Generalized Kinetic Equations for a System of Interacting Atoms and Photons: Theory and Simulations

TL;DR

This paper develops generalized kinetic equations for systems of interacting atoms and photons with broad statistical assumptions, analyzes their equilibrium and stability, and performs numerical simulations of perturbed systems.

Contribution

It introduces a novel framework of generalized kinetic equations for atom-photon systems and explores their equilibrium and stability properties.

Findings

Equilibrium states are characterized and their stability analyzed.

Numerical simulations show system response to external perturbations.

The model applies to photons in gases and atoms in radiation backgrounds.

Abstract

In the present paper we introduce generalized kinetic equations describing the dynamics of a system of interacting gas and photons obeying to a very general statistics. In the space homogeneous case we study the equilibrium state of the system and investigate its stability by means of Lyapounov's theory. Two physically relevant situations are discussed in details: photons in a background gas and atoms in a background radiation. After having dropped the statistics generalization for atoms but keeping the statistics generalization for photons, in the zero order Chapmann-Enskog approximation, we present two numerical simulations where the system, initially at equilibrium, is perturbed by an external isotropic Dirac's delta and by a constant source of photons.