Formulation and use of a model for the phonon Umklapp collision operator

A new derivation is given of the Callaway model for the linearized phonon N-process collision operator. This is extended to cover the case of U processes, and the model is then applied in a simple case to calculate the thermal conductivity of a dielectric. The result obtained is about one half of that given by the usual relaxation time approximation, and this agrees with a simple qualitative analysis of the situation. A discussion is given of the difference between the present approach and that of Hamilton (1973).