Vibrations of a Columnar Vortex in a Trapped Bose-Einstein Condensate

TL;DR

This paper derives a governing equation and dispersion relation for Kelvin waves on vortex lines in a trapped Bose-Einstein condensate, providing improved analytical results consistent with numerical calculations.

Contribution

The authors present a new analytical derivation of Kelvin wave dispersion in trapped BECs, extending previous work and aligning well with numerical spectra.

Findings

Analytical dispersion relation matches numerical Bogoliubov spectra

Derived equations applicable to various trap geometries

Improves upon previous analytical models

Abstract

We derive a governing equation for a Kelvin wave supported on a vortex line in a Bose-Einstein condensate, in a rotating cylindrically symmetric parabolic trap. From this solution the Kelvin wave dispersion relation is determined. In the limit of an oblate trap and in the absence of longitudinal trapping our results are consistent with previous work. We show that the derived Kelvin wave dispersion in the general case is in quantitative agreement with numerical calculations of the Bogoliubov spectrum and offer a significant improvement upon previous analytical work.