The quantum Langevin equation is used to calculate an exact expression for the free energy of a quantum oscillator interacting, via dipole coupling, with a blackbody radiation field. In particular, we obtain a temperature-dependent shift in the free energy. This result may then be used to obtain corresponding results for the energy, the partition function, and other thermodynamic quantities.

• Received 17 October 1984

DOI:https://doi.org/10.1103/PhysRevLett.55.2273