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Number-conserving approaches to n-component Bose-Einstein condensates

Mason, P.; Gardiner, S.A.

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P. Mason


We develop the number-conserving approach, which has previously been used in a single-component Bose-Einstein condensed dilute atomic gas, to describe consistent coupled condensate and noncondensate number dynamics, to an n -component condensate. The resulting system of equations is comprised, for each component, of a generalized Gross-Pitaevskii equation coupled to modified Bogoliubov–de Gennes equations. Lower order approximations yield general formulations for multicomponent Gross-Pitaevskii equations, and systems of multicomponent Gross-Pitaevskii equations coupled to multicomponent modified number-conserving Bogoliubov–de Gennes equations. The analysis is left general, such that, in the n -component condensate, there may or may not be mutually coherent components. An expansion in powers of the ratio of noncondensate-to-condensate particle numbers for each coherent set is used to derive the self-consistent, second-order, dynamical equations of motion. The advantage of the analysis developed in this article is in its applications to dynamical instabilities that appear when two (or more) components are in conflict and where a significant noncondensed fraction of atoms is expected to appear.


Mason, P., & Gardiner, S. (2014). Number-conserving approaches to n-component Bose-Einstein condensates. Physical Review A, 89(4), Article 043617.

Journal Article Type Article
Publication Date Apr 1, 2014
Deposit Date May 16, 2014
Publicly Available Date May 19, 2014
Journal Physical review. A.
Print ISSN 1050-2947
Electronic ISSN 1094-1622
Publisher American Physical Society
Peer Reviewed Peer Reviewed
Volume 89
Issue 4
Article Number 043617


Published Journal Article (497 Kb)

Copyright Statement
Reprinted with permission from the American Physical Society: Peter Mason and Simon A. Gardiner, Physical Review A, 89, 043617, 2014. © 2014 by the American Physical Society. Readers may view, browse, and/or download material for temporary copying purposes only, provided these uses are for noncommercial personal purposes. Except as provided by law, this material may not be further reproduced, distributed, transmitted, modified, adapted, performed, displayed, published, or sold in whole or part, without prior written permission from the American Physical Society.

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