# Local equilibration of fermions and bosons

## TL;DR

This paper introduces a nonlinear diffusion model for local kinetic equilibration of fermions and bosons, providing exact solutions and a realistic alternative to the relaxation-time approximation, with applications in heavy-ion collisions and cold quantum gases.

## Contribution

It presents an exact solution to a nonlinear diffusion equation modeling local equilibration, incorporating proper quantum statistics and replacing the relaxation-time approximation.

## Key findings

- Model reproduces Fermi-Dirac and Bose-Einstein equilibrium limits.
- Applicable to quark-gluon plasma initial stages in heavy-ion collisions.
- Relevant for cold quantum gases at low energies.

## Abstract

Local kinetic equilibration is a prerequisite for hydrodynamics to be valid. Here it is described through a nonlinear diffusion equation for finite systems of fermions and bosons. The model is solved exactly for constant transport coefficients in both cases. It has the proper Fermi-Dirac and Bose-Einstein equilibrium limits and can replace the relaxation-time approximation (RTA). The microscopic transport coefficients are determined through the macroscopic variables temperature and local equilibration time. Applications to the transverse energy of quarks and gluons in the initial stages of central relativistic heavy-ion collisions, and to bosonic and fermionic atoms at low energies appropriate for cold quantum gases are discussed.