Nonlinear diffusion of gluons

TL;DR

This paper models gluon thermalization in heavy-ion collisions as a nonlinear diffusion process in momentum space, deriving analytical solutions and comparing them with numerical QCD results.

Contribution

It introduces a nonlinear boson diffusion equation with analytical solutions to describe gluon thermalization in heavy-ion collisions.

Findings

Analytical solutions match numerical QCD results.

Time evolution of gluon systems toward thermal equilibrium.

Effective description of inelastic gluon scatterings.

Abstract

It is proposed to consider the fast thermalization of gluons in relativistic heavy-ion collisions as a diffusion process in momentum space. Closed-form analytical solutions of a nonlinear boson diffusion equation (NBDE) with constant drift and diffusion coefficients v, D and boundary conditions at the singularity are derived. The time evolution towards local central temperatures T< 600 MeV through inelastic gluon scatterings in heavy-ion collisions is calculated for under- and overoccupied systems in the full momentum range. The results are consistent with QCD-based numerical calculations for gluon thermalization via inelastic gluon collisions.