Equilibration in fermionic systems

TL;DR

This paper studies how finite fermion systems evolve towards equilibrium using analytical solutions of a nonlinear diffusion equation, with applications to hadron and quark systems at various energy scales.

Contribution

It provides closed-form solutions to a fermionic diffusion equation and applies them to different energy regimes, including particle-antiparticle production.

Findings

Exact solutions for fermionic diffusion equations derived.

Application to low-energy hadron systems and high-energy quark systems.

Discussion of conservation laws including antiparticle creation.

Abstract

The time evolution of a finite fermion system towards statistical equilibrium is investigated using analytical solutions of a nonlinear partial differential equation that had been derived earlier from the Boltzmann collision term. The solutions of this fermionic diffusion equation are rederived in closed form, evaluated exactly for simplified initial conditions, and applied to hadron systems at low energies in the MeV-range, as well as to quark systems at relativistic energies in the TeV-range where antiparticle production is abundant. Conservation laws for particle number including created antiparticles, and for the energy are discussed.