Analytic Vortex Dynamics in an Annular Bose-Einstein Condensate

TL;DR

This paper provides an analytical framework for understanding vortex dynamics in an annular Bose-Einstein condensate, including energy expressions, vortex precession, and lifetime bounds, advancing the theoretical modeling of such systems.

Contribution

It introduces a closed-form analytical approach for vortex interactions in an annular BEC, applicable in the incompressible limit, and derives bounds for vortex lifetimes.

Findings

Derived expressions for free energy and vortex precession rates.

Established lower bounds for vortex lifetime in the annulus.

Provided a foundation for analytical vortex dynamics in complex geometries.

Abstract

We consider analytically the dynamics of an arbitrary number and configuration of vortices in an annular Bose-Einstein condensate obtaining expressions for the free energy and vortex precession rates to logarithmic accuracy. We also obtain lower bounds for the lifetime of a single vortex in the annulus. Our results enable a closed-form analytic treatment of vortex-vortex interactions in the annulus that is exact in the incompressible limit. The incompressible hydrodynamics that is developed here paves the way for more general analytical treatments of vortex dynamics in non-simply connected geometries.