Comparison of Boltzmann Kinetics with Quantum Dynamics for a Chiral Yukawa Model Far From Equilibrium

TL;DR

This paper compares Boltzmann and Kadanoff-Baym equations within a chiral Yukawa model, revealing significant qualitative and quantitative differences, especially in late-time universality and time scale separation, highlighting limitations of Boltzmann equations.

Contribution

It provides a detailed numerical comparison between Boltzmann and Kadanoff-Baym equations in a quantum field theory, illustrating their differences in describing non-equilibrium dynamics.

Findings

Significant quantitative differences between the equations.

Boltzmann equations lack late-time universality seen in Kadanoff-Baym.

Kadanoff-Baym equations separate kinetic and chemical equilibration time scales.

Abstract

Boltzmann equations are often used to describe the non-equilibrium time-evolution of many-body systems in particle physics. Prominent examples are the computation of the baryon asymmetry of the universe and the evolution of the quark-gluon plasma after a relativistic heavy ion collision. However, Boltzmann equations are only a classical approximation of the quantum thermalization process, which is described by so-called Kadanoff-Baym equations. This raises the question how reliable Boltzmann equations are as approximations to the complete Kadanoff-Baym equations. Therefore, we present in this article a detailed comparison of Boltzmann and Kadanoff-Baym equations in the framework of a chirally invariant Yukawa-type quantum field theory including fermions and scalars. The obtained numerical results reveal significant differences between both types of equations. Apart from quantitative differences, on a qualitative level the late-time universality respected by Kadanoff-Baym equations is severely restricted in the case of Boltzmann equations. Furthermore, Kadanoff-Baym equations strongly separate the time scales between kinetic and chemical equilibration. In contrast to this standard Boltzmann equations cannot describe the process of quantum-chemical equilibration, and consequently also cannot feature the above separation of time scales.