Lowest-Order Contribution to the Lattice Thermal Conductivity

Abstract

In a previous paper the correlation function formula for the thermal conductivity was used to derive equations for the lowest‐order contribution to the lattice thermal conductivity K^ij. An explicit but formal solution of these equations is obtained here, and it is shown how this solution simplifies in the limit of infinite volume. Transport equations equivalent to the familiar Boltzmann equation are derived for perturbations describing both anharmonic forces and lattice imperfections. No approximations are made beyond the restriction to lowest order in the perturbation. It is demonstrated that K^ij is symmetric.