Stability of regular vortex polygons in Bose--Einstein condensate

A. A. Kilin ; E. M. Artemova

Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 56 (2020), pp. 20-29.

Résumé

We consider the problem of the stability of rotating regular vortex $N$-gons (Thomson configurations) in a Bose–Einstein condensate in a harmonic trap. The dependence of the rotation velocity $\omega$ of the Thomson configuration around the center of the trap is obtained as a function of the number of vortices $N$ and the radius of the configuration $ R $. The analysis of the stability of motion of such configurations in the linear approximation is carried out. For $N \leqslant 6$, regions of orbital stability of configurations in the parameter space are constructed. It is shown that vortex $N$-gons for $N > 6$ are unstable for any parameters of the system.

Détail

Keywords: vortex dynamics, Bose–Einstein condensate, linear stability.
Mots-clés : Thomson configurations

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