Towards a full solution of relativistic Boltzmann equation for quark-gluon matter on GPUs

TL;DR

This paper presents a GPU-accelerated numerical framework for solving the relativistic Boltzmann equations in quark-gluon matter, enabling detailed simulation of its evolution towards thermal equilibrium.

Contribution

It introduces a GPU-based method including all relevant scattering processes for quarks and gluons, with a symmetrical sampling technique ensuring particle number conservation.

Findings

High-performance simulation of quark-gluon evolution.

Observation of gluon accumulation in the soft region.

Potential indication of gluon condensation.

Abstract

We have developed a numerical framework for a full solution of the relativistic Boltzmann equations for the quark-gluon matter using the multiple Graphics Processing Units (GPUs) on distributed clusters. Including all the $2 \to 2$ scattering processes of 3-flavor quarks and gluons, we compute the time evolution of distribution functions in both coordinate and momentum spaces for the cases of pure gluons, quarks and the mixture of quarks and gluons. By introducing a symmetrical sampling method on GPUs which ensures the particle number conservation, our framework is able to perform the space-time evolution of quark-gluon system towards thermal equilibrium with high performance. We also observe that the gluons naturally accumulate in the soft region at the early time, which may indicate the gluon condensation.