On some configurations of oppositely charged trapped vortices in the plane
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...
| Main Authors: | , , , , |
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| Format: | Journal article |
| Language: | English |
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Elsevier
2020
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| _version_ | 1826259283245793280 |
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| author | Dufresne, E Harrington, HA Hauenstein, JD Kevrekidis, PG Tripoli, P |
| author_facet | Dufresne, E Harrington, HA Hauenstein, JD Kevrekidis, PG Tripoli, P |
| author_sort | Dufresne, E |
| collection | OXFORD |
| description | 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. 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. |
| first_indexed | 2024-03-06T18:47:24Z |
| format | Journal article |
| id | oxford-uuid:0efa02aa-d41a-452e-9629-0159622391db |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T18:47:24Z |
| publishDate | 2020 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | oxford-uuid:0efa02aa-d41a-452e-9629-0159622391db2022-03-26T09:49:00ZOn some configurations of oppositely charged trapped vortices in the planeJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:0efa02aa-d41a-452e-9629-0159622391dbEnglishSymplectic ElementsElsevier2020Dufresne, EHarrington, HAHauenstein, JDKevrekidis, PGTripoli, POur 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. 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. |
| spellingShingle | Dufresne, E Harrington, HA Hauenstein, JD Kevrekidis, PG Tripoli, P On some configurations of oppositely charged trapped vortices in the plane |
| title | On some configurations of oppositely charged trapped vortices in the plane |
| title_full | On some configurations of oppositely charged trapped vortices in the plane |
| title_fullStr | On some configurations of oppositely charged trapped vortices in the plane |
| title_full_unstemmed | On some configurations of oppositely charged trapped vortices in the plane |
| title_short | On some configurations of oppositely charged trapped vortices in the plane |
| title_sort | on some configurations of oppositely charged trapped vortices in the plane |
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