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

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.

12 pages with 3 figures

References in corpus (2)

• Kelvin Waves of Quantized Vortex Lines in Trapped Bose-Einstein Condensates
• Vortex waves in trapped Bose-Einstein condensates

Cited by in corpus (10)

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• Vibrations of a Columnar Vortex in a Trapped Bose-Einstein Condensate
• Coupling vortex dynamics with collective excitations in Bose-Einstein Condensates
• Acoustic radiation from vortex-barrier interaction in atomic Bose-Einstein condensate
• A method for the dynamics of vortices in a Bose-Einstein condensate: analytical equations of the trajectories of phase singularities
• High precision solutions to quantized vortices within Gross-Pitaevskii equation