Phonon-Quasiparticle Interactions in Dilute Solutions ofHe3in SuperfluidHe4: I. Phonon Thermal Conductivity and Ultrasonic Attenuation

Expressing the interaction between long-wavelength phonons and ${\mathrm{He}}^3$ quasiparticles in dilute solutions of ${\mathrm{He}}^3$ in ${\mathrm{He}}^4$ entirely in terms of macroscopic observables, we calculate the attenuation of first sound due to the ${\mathrm{He}}^3$ viscosity, and the rate of scattering of phonons from the ${\mathrm{He}}^3$. The results for the attenuation are in excellent agreement with recent experiments. In addition, we calculate the thermal conduction due to phonons for $T\lesssim 0.6$ °K; the conductivity is limited at very low temperatures by ultrasonic attenuation, while at higher temperatures it is predominantly limited by elastic phonon-quasiparticle scattering.