By the same authors

On Some Configurations of Oppositely Charged Trapped Vortices in the Plane

Research output: Contribution to journalArticlepeer-review

Published copy (DOI)

Author(s)

  • Emilie Dufresne
  • Heather A Harrington
  • Panayotis G Kevrekidis
  • Paolo Tripoli
  • Jonathan D. Hauenstein

Department/unit(s)

Publication details

JournalAdvances in Applied Mathematics
DateSubmitted - 26 Oct 2018
DateAccepted/In press - 4 Aug 2020
DateE-pub ahead of print (current) - 16 Dec 2020
Early online date16/12/20
Original languageEnglish

Abstract

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.

Bibliographical note

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.

    Research areas

  • Bose-Einstein condensates, standing wave vortex configurations in the plane, symbolic computational methods, Invariant theory

Discover related content

Find related publications, people, projects, datasets and more using interactive charts.

View graph of relations