A Method for Evaluating Statistical Averages,
Abstract
Many problems in solid state physics and related areas involve the calculation of statistical averages over grand canonical ensembles for one or more components of the system of interest. This report describes a statistical variant of a generalized Wick's theorem which can often be used to transform such statistical averages so as to obtain alternative expressions which more obviously display the physics of the problem or which are better suited for the introduction of approximations. An application of the method to the calculation of an expression for the absorption coefficient of a physical system interacting with the electromagnetic field is then given. In the framework of the usual infinite system model, a simple relation giving the absorption coefficient in terms of a double-time Green's functions for the system is obtained; this relation is exact to all orders in the electromagnetic field, and therefore includes such features as natural line widths, which are lost in the standard calculation. To illustrate further the use of the technique being described, an application to the problem of computing energy transfer in an electron-photon-phonon system is also given, to show how the method may be used when the statistical nature of the system plays a more direct role. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 30, 1968
- Accession Number
- AD0846683
Entities
People
- C. Alton Coulter
- D. W. Howgate