Nonlinear diffusion of fermions and bosons

TL;DR

This paper introduces a nonlinear diffusion equation that models thermalization in fermionic and bosonic systems, providing exact solutions and analyzing local equilibration times relevant to heavy-ion collisions and ultracold atoms.

Contribution

It presents a novel nonlinear diffusion model with analytical solutions that describe thermalization processes in quantum many-body systems.

Findings

Fermi-Dirac and Bose-Einstein distributions are stationary solutions.

Exact time-dependent solutions are derived for constant transport coefficients.

Applications include thermalization in heavy-ion collisions and ultracold atomic gases.

Abstract

A nonlinear diffusion equation is proposed to account for thermalization in fermionic and bosonic systems through analytical solutions. For constant transport coefficients, exact time-dependent solutions are derived through nonlinear transformations, and the corresponding local equilibration times are deduced. Fermi-Dirac and Bose-Einstein distributions emerge as stationary solutions of the nonlinear equation. As examples, local thermalization of quarks and gluons in relativistic heavy-ion collisions, and of ultracold atoms including time-dependent Bose-Einstein condensate formation are discussed.