Mathematical models and numerical methods for spinor Bose-Einstein condensates
arXiv:1709.03840 · doi:10.4208/cicp.2018.hh80.14
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.
A review paper with 70 pages
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- Exciton vortices in two-dimensional hybrid perovskite monolayers
- i-SPin 2: An integrator for general spin-s Gross-Pitaevskii systems
- Computing the least action ground state of the nonlinear Schrödinger equation by a normalized gradient flow
- Spatial order in a two-dimensional spin-orbit-coupled spin-1/2 condensate: superlattice, multi-ring and stripe formation
- Quasi-two-dimensional soliton in a self-repulsive spin-orbit-coupled dipolar binary condensate