Condensation of excitons in a two-dimensional harmonic trap

We study the condensation of a two-dimensional exciton gas in a harmonic trap using a quantum Boltzmann equation. The excitons interact with a lattice that is kept at a constant temperature and we also include exciton-photon coupling (dissipation) and exciton-exciton interactions. We compare the condensation time for both an interacting and a non-interacting exciton gas. For a non-interacting gas anti-Stokes type processes dominate the relaxation rate of low-energy states. The condensation time-scale is determined by the (phonon) scattering rate into the ground state. The presence of dissipation results in a heating effect which increases the mean number of Bose particles required for the onset of condensation. For a dissipative gas the steady state is a nonequilibrium conderisate (exciton matter laser), where the exciton temperature remains above the lattice temperature. We also discuss the effects of dimensionality and trapping on the relaxation process, which has a fundamental role in establishing the condensation time-scale.