Efficient and accurate methods for solving the time-dependent spin-1 Gross-Pitaevskii equation

We develop a numerical method for solving the spin-1 Gross-Pitaevskii equation. The basis of our work is a two-way splitting of the spin-1 evolution equation that leads to two exactly solvable flows. We use this to implement a second-order and a fourth-order symplectic integration method. These are...

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Bibliographic Details
Published in:Physical review. E 2016-05, Vol.93 (5), p.053309-053309, Article 053309
Main Authors: Symes, L M, McLachlan, R I, Blakie, P B
Format: Article
Language:English
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Summary:We develop a numerical method for solving the spin-1 Gross-Pitaevskii equation. The basis of our work is a two-way splitting of the spin-1 evolution equation that leads to two exactly solvable flows. We use this to implement a second-order and a fourth-order symplectic integration method. These are the first fully symplectic methods for evolving spin-1 condensates. We develop two nontrivial numerical tests to compare our methods against two other approaches.
ISSN:2470-0045
2470-0053
DOI:10.1103/physreve.93.053309