Population dynamics of a Bose gas near saturation

At low density a gas of bosons achieves a classical equilibrium distribution of energies within just a few characteristic scattering times. At sufficiently high densities, stimulated emission comes into play, increasing the rate of scattering into low-energy states. This results in the well-known Bose-Einstein equilibrium distribution. In this paper we show---by numerical calculation---that for a weakly interacting Bose gas the number of characteristic scattering times required to achieve an equilibrium Bose-Einstein distribution increases with increasing degeneracy. However, we find that the characteristic scattering time for the degenerate gas is significantly shortened by the stimulated emission, with the net result that equilibration times may be comparable to the classical case. These results have a bearing on recent experiments that produced degenerate Bose distributions of excitons. A basic question from these experiments is whether Bose-Einstein condensation can occur within the particle lifetime. Our calculations indicate that condensation may take place. We also show in this paper that exciton-phonon interactions will not significantly increase the rate of approach to condensation.