Theory of thermal motions in anharmonic crystals

Abstract

A general theoretical treatment of transport properties of an anharmonic crystal is given, based on Green's function technique. Equations of motion for the phonon spectral function and for the generalized phonon number density at non-equilibrium are derived with no restriction on the frequency and wave vector of the thermal disturbance. The latter equation constitutes a generalized Boltzmann equation for the phonons. Based on these equations we are able to discuss in detail propagation and damping of “phonons” throughout the whole frequency range, stretching from the high frequency, essentially collisionless regime down to the low frequency, collision dominated, hydrodynamic regime. Particular attention is given to the interesting transition region between these two regimes. Here we have confined ourselves to the main lines. The general explicit solution of the generalized Boltzmann equation and a detailed discussion of propagation and damping of sound waves is given in a separate forthcoming paper.