Phonon-assisted Boltzmann kinetics of a Bose gas: Generic solution for T⩽ T c

The relaxation kinetics of an ideal Bose gas coupled to a phonon bath at temperatures below or equal to the critical temperature ${\mathrm{T}}_{\mathrm{c}}$ is given within a unique scenario. During the first transient stage, which lasts a few characteristic scattering times, the initial distribution disappears. The following nonexponential relaxation towards a quantum degenerate equilibrium state with a Bose-Einstein condensate is a slow adiabatic process. For this second kinetic stage we find an analytic generic solution of the Boltzmann equation. The generic solution is independent of the initial distribution and completely defined by the ratio ${\mathrm{T}}_{\mathrm{c}}$/${\mathrm{T}}_{\mathrm{b}}$ of the critical and bath temperatures.