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Mathematical Models and Numerical Methods for Spinor Bose-Einstein Condensates.

Mathematical Models and Numerical Methods for Spinor Bose-Einstein Condensates.
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Year:    2018

Communications in Computational Physics, Vol. 24 (2018), Iss. 4 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.2018.hh80.14

Communications in Computational Physics, Vol. 24 (2018), Iss. 4 : pp. 899–965

Published online:    2018-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    67

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

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