Dynamic structure factor of liquid 4He across the normal-superfluid transition

TL;DR

This study uses path integral Monte Carlo and stochastic optimization to analyze the dynamic structure factor of liquid helium-4 across the superfluid transition, revealing the behavior of quasiparticle peaks and phonon-roton spectrum changes.

Contribution

It provides a microscopic analysis of the dynamic structure factor across the transition, employing novel stochastic optimization to invert the Laplace transform.

Findings

Identification of the rapid decrease of roton peak amplitude at transition

Observation of broad multiphonon contributions in the response

Agreement with experimental data on static and dynamic properties

Abstract

We have carried out a microscopic study of the dynamic structure factor of liquid $^4$He across the normal-superfluid transition temperature using the path integral Monte Carlo method. The ill-posed problem of the inverse Laplace transform, from the imaginary-time intermediate scattering function to the dynamic response, is tackled by stochastic optimization. Our results show a quasi-particle peak and a small and broad multiphonon contribution. In spite of the lack of strength in the collective peaks, we clearly identify the rapid dropping of the roton peak amplitude when crossing the transition temperature $T_\lambda$. Other properties such as the static structure factor, static response, and one-phonon contribution to the response are also calculated at different temperatures. The changes of the phonon-roton spectrum with the temperature are also studied. An overall agreement with available experimental data is achieved.