Correlation Function Calculation of Thermal Conductivity

Recent theories of transport in fluids express the thermal conductivity in terms of correlation functions of the thermal flux. It is shown here that such an expression for the thermal conductivity reduces to that conventionally obtained by use of the Boltzmann transport equation for phonon scattering in crystals, if the rate of change of phonon occupation numbers due to scattering may be characterized by a relaxation time per mode of vibration. The elastic scattering of phonons by randomly arranged scatterers in anisotropic crystals is also discussed. We show that a new relaxation mechanism can, in certain cases, simply characterize the thermal conductivity.