Boltzmann Equation in a Phonon System

Abstract

The Green's function approach is developed to derive the Boltzmann equation for a phonon system having cubic anharmonic interactions. Within the framework of the lowest order scattering process, it is found that the steady-state Boltzmann equation obtained is identical with the Peierls integral equation, except for small correction terms. These correction terms can be absorbed into the transport term by replacing the phonon group velocity appearing in the transport term by the renormalized one, including kinetic and dynamical effects of collisions. Several remarks are made on the generalization of the Boltzmann equation.