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Master Equation for the Motion of a Polarizable Particle in a Multimode Cavity

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.