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

We calculate the contribution to the damping of condensate collective excitations at finite temperatures arising from the lack of equilibrium between the condensate and thermal atoms. Limiting our attention to collective modes that mainly involve the motion of the condensate, we treat the noncondensate as static as a first approximation. We derive a set of generalized Bogoliubov equations for finite temperatures that contain an explicit damping term due to the 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. These results agree quite well with our recent work based on the Thomas-Fermi approximation but predict a much larger damping near the transition temperature.