Thermal conductivity and first viscosity via temperature-dependent elementary excitation spectra in thin and bulk liquid 4He

Abstract

The coefficients of thermal conductivity (ϰ) and first viscosity (η) in thin and bulk liquid 4He are evaluated explicitly as a function of temperature via the zero-temperature and temperature-dependent two- and three-dimensional elementary excitation spectra that are microscopic only in the long-wavelength limit. The coefficients ϰ( T) and η( T) obtained from the temperature-dependent spectrum have slightly larger values than those of the zero-temperature spectrum through the whole range of temperatures, while as the temperature approaches absolute zero, the coefficients ϰ( T) and η( T) coincide with each other in both spectra. Below about 0.8 K, both coefficients increase exponentially with decreasing temperature. At temperatures below about 0.3 K, ϰ( T) in the thin and bulk cases have T -5 and T -6 dependences, respectively, whereas η ph( T) has a T -1 dependence in both dimensions with extra temperature-dependent terms, which originate from three-phonon processes for both excitation spectra.