Neutral vortex necklace in a trapped planar superfluid

TL;DR

This paper investigates a stable, exact vortex necklace configuration in a trapped superfluid, analyzing its stability and potential to induce turbulence using both point-vortex and Gross-Pitaevskii models.

Contribution

It provides an exact stationary solution for a neutral vortex necklace in a superfluid and examines its stability within two different models, linking theoretical and numerical insights.

Findings

Exact stationary solution for vortex necklace identified

Vortex necklace stability confirmed in both models

Perturbed vortex necklace can lead to turbulence

Abstract

We study quantum vortex states consisting of a ring of vortices with alternating sign, in a homogeneous superfluid confined to a circular domain. We find an exact stationary solution of the point vortex model for the neutral vortex necklace. We investigate the stability of the necklace state within both the point-vortex model and the Gross-Pitaevskii equation describing a trapped atomic Bose-Einstein condensate at low temperature. The point-vortex stationary states are found to also be stationary states of the Gross-Pitaevskii equation provided the finite thickness of the outer fluid boundary is accounted for. Under significant perturbation, the Gross-Pitaevskii evolution and point-vortex model exhibit instability as expected for metastable states. The perturbed vortex necklace exhibits sensitivity to the perturbation, suggesting a route to seeding vortex chaos or quantum turbulence.