On Some Configurations of Oppositely Charged Trapped Vortices in the Plane

TY - JOUR

T1 - On Some Configurations of Oppositely Charged Trapped Vortices in the Plane

AU - Dufresne, Emilie

AU - Harrington, Heather A

AU - Kevrekidis, Panayotis G

AU - Tripoli, Paolo

AU - Hauenstein, Jonathan D.

N1 - 29 pages, 3 figures © 2020 Elsevier Inc. All rights reserved. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy.

PY - 2021/3/1

Y1 - 2021/3/1

N2 - Our aim in the present work is to identify all the possible standing wave configurations involving few vortices of different charges in an atomic Bose-Einstein condensate (BEC). In this effort, we deploy the use of a computational algebra approach in order to identify stationary multi-vortex states with up to 6 vortices. The use of invariants and symmetries enables deducing a set of equations in elementary symmetric polynomials, which can then be fully solved via computational algebra packages within Maple. We retrieve a number of previously identified configurations, including collinear ones and polygonal (e.g. quadrupolar and hexagonal) ones. However, importantly, we also retrieve a configuration with 4 positive charges and 2 negative ones which is unprecedented, to the best of our knowledge, in BEC studies. We corroborate these predictions via numerical computations in the fully two-dimensional PDE system of the Gross-Pitaevskii type which characterizes the BEC at the mean-field level.

AB - Our aim in the present work is to identify all the possible standing wave configurations involving few vortices of different charges in an atomic Bose-Einstein condensate (BEC). In this effort, we deploy the use of a computational algebra approach in order to identify stationary multi-vortex states with up to 6 vortices. The use of invariants and symmetries enables deducing a set of equations in elementary symmetric polynomials, which can then be fully solved via computational algebra packages within Maple. We retrieve a number of previously identified configurations, including collinear ones and polygonal (e.g. quadrupolar and hexagonal) ones. However, importantly, we also retrieve a configuration with 4 positive charges and 2 negative ones which is unprecedented, to the best of our knowledge, in BEC studies. We corroborate these predictions via numerical computations in the fully two-dimensional PDE system of the Gross-Pitaevskii type which characterizes the BEC at the mean-field level.

KW - Bose-Einstein condensates

KW - standing wave vortex configurations in the plane

KW - symbolic computational methods

KW - Invariant theory

U2 - 10.1016/j.aam.2020.102099

DO - 10.1016/j.aam.2020.102099

M3 - Article

SN - 0196-8858

VL - 124

JO - Advances in Applied Mathematics

JF - Advances in Applied Mathematics

M1 - 102099

ER -