A tale of two distributions: from few to many vortices in quasi-two-dimensional Bose–Einstein condensates

Motivated by the recent successes of particle models in capturing the precession and interactions of vortex structures in quasi-two-dimensional Bose–Einstein condensates, we revisit the relevant systems of ordinary differential equations. We consider the number of vortices N as a parameter and explo...

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Bibliographic Details
Published in:Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences Mathematical, physical, and engineering sciences, 2014-08, Vol.470 (2168), p.1-18
Main Authors: Kolokolnikov, T., Kevrekidis, P. G., Carretero-González, R.
Format: Article
Language:English
Subjects:
Aggregation
Angular momentum
Bose Einstein condensates
Eigenvalues
Ground state
Mathematical lattices
Mathematical rings
Mathematics
Precession
Rotation
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Summary:Motivated by the recent successes of particle models in capturing the precession and interactions of vortex structures in quasi-two-dimensional Bose–Einstein condensates, we revisit the relevant systems of ordinary differential equations. We consider the number of vortices N as a parameter and explore the prototypical configurations ('ground states') that arise in the case of few or many vortices. In the case of few vortices, we modify the classical result illustrating that vortex polygons in the form of a ring are unstable for N ≥ 7. Additionally, we reconcile this modification with the recent identification of symmetry-breaking bifurcations for the cases of N = 2,...,5. We also briefly discuss the case of a ring of vortices surrounding a central vortex (socalled N + 1 configuration). We finally examine the opposite limit of large N and illustrate how a coarse-graining, continuum approach enables the accurate identification of the radial distribution of vortices in that limit.
ISSN:1364-5021