Low-Temperature Thermal Conductivity of Impure Insulators

Abstract
The low-temperature thermal transport properties of an insulating crystal with an arbitrary concentration of randomly located phonon scattering centers are found for slab geometry. The phonon distribution function, the distribution of temperature, the Kapitza resistance at the boundaries, and the heat flux are evaluated by analytically and numerically solving the complete Boltzmann equation with energy-dependent scattering cross section.