Thermal Conductivity and Viscosity in Dilute 3He-4He Mixtures Below 0.6 K

The effects of three-phonon processes on the phonon thermal conductivity and phonon viscosity in dilute 3He-4He mixtures below 0.6 K are investigated. The characteristic scattering times for phonon-phonon interaction-limited thermal conductivity and viscosity are calculated from a collision matrix which contains information on the three-phonon processes. We find that due to phonon-3He interactions the phonon momentum range in which three-phonon processes occur is reduced in comparison with that of the pure 4He case. Results for thermal conductivity and viscosity show good agreement with experimental data without having to adjust the rates of phonon absorption by 3He and the rates of elastic scattering of phonons with 3He.