TY - JOUR
T1 - Mathematical Models and Numerical Methods for Spinor Bose-Einstein Condensates. 
JO - Communications in Computational Physics
VL - 4
SP - 899
EP - 965
PY - 2018
DA - 2018/06
SN - 24
DO - http://doi.org/10.4208/cicp.2018.hh80.14
UR - https://global-sci.org/intro/article_detail/cicp/12313.html
KW - Bose-Einstein condensate, Gross-Pitaeskii equation, spin-orbit, spin-1, spin-2, ground state, dynamics, numerical methods.
AB - <p style="text-align: justify;">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.</p>