Interacting Phonon Systems

Abstract

In the absence of free charges, as in insulators and non-doped semiconductors, the transport phenomena in solids are determined by the kinetics of interacting phonon modes. Besides, the relaxation properties of the phonon system often control the energy and momentum transfer from non-equilibrium electrons to the lattice. Therefore, the kinetics of interacting phonons deserves a special consideration. Below we derive and analyze the kinetic equation for phonons involving phonon-phonon collisions and describe, on its basis, the thermal conduction of insulators, the thermal waves (second sound), and the features of non-equilibrium phonon relaxation determined by the dynamical properties of phonons. We consider perfect crystals, where the interaction of phonons with impurities can be neglected. The last section of this chapter contains a discussion of phonon-photon interaction and the calculation of the complex dielectric function of ionic crystals with the aid of the linear response theory and the formalism of double-time Green’s functions.