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On the quantum statistical theory of thermal conductivity Griffin, Peter Allan

Abstract

A critical survey of the present state of the quantum statistical theory of thermal conductivity is given. Recently several attempts have been made to extend Kubo's treatment of electrical conduction to other irreversible transport processes in -which the interaction between the driving system and the system of interest is not precisely known. No completely satisfactory solution of the problems involved is contained in the literature. In this thesis, a detailed derivation of a Kubo-type formula for thermal conductivity is given, using essentially the concepts and methods of Nakajima and Mori, with no pretense that it settles the problem completely. Some general remarks are made on the evaluation of a Kubo-type expression, in particular, the use of Van Hove's master equations and the reduction of the usual N-particle formula to a single particle formula. An explicit calculation of thermal conductivity is made for the simple model of elastic electron scattering by randomly distributed, spherically symmetric impurities.

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