Landau damping in trapped Bose-condensed gases

We study Landau damping in dilute Bose-Einstein condensed gases in both spherical and prolate ellipsoidal harmonic traps. We solve the Bogoliubov equations for the mode spectrum in both of these cases, and calculate the damping by summing over transitions between excited quasiparticle states. The results for the spherical case are compared to those obtained in the Hartree-Fock approximation, where the excitations take on a single-particle character, and excellent agreement between the two approaches is found. We have also taken the semiclassical limit of the Hartree-Fock approximation and obtain a novel expression for the Landau damping rate involving the time dependent self-diffusion function of the thermal cloud. As a final approach, we study the decay of a condensate mode by making use of dynamical simulations in which both the condensate and thermal cloud are evolved explicitly as a function of time. A detailed comparison of all these methods over a wide range of sample sizes and trap geometries is presented.