Volume element structure and roton-maxon-phonon excitations in superfluid helium beyond the Gross-Pitaevskii approximation

TL;DR

This paper introduces a new theoretical framework for superfluid helium that models volume elements with a nested approach, accurately describing phonon, maxon, and roton excitations and aligning well with experimental data.

Contribution

It presents a novel two-model approach combining microscopic structure and many-body dynamics to unify the description of superfluid helium excitations.

Findings

Accurately reproduces the roton minimum and local maximum

Matches experimental sound velocity and structure factor

Provides a unified description of phonon, maxon, and roton excitations

Abstract

We propose a theory which deals with the structure and interactions of volume elements in liquid helium II. The approach consists of two nested models linked via parametric space. The short-wavelength part describes the interior structure of the fluid element using a non-perturbative approach based on the logarithmic wave equation; it suggests the Gaussian-like behaviour of the element's interior density and interparticle interaction potential. The long-wavelength part is the quantum many-body theory of such elements which deals with their dynamics and interactions. Our approach leads to a unified description of the phonon, maxon and roton excitations, and has noteworthy agreement with experiment: with one essential parameter to fit we reproduce at high accuracy not only the roton minimum but also the neighboring local maximum as well as the sound velocity and structure factor.