Thermal conductivity and viscosity via phonon-phonon, phonon-roton, and roton-roton scattering in thin 4He films.

Abstract

The coefficients of the thermal conductivity (\ensuremath{\kappa}) and first viscosity (\ensuremath{\eta}) in thin helium films are evaluated explicitly as a function of temperature via phonon-phonon, phonon-roton, and roton-roton scattering. Above about 0.8 K, phonon-roton scattering and five-phonon processes are the main contributors to both coefficients. Below about 0.8 K, both coefficients increase exponentially with decreasing temperature. At temperatures below 0.3 K, ${\ensuremath{\kappa}}_{\mathrm{ph}}$ has a ${T}^{\mathrm{\ensuremath{-}}5}$ dependence, while ${\ensuremath{\eta}}_{\mathrm{ph}}$ shows exponential and ${T}^{\mathrm{\ensuremath{-}}1}$ dependencies. In the case of ${\ensuremath{\eta}}_{\mathrm{ph}}$, the former is due to phonon-roton scattering and the latter originates from three-phonon processes. The coefficient ${\ensuremath{\kappa}}_{r}$ from roton-roton scattering varies as ${T}^{\mathrm{\ensuremath{-}}1}$, and the roton part ${\ensuremath{\eta}}_{r}$ of the first viscosity is independent of temperature.