Few-Particle Vortex Cluster Equilibria in Bose-Einstein Condensates: Existence and Stability

TL;DR

This paper investigates the existence and stability of small vortex clusters in Bose-Einstein condensates using particle models and PDE comparisons, providing new insights into their configurations and stability properties.

Contribution

It systematically analyzes stationary vortex configurations for up to six vortices and compares particle model predictions with full PDE results, including new theoretical and conjectural findings.

Findings

Stable vortex polygon configurations identified

Comparison between particle models and PDE predictions

Conjectures proposed for vortex line equilibria

Abstract

Motivated by recent experimental and theoretical studies of fewparticle vortex clusters in Bose-Einstein condensates, we consider the ordinary differential equations of motion and systematically examine settings for up to N = 6 vortices. We analyze the existence of corresponding stationary state configurations and also consider their spectral stability properties. We compare our particle model results with the predictions of the full partial differential equation system. Whenever possible, we propose generalizations of these results in the context of clusters of N vortices. Some of these, we can theoretically establish, especially so for the N-vortex polygons, while others we state as conjectures, e.g. for the N-vortex line equilibrium.