Kinetic description of Bose-Einstein condensation with test particle simulations

We present a kinetic description of Bose-Einstein condensation for particle systems being out of thermal equilibrium, which may happen for gluons produced in the early stage of ultra-relativistic heavy-ion collisions. The dynamics of bosons towards equilibrium is described by a Boltzmann equation including Bose factors. To solve the Boltzmann equation with the presence of a Bose-Einstein condensate we make further developments of the kinetic transport model BAMPS (Boltzmann Approach of MultiParton Scatterings). In this work we demonstrate the correct numerical implementations by comparing the final numerical results to the expected solutions at thermal equilibrium for systems with and without the presence of Bose-Einstein condensate. In addition, the onset of the condensation in an over-populated gluon system is studied in more details. We find that both expected power-law scalings denoted by the particle and energy cascade are observed in the calculated gluon distribution function at infrared and intermediate momentum regions, respectively. Also, the time evolution of the hard scale exhibits a power-law scaling in a time window, which indicates that the distribution function is approximately self-similar during that time.