The quantum radiative transfer equation: quantum damping, Kirchoff's Law, and the approach to equilibrium of photons in a quantum plasma

Abstract

A method is presented based on the theory of quantum damping, 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 for approximately including the effects of a background plasma on a photon distribution function by replacing the influence of the plasma degrees of freedom with quantum fluctuation and damping terms in the radiation transport equation. We consider the Markov limit where the electron relaxation time scale is short compared to the photon relaxation time scale. 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 undergoing electron scattering due to emission and absorption of photons. 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. The fluctuations of the quantum noise operator yield the deviations from the Kirchoff–Planck relation. Using the quantum radiative transfer equation, transient fluctuations in the photon number are computed.