## Abstract

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

Original language | English (US) |
---|---|

Pages (from-to) | 200-228 |

Number of pages | 29 |

Journal | Journal of Low Temperature Physics |

Volume | 178 |

Issue number | 3-4 |

DOIs | |

State | Published - Feb 2014 |

## Keywords

- Boltzmann equation
- Diffusion
- Dilute solutions of He in He
- Fokker–Planck equation
- Neutron electric dipole moment experiment
- Thermal conductivity
- Transport

## ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics
- Materials Science(all)
- Condensed Matter Physics