Damped Bogoliubov excitations of a condensate interacting with a static thermal cloud

We calculate the damping of condensate collective excitations at finite temperatures arising from the lack of equilibrium between the condensate and thermal atoms. We neglect the non-condensate dynamics by fixing the thermal cloud in static equilibrium. We derive a set of generalized Bogoliubov equations for finite temperatures that contain an explicit damping term due to collisional exchange of atoms between the two components. We have numerically solved these Bogoliubov equations to obtain the temperature dependence of the damping of the condensate modes in a harmonic trap. We compare these results with our recent work based on the Thomas-Fermi approximation.