Relativistic Boltzmann transport approach with Bose-Einstein statistics and the onset of gluon condensation

Abstract

We study the evolution of a gluon system under conditions of density and temperature similar to those explored in the early stage of ultra-relativistic heavy-ion collisions. We first describe the implementation of Relativistic Boltzmann-Nordheim (RBN) transport approach that includes in the collision integral the quantum effects of Bose-Einstein Statistics. Then, we describe the evolution of a spatially uniform gluon system in a box under elastic collisions solving the RBN for various initial conditions. We discuss the critical phase-space density that leads to the onset of a Bose-Einstein condensate (BEC) and the time scale for this process to occur. In particular, thanks to the fact that RBN allows to relax the small angle approximation, we study the effect at both small and large screening mass $ m_{D} $. For small $ m_{D}\ll T $ we see that our solution of RBN is in agreement with the recent extensive studies within a Fokker-Planck scheme in small angle approximation. For the same total cross section but with large $ m_{D}\simeq 2\, T $ (large angle scatterings), we see a significant time speed-up of the onset of BEC respect to small $m_{D}\ll T$. This further strengthen the possibility that at least a transient BEC is formed in the early stage of ultra-relativistic heavy-ion collisions.