Phonon-assisted relaxation kinetics of a degenerate bose gas

The relaxation kinetics of an ideal Bose gas coupled to a phonon thermostat at temperature T-b below or equal to the critical temperature T-c consists of an initial transient and the following adiabatic stage. The transient depends on the initial distribution of bosons at t = 0 and lasts a few characteristic scattering times. The following nonexponential relaxation towards a quantum degenerate equilibrium state with a Bose-Einstein (BE) condensate is a slow adiabatic process. We find a generic solution of the phonon-assisted Boltzmann kinetics at the adiabatic stage. This solution is completely defined by the ratio T-c/T-b. Here, one has a unique example of the fundamental solution of Boltzmann kinetics that is insensitive to the initial distribution. For T-b --> T-c from above, we develop a theory of the thermodynamic critical slowing-down which also leads to the nonexponential thermalization of bosons. We apply our results to the relaxation kinetics of para-excitons in Cu2O and reinterpret the recent reports on the observation of BE condensation of para-excitons.