Population Dynamics of Excitons and Excitonic Molecules

The Fokker-Planck equation for the number density in energy space of exciton or excitonic molecule which interact with acoustic phonons is derived from the Kolmogorov-Chapman equation in the momentum space. The equation linear in the number density is solved numerically for the weak excitation. The boson character of excitonic molecules plays an important role in the population dynamics so that the Bose-condensation of these particles is expected at high concentration and low temperature. It is discussed how the initial distribution approaches the Bose-condensation, and it is shown for example that the time of an order of sub-nano second is required for the onset of the Bose-condensation in CdS.