Low Temperature Transport Properties of Very Dilute Classical Solutions of 3He in Superfluid 4He
Abstract
We report microscopic calculations of the thermal conductivity, diffusion constant and thermal diffusion constant for classical solutions of 3He in superfluid 4He at temperatures T 0.6~K, where phonons are the dominant excitations of the 4He. We focus on solutions with 3He concentrations \,10-3, for which the main scattering mechanisms are phonon-phonon scattering via 3-phonon Landau and Beliaev processes, which maintain the phonons in a drifting equilibrium distribution, and the slower process of 3He-phonon scattering, which is crucial for determining the 3He distribution function in transport. We use the fact that the relative changes in the energy and momentum of a 3He atom in a collision with a phonon are small to derive a Fokker-Planck equation for the 3He distribution function, which we show has an analytical solution in terms of Sonine polynomials. We also calculate the corrections to the Fokker-Planck results for the transport coefficients.
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.