Volume 24, Issue 4
Review Article: Mathematical Models and Numerical Methods for Spinor Bose-Einstein Condensates.

Weizhu Bao & Yongyong Cai

Commun. Comput. Phys., 24 (2018), pp. 899-965.

Published online: 2018-06

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  • Abstract

In this paper, we systematically review mathematical models, theories and numerical methods for ground states and dynamics of spinor Bose-Einstein condensates (BECs) based on the coupled Gross-Pitaevskii equations (GPEs). We start with a pseudo spin-1/2 BEC system with/without an internal atomic Josephson junction and spin-orbit coupling including (i) existence and uniqueness as well as non-existence of ground states under different parameter regimes, (ii) ground state structures under different limiting parameter regimes, (iii) dynamical properties, and (iv) efficient and accurate numerical methods for computing ground states and dynamics. Then we extend these results to spin-1 BEC and spin-2 BEC. Finally, extensions to dipolar spinor systems and/or general spin-F (F≥3) BEC are discussed.

  • Keywords

Bose-Einstein condensate, Gross-Pitaeskii equation, spin-orbit, spin-1, spin-2, ground state, dynamics, numerical methods.

  • AMS Subject Headings

35Q55, 35P30, 65M06, 65M70, 65Z05, 81Q05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-24-899, author = {}, title = {Review Article: Mathematical Models and Numerical Methods for Spinor Bose-Einstein Condensates. }, journal = {Communications in Computational Physics}, year = {2018}, volume = {24}, number = {4}, pages = {899--965}, abstract = {

In this paper, we systematically review mathematical models, theories and numerical methods for ground states and dynamics of spinor Bose-Einstein condensates (BECs) based on the coupled Gross-Pitaevskii equations (GPEs). We start with a pseudo spin-1/2 BEC system with/without an internal atomic Josephson junction and spin-orbit coupling including (i) existence and uniqueness as well as non-existence of ground states under different parameter regimes, (ii) ground state structures under different limiting parameter regimes, (iii) dynamical properties, and (iv) efficient and accurate numerical methods for computing ground states and dynamics. Then we extend these results to spin-1 BEC and spin-2 BEC. Finally, extensions to dipolar spinor systems and/or general spin-F (F≥3) BEC are discussed.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.2018.hh80.14}, url = {http://global-sci.org/intro/article_detail/cicp/12313.html} }
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