Casimir-Polder potential in a dielectric medium out of thermal equilibrium

The Casimir-Polder potential between a pair of atoms or molecules, either one of which may be excited, in a dielectric medium out of thermal equilibrium is obtained using a field operator that accounts for the attenuation or amplification of the radiation. Two contributions to the intermolecular potential are identified. One term is that induced by the excitations and relaxations that the interacting molecules experience due to the thermal bath, obtained using the resonance energy transfer rate and the Wigner-Weisskopf model. The second contribution arises as a consequence of the polarization induced in the interacting molecules by vacuum and thermal radiation. A number of disagreements between the present theory and several previously reported formulations examining this intermolecular potential are revealed.