Superfluid vortex dynamics on a spherical film

TL;DR

This paper investigates the energy and motion of quantized vortices on a spherical superfluid shell, relevant for Bose-Einstein condensates in microgravity, revealing complex vortex behaviors and dynamics.

Contribution

It introduces a method to analyze vortex dynamics on spherical shells using stereographic projection, providing new insights into vortex interactions on curved surfaces.

Findings

Single vortex dipole follows a simple orbit

Four vortices exhibit complex configurations

Two small vortex dipoles analyzed in detail

Abstract

Motivated by ongoing experimental efforts to make closed Bose-Einstein condensate (BEC) shells in microgravity environments, this work studies the energy and dynamics of singly quantized vortices on a thin spherical superfluid shell, where the overall vortex charge must vanish (as on any compact surface). For each vortex, stereographic projection yields the corresponding complex potential on the tangent plane. The resulting stream function then provides both the total energy and the dynamics of a system of overall neutral vortices on a spherical film. Although a single vortex dipole follows a simple dynamical orbit, four vortices can present a variety of situations. We study a few symmetric initial configurations and then focus on the special case of two small vortex dipoles.