Damping of condensate collective modes due to equilibration with the noncondensate

We consider the damping of condensate collective modes in the collisionless regime at finite temperatures arising from lack of equilibrium between the condensate and the noncondensate atoms, an effect that is ignored in the usual discussion of the collisionless region. As a first approximation, we ignore the dynamics of the thermal cloud. Our calculations should be applicable to collective modes of the condensate that are oscillating out-of-phase with the thermal cloud. We obtain a generalized Stringari equation of motion for the condensate at finite temperatures, which includes a damping term associated with the fact that the condensate is not in diffusive equilibrium with the static thermal cloud. This intercomponent collisional damping of the condensate modes is comparable in magnitude to the Landau damping considered in the recent literature.