Transport and Phonon Damping in ⁴ He

The dynamic structure function S(k, ω) informs about the dispersion and damping of excitations. We have recently (Beauvois et al. in Phys Rev B 97:184520, 2018) compared experimental results for S(k, ω) from high-precision neutron scattering experiments and theoretical results using the “dynamic many-body theory” (DMBT), showing excellent agreement over the whole experimentally accessible pressure regime. This paper focuses on the specific aspect of the propagation of low-energy phonons. We report calculations of the phonon mean-free path and phonon lifetime in liquid ⁴He as a function of wavelength and pressure. Historically, the question was of interest for experiments of quantum evaporation. More recently, there is interest in the potential use of ⁴He as a detector for low-energy dark matter (Schulz and Zurek in Phys Rev Lett 117:121302/1, 2016). While the mean-free path of long wavelength phonons is large, phonons of intermediate energy can have a short mean-free path of the order of μ m. Comparison of different levels of theory indicates that reliable predictions of the phonon mean-free path can be made only by using the most advanced many-body method available, namely DMBT.