2017/09/30 by Weizhu Bao, Weizhu Bao null, Yongyong Cai
Mathematics · Physics and Astronomy · #Bose–Einstein condensate #Cold Atom Physics and Bose-Einstein Condensates #Dipole #Ground state #Mathematical analysis #Mathematics #Numerical analysis #Physics #Physics of Superconductivity and Magnetism #Quantum mechanics #Spin (aerodynamics) #Spinor #Strong Light-Matter Interactions #Theoretical physics #Uniqueness #cond-mat.quant-gas
paper · pdf · doi:10.4208/cicp.2018.hh80.14
published as Commun. Comput. Phys., Vol. 24 (2018), pp. 899-965 · A review paper with 70 pages
openalex created_date 2017/09/25 · arxiv created 2018/04/24 · openalex publication_date 2018/06/01 · arxiv updated 2018/06/20 · openalex updated_date 2026/08/05
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.