Static spectroscopy of a dense superfluid

TL;DR

This paper demonstrates that the static density oscillations near singularities in dense superfluids are governed by the roton minimum, enabling characterization of the roton spectrum through static observations, especially around vortices.

Contribution

It establishes a direct link between static density oscillations and the roton minimum in dense superfluids, providing a method to infer roton characteristics from static ground state measurements.

Findings

Density oscillation period depends on roton minimum position and width.

Oscillation amplitude and phase depend on interaction potential details.

Oscillations have negligible energy compared to kinetic energy, affecting vortex dynamics at high curvatures.

Abstract

Dense Bose superfluids, as HeII, differ from dilute ones by the existence of a roton minimum in their excitation spectrum. It is known that this roton minimum is qualitatively responsible for density oscillations close to any singularity, such as vortex cores, or close to solid boundaries. We show that the period of these oscillations, and their exponential decrease with the distance to the singularity, are fully determined by the position and the width of the roton minimum. Only an overall amplitude factor and a phase shift are shown to depend on the details of the interaction potential. Reciprocally, it allows for determining the characteristics of this roton minimum from static "observations" of a disturbed ground state, in cases where the dynamics is not easily accessible. We focus on the vortex example. Our analysis further shows why the energy of these oscillations is negligible compared to the kinetic energy, which limits their influence on the vortex dynamics, except for high curvatures.