Properties of the Boltzmann equation in the classical approximation

2014/09/02 by Thomas Epelbaum, François Gelis, Francois Gelis +2
Engineering · Mathematics · Physics and Astronomy · #Boltzmann constant #Boltzmann equation #Boltzmann's entropy formula #Gas Dynamics and Kinetic Theory #High-Energy Particle Collisions Research #Mathematics #Nuclear reactor physics and engineering #Physics #Poisson–Boltzmann equation #Quantum mechanics #Statistical physics #Thermodynamics #hep-ph #nucl-th

paper · pdf · doi:10.1103/physrevd.90.125032

published as Phys. Rev. D 90, 125032 (2014) · 37 pages, 21 figures

arxiv created 2014/09/02 · openalex publication_date 2014/12/30 · arxiv updated 2015/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We study the Boltzmann equation with elastic pointlike scalar interactions in two different versions of the classical approximation. Although solving numerically the Boltzmann equation with the unapproximated collision term poses no problem, this allows one to study the effect of the ultraviolet cutoff in these approximations. This cutoff dependence in the classical approximations of the Boltzmann equation is closely related to the nonrenormalizability of the classical statistical approximation of the underlying quantum field theory. The kinetic theory setup that we consider here allows one to study in a much simpler way the dependence on the ultraviolet cutoff, since one also has access to the nonapproximated result for comparison.

Citations

• Universal attractor in a highly occupied non-Abelian plasma
• Quark production, Bose–Einstein condensates and thermalization of the quark–gluon plasma
• Statistical-Mechanical Theory of Irreversible Processes. I. General Theory and Simple Applications to Magnetic and Conduction Problems
• On the equivalence between the Boltzmann equation and classical field theory at large occupation numbers
• Theory of Many-Particle Systems. I
• The evolving Glasma
• Nonlinear amplification of instabilities with longitudinal expansion
• The Color Glass Condensate