Numerical solution of the nonlinear boson diffusion equation for gluons

TL;DR

This paper develops a numerical approach to solve the nonlinear boson diffusion equation with energy-dependent coefficients, modeling gluon thermalization in heavy-ion collisions and exploring gluon-condensate formation.

Contribution

It introduces a numerical method for the nonlinear boson diffusion equation with realistic energy-dependent coefficients, extending previous exact solutions.

Findings

Numerical solutions match analytical results for constant coefficients.

Energy-dependent coefficients influence thermalization dynamics.

Implications for gluon-condensate formation in overoccupied systems.

Abstract

The nonlinear boson diffusion equation is taken as a basis to account for the fast thermalization of gluons in the initial stages of relativistic heavy-ion collisions. For constant drift and diffusion coefficients with schematic initial conditions, this equation has previously been solved exactly. In order to achieve a more realistic time evolution towards thermalization, energy-dependent transport coefficients are introduced, requiring numerical solutions of the nonlinear equation. Their accuracy is tested against the exact analytical results in the limit of constant coefficients. The consequences for transient gluon-condensate formation through elastic scatterings in overoccupied systems are discussed.