Abstract
The problem of computing the phonon distribution and thermal conductivity in the presence of N processes is examined in the framework of the Boltzmann-Peierls equation. A heat flow may be associated with drift and diffusive distributions respectively; this intuitive concept is given specific mathematical basis as a natural method to solve the Boltzmann equation. A general operator form of this equation is used and the solution is expressed as the sum of an eigenstate of the N-process collision operator having zero eigenvalue plus a second term; the former is a drift term and the latter is diffusive. The amount of drift is determined by making the drift term orthogonal to the diffusive term; this is equivalent to a phonon momentum balance condition. As a special case, the general method may be approximated by relaxation time representation of the collision operators. The Callaway equation follows directly.