Kinetic Theory for the Interpretation of Measurements on Fluctuations in Radiation Distributions in Finite, Inhomogeneous Systems

Abstract

A kinetic (transport) theory is presented for the first- and second-order (and, if necessary, higher) statistical moments of the number densities of the various particles and/or photons that describe the observable fluctuations in the radiation distribution from an emitting system. This treatment is particularly suitable for the analysis of finite, inhomogeneous systems that may be composed of detectors located outside of a radiating source. Because we are largely concerned with the utility of kinetic theory as a physical theory, considerable emphasis is placed upon an appropriate theoretical description of the actual observables of given experimental situations. The quantum Liouville equation is used to generate the coupled set of transport equations, and basic criteria for the applicability of transport and wave theories are discussed. Quantum-statistical effects are also quite naturally accounted for in cases where they are relevant. It is seen that fluctuation measurements are useful for inferring information relevant to the dynamic interactions within a given system. Such measurements often enjoy the feature of being passive with respect to the interacting system of interest. To illustrate the use of this spatially dependent form of kinetic theory on a system emitting optical radiation, we consider an example that interprets a fluctuation measurement on the radiation emergent from a finite nondispersive blackbody. We conclude by discussing the problems of statistical coupling between the radiation field and detector atom distributions.