# Transport and Phonon Damping in $^{\bf 4}$He

## TL;DR

This paper investigates phonon propagation and damping in liquid helium-4, providing detailed calculations of phonon mean-free path and lifetime across different pressures using advanced many-body theory, relevant for quantum experiments and dark matter detection.

## Contribution

It offers the first detailed calculation of phonon mean-free path and lifetime in liquid helium-4 using dynamic many-body theory, highlighting the importance of advanced methods for accurate predictions.

## Key findings

- Long wavelength phonons have large mean free paths.
- Intermediate energy phonons can have mean free paths of micrometers.
- Advanced many-body methods are essential for reliable predictions.

## Abstract

The dynamic structure function $S(k,\omega)$ informs about the dispersion and damping of excitations. We have recently (Phys. Rev. B {\bf 97}, 184520 (2018)) compared experimental results for $S(k,\omega)$ from high-precision neutron scattering experiment 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 life time in liquid \he4 as a function of wave length and pressure. Historically, the question was of interest for experiments of quantum evaporation. More recently, there is interest in the potential use of $^4$He as a detector for low-energy dark matter (K. Schulz and Kathryn M. Zurek, Phys. Rev. Lett. {\bf 117}, 121302 (2016)). While the mean free path of long wave length phonons is large, phonons of intermediate energy can have a short mean free path of the order of $\mu$m. Comparison of different levels of theory indicate that reliable predictions of the phonon mean free path can be made only by using the most advanced many--body method available, namely, DMBT.