The stochastic radiative transfer equation: Quantum damping, Kirchoffs law and NLTE

A method based on the theory of quantum damping is presented, for deriving a self consistent but approximate form of the quantum transport for photons interacting with a fully ionized electron plasma. Specifically, we propose in this paper a technique of approximately including the effects of background plasma on a photon distribution function without directly solving any kinetic equations for the plasma itself. The result is a quantum Langevin equation for the photon number operator; the quantum radiative transfer equation. A dissipation term appears which is the imaginary part of the dielectric function for an electron gas with photon mediated electron-electron interactions due to absorption and re-emission. It depends only on the initial state of the plasma. A quantum noise operator also appears as a result of spontaneous emission of photons from the electron plasma. The thermal expectation value of this noise operator yields the emissivity which is exactly of the form of the Kirchoff-Planck relation. This non-zero thermal expectation value is a direct consequence of a fluctuation-dissipation relation (FDR).