Exact solution of the nonlinear boson diffusion equation for gluon scattering

TL;DR

This paper presents an exact analytical solution to the nonlinear boson diffusion equation, modeling gluon scattering in heavy-ion collisions and estimating gluon-condensate formation over time.

Contribution

It provides the first exact solution to the NBDE with applications to gluon dynamics in relativistic heavy-ion collisions.

Findings

Analytical solution describes evolution towards Bose-Einstein equilibrium.

Estimates time-dependent gluon-condensate formation in Pb-Pb collisions.

Models inelastic and elastic collisions with constant transport coefficients.

Abstract

An exact analytical solution of the nonlinear boson diffusion equation (NBDE) is presented. It accounts for the time evolution towards the Bose-Einstein equilibrium distribution through inelastic and elastic collisions in case of constant transport coefficients. As a currently interesting application, gluon scattering in relativistic heavy-ion collisions is investigated. An estimate of time-dependent gluon-condensate formation in overoccupied systems through number-conserving elastic scatterings in Pb-Pb collisions at relativistic energies is given.