  We consider the damping of condensate collective modes at finite temperatures
arising from lack of equilibrium between the condensate and the non-condensate
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
which 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
inter-component collisional damping of the condensate modes is comparable in
magnitude to the Landau damping considered in the recent literature.

Condensed Matter