Exact solution of the nonlinear boson diffusion equation for gluon scattering

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.