Semiclassical kinetic equations for composite bosons

We derive semiclassical Boltzmann equations describing thermalization of an ensemble of excitons due to exciton-phonon interactions, taking into account the fact that excitons are not ideal bosons but composite particles consisting of electrons and holes. We demonstrate that, with a standard definition of excitonic creation and annihilation operators, one faces a problem of the total particle number nonconservation, and we propose its possible solution based on the introduction of operators with angular momentum algebra. We then derive a set of kinetic equations describing the evolution of the excitonic density in the reciprocal space and analyze how the composite statistics of the excitons affects the thermalization processes in the system.