Perturbative behaviour of a vortex in a trapped Bose-Einstein condensate

TL;DR

This paper develops a mathematical framework to describe the shape and dynamics of a perturbed vortex line in a trapped Bose-Einstein condensate, correcting previous derivations and enabling comparison with numerical simulations.

Contribution

It introduces a new set of equations for vortex line behavior in BECs, improving upon previous models and facilitating comparison with numerical data.

Findings

Derived equations for vortex shape and motion

Corrected previous theoretical derivation

Enabled comparison with numerical results

Abstract

We derive a set of equations that describe the shape and behaviour of a single perturbed vortex line in a Bose-Einstein condensate. Through the use of a matched asymptotic expansion and a unique coordinate transform a relation for a vortex's velocity, anywhere along the line, is found in terms of the trapping, rotation, and distortion of the line at that location. This relation is then used to find a set of differential equations that give the line's specific shape and motion. This work corrects a previous similar derivation by Anatoly A. Svidzinsky and Alexander L. Fetter [Phys. Rev. A \textbf{62}, 063617 (2000)], and enables a comparison with recent numerical results.