (0+1)-dimensional Boltzmann equation for massive Bose-Einstein and Fermi-Dirac gases, highlighting the effects of quantum statistics.

Findings

Quantum effects are negligible for thermodynamic functions.

Quantum statistics minimally influence shear viscosity.

Quantum effects are significant for bulk viscosity.

Abstract

We present the exact solution of the (0+1)-dimensional Boltzmann equation for massive Bose-Einstein and Fermi-Dirac gases. For the initial conditions used typically in ultra-relativistic heavy-ion collisions, we find that the effects of quantum statistics are very small for thermodynamics-like functions such as the effective temperature, energy density or transverse and longitudinal pressures. Similarly, the inclusion of quantum statistics affects very little the shear viscosity. On the other hand, the quantum statistics becomes important for description of the phenomena connected with the bulk viscosity.