CONDENSATION OF EXCITONS IN A 2-DIMENSIONAL HARMONIC TRAP

We study the condensation of a two-dimensional exciton gas in a harmon ic trap using a quantum Boltzmann equation. The excitons interact with a lattice that is kept at a constant temperature and Rie also include exciton-photon coupling (dissipation) and exciton-exciton interaction s. We compare the condensation time for both an interacting and a non- interacting exciton gas. For a non-interacting gas anti-Stokes type pr ocesses dominate the relaxation rate of low-energy states. The condens ation time-scale is determined by the (phonon) scattering rate into th e ground state. The presence of dissipation results in a heating effec t which increases the mean number of Bose particles required for the o nset of condensation. For a dissipative gas the steady state is a none quilibrium condensate (exciton matter laser). where the exciton temper ature remains above the lattice temperature. We also discuss the effec ts of dimensionality and trapping on the relaxation process, which has a fundamental role in establishing the condensation time-scale.