Collective light forces on atoms in a high-finesse cavity

We solve the quantum Langevin equations of motion for N pointlike two-level atoms moving in an externally pumped cavity field. In the limit of the low saturation of the atoms, we obtain analytical expressions for the dipole f orce, the velocity-dependent force and the momentum diffusion coefficient f or each atom in the presence of other atoms. The expressions show that in g eneral the forces on each atom depend on the position and the velocity of a ll the other atoms.