Low-Temperature Transport Properties of Very Dilute Classical Solutions of He in Superfluid He

• We report microscopic calculations of the thermal conductivity, diffusion constant, and thermal diffusion constant for classical solutions of He in superfluid He at temperatures K, where phonons are the dominant excitations of the He. We focus on solutions with He concentrations , 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 He-phonon scattering, which is crucial for determining the He distribution function in transport. We use the fact that the relative changes in the energy and momentum of a He atom in a collision with a phonon are small to derive a Fokker-Planck equation for the He 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.

Ämnesord

NATURVETENSKAP  -- Fysik (hsv//swe)

NATURAL SCIENCES  -- Physical Sciences (hsv//eng)

Nyckelord

Dilute solutions of He-3 in He-4

Transport

Diffusion

Thermal conductivity

Boltzmann equation

Fokker-Planck equation

Neutron electric dipole moment experiment

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