Effectiveness of parton cascade in solving the relativistic Boltzmann equation in a box

TL;DR

This paper benchmarks the ZPC parton cascade against an exact solution of the relativistic Boltzmann equation, demonstrating high accuracy in modeling a homogeneous, massless gas with improved collision schemes.

Contribution

The study introduces generalized collision schemes that significantly enhance the accuracy of the ZPC parton cascade in solving the relativistic Boltzmann equation.

Findings

ZPC reproduces the time evolution of the distribution function with high accuracy.

Generalized collision schemes improve accuracy to better than 1%.

ZPC remains accurate even at high opacities where failure was expected.

Abstract

We benchmark the ZPC parton cascade with an exact analytical solution of the relativistic Boltzmann equation for a homogeneous and massless gas with a constant and isotropic elastic cross section. We measure the accuracy of ZPC with the relative mean deviation between its momentum distribution and the exact solution. We use two generalized collision schemes to further improve the accuracy of ZPC over the recent $t$-minimum collision scheme. We find that ZPC can reproduce very well the time evolution of the single-particle distribution function for the exact solution's initial condition, with one generalized collision scheme giving an accuracy better than $1\%$ for the momentum distribution at any time in all studied cases, including very high opacities where naively the parton cascade approach is expected to fail.