Quantum approach to electromagnetic energy transfer between two dielectric bodies

The problem of radiative heat transfer between two dielectric bodies is analyzed from the point of view of elementary quantum electrodynamics. The dielectric properties of the bodies are assumed to be linear, but dispersion and losses are allowed. Quantization of the electromagnetic field in inhomogeneous, dispersive, and lossy dielectrics is performed with the help of the Huttner-Barnett procedure. The electromagnetic energy flux is expressed through the expectation value of the Poynting vector. In order to compute the Poynting vector, two techniques suitable for nonequilibrium processes are employed: the Heisenberg equations of motion and the diagrammatic Keldysh procedure. They are shown to give identical final results. These quantum-mechanical calculations provide a solid basis for the further, mainly numerical, development of the theory of thermal scanning microscopy.