Unified Approach to Interacting Phonon Problems

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Abstract
A unified treatment of the behavior of a system of interacting phonons is presented. This treatment is based on the physically measurable atomic-displacement correlation function or structure function. The perturbation treatment of its high-frequency behavior is briefly summarized. Its more complex behavior at low frequencies is studied in detail. Using a simple model of longitudinal phonons with cubic anharmonic interactions and without umklapp processes, two modes, representing damped first and second sound, are obtained. The parameters which occur in the calculated correlation function are shown to agree with those expected more generally from a phenomenological analysis which is also presented. The paper clarifies certain paradoxes relating to the difference between phonon, ordinary sound, and second sound, by showing that there is no fundamental distinction between these concepts in the only physical quantity, the displacement correlation function.

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