Perturbation Expansion for Lattice Thermal Conductivity

Abstract

A method is given for obtaining a perturbation expansion for the correlation function formula for thermal conductivity. The problem is reduced to the determination of the matrix elements of the products of resolvent operators X_ll′ and Y_ll′ to different orders in the perturbation λH′. The coefficients in the general equations for X_ll′ and Y_ll′ derived by Van Hove, Janner, and Swenson are iterated, and the resulting approximate equations are used to deduce the formulas for the contributions to the lattice thermal conductivity proportional to λ⁻² (lowest order) and to λ⁻¹.