Monte-Carlo approach to particle-field interactions and the kinetics of the chiral phase transition

TL;DR

This paper presents a Monte-Carlo method to simulate particle-field interactions during the chiral phase transition, capturing fluctuations and dynamics more accurately than traditional stochastic approaches.

Contribution

It introduces a Monte-Carlo semiclassical approach combining mean-field meson dynamics with test-particle quark interactions, respecting quantum field theory rules.

Findings

Successfully models fluctuations without ad hoc assumptions.

Accurately describes quark-antiquark annihilation and meson decay processes.

Provides insights into the kinetics of the chiral phase transition.

Abstract

The kinetics of the chiral phase transition is studied within a linear quark-meson-$\sigma$ model, using a Monte-Carlo approach to semiclassical particle-field dynamics. The meson fields are described on the mean-field level and quarks and antiquarks as ensembles of test particles. Collisions between quarks and antiquarks as well as the $q\overline{q}$ annihilation to $\sigma$ mesons and the decay of $\sigma$ mesons is treated, using the corresponding transition-matrix elements from the underlying quantum field theory, obeying strictly the rule of detailed balance and energy-momentum conservation. The approach allows to study fluctuations without making ad hoc assumptions concerning the statistical nature of the random process as necessary in Langevin-Fokker-Planck frameworks.