title: A tale of two distributions: from few to many vortices in quasi-two-dimensional Bose-Einstein condensates.
abstract: 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 vorticesNas 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 forN≥7. Additionally, we reconcile this modification with the recent identification of symmetry-breaking bifurcations for the cases ofN=2,…,5. We also briefly discuss the case of a ring of vortices surrounding a central vortex (so-calledN+1 configuration). We finally examine the opposite limit of largeNand illustrate how a coarse-graining, continuum approach enables the accurate identification of the radial distribution of vortices in that limit.
authors.affiliation: Department of Mathematics and Statistics , Dalhousie University Halifax , Nova Scotia, Canada B3H3J5.
authors.forename: T
authors.initials: T
authors.lastname: Kolokolnikov
authors.affiliation: Department of Mathematics and Statistics , University of Massachusetts , Amherst, MA 01003-4515, USA.
authors.forename: P G
authors.initials: PG
authors.lastname: Kevrekidis
authors.affiliation: Nonlinear Dynamical Systems Group, Department of Mathematics and Statistics, and Computational Science Research Center , San Diego State University , San Diego, CA 92182-7720, USA.
authors.forename: R
authors.initials: R
authors.lastname: Carretero-González
keywords: Bose–Einstein condensates; vortex dynamics; vortex lattices
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