Rotating He-3 droplets

TL;DR

This study uses Density Functional Theory to analyze the shapes and stability of rotating He-3 droplets, comparing quantum and classical models and providing insights relevant for ongoing experiments.

Contribution

It presents a detailed quantum-mechanical analysis of rotating He-3 droplets, extending classical models to include quantum effects and size-dependent deviations.

Findings

Droplet shapes evolve from oblate to two-lobed with increasing angular momentum.

Small deviations from classical models are due to surface and quantum effects.

Classical models become more accurate as droplet size increases.

Abstract

Motivated by recent experiments, we study normal-phase rotating He-3 droplets within Density Functional Theory in a semi-classical approach. The sequence of rotating droplet shapes as a function of angular momentum are found to agree with those of rotating classical droplets, evolving from axisymmetric oblate to triaxial prolate to two-lobed shapes as the angular momentum of the droplet increases. Our results, which are obtained for droplets of nanoscopic size, are rescaled to the mesoscopic size characterizing ongoing experimental measurements, allowing for a direct comparison of shapes. The stability curve in the angular velocity-angular momentum plane shows small deviations from the classical rotating drop model predictions, whose magnitude increases with angular momentum. We attribute these deviations to effects not included in the simplified classical model description of a rotating fluid held together by surface tension, i.e. to surface diffuseness, curvature and finite compressibility, and to quantum effects associated with deformation of the He-3 Fermi surface. The influence of all these effects is expected to diminish as the droplet size increases, making the classical rotating droplet model a quite accurate representation of He-3 rotation.