Statistical kinetic treatment of relativistic binary collisions

TL;DR

This paper develops a relativistically consistent Monte Carlo method for binary collisions, ensuring physically accurate results and correct equilibrium distributions in relativistic particle systems.

Contribution

It introduces a new sampling procedure for relativistic collisions that corrects nonrelativistic methods and is validated through three-dimensional simulations.

Findings

Nonrelativistic sampling yields incorrect equilibrium distributions.

The proposed method ensures physically meaningful relativistic collision results.

Validated with 3D Monte Carlo simulations.

Abstract

In particle-based algorithms, the effect of binary collisions is commonly described in a statistical way, using Monte Carlo techniques. It is shown that, in the relativistic regime, stringent constraints should be considered on the sampling of particle pairs for collision, which are critical to ensure physically meaningful results, and that nonrelativistic sampling criteria (e.g., uniform random pairing) yield qualitatively wrong results, including equilibrium distributions that differ from the theoretical J\"uttner distribution. A general procedure for relativistically consistent algorithms is provided, and verified with three-dimensional Monte Carlo simulations, thus opening the way to the numerical exploration of the statistical properties of collisional relativistic systems.