  We derive a master equation for the motion of a polarizable particle weakly
interacting with one or several strongly pumped cavity modes. We focus here on
massive particles with complex internal structure such as large molecules and
clusters, for which we assume a linear scalar polarizability mediating the
particle-light interaction. The predicted friction and diffusion coefficients
are in good agreement with former semiclassical calculations for atoms and
small molecules in weakly pumped cavities, while the current rigorous quantum
treatment and numerical assessment sheds a light on the feasibility of
experiments that aim at optically manipulating beams of massive molecules with
multimode cavities.
