期刊
SIAM JOURNAL ON SCIENTIFIC COMPUTING
卷 42, 期 4, 页码 B983-B1013出版社
SIAM PUBLICATIONS
DOI: 10.1137/19M1271117
关键词
Gross-Pitaevskii theory; spinor condensates; spin-2 ground state; spin-3 ground state; energy minimization
资金
- NSFC [11831002, 1142110, 11771036, 91630204, 11971120, 91730302]
- Shanghai Science and Technology Commission [17XD1400500]
- Beijing Academy of Artificial Intelligence
The computation of the ground states of spin-F Bose-Einstein condensates (BECs) can be formulated as an energy minimization problem with two quadratic constraints. We discretize the energy functional and constraints using the Fourier pseudospectral schemes and view the discretized problem as an optimization problem on manifold. Three different types of retractions to the manifold are designed. They enable us to apply various optimization methods on manifold to solve the problem. Specifically, an adaptive regularized Newton method is used together with a cascadic multigrid technique to accelerate the convergence. Our method is the first applicable algorithm for BECs with an arbitrary integer spin, including the complicated spin-3 BECs. Extensive numerical results on ground states of spin-1, spin-2, and spin-3 BECs with diverse interaction and optical lattice potential in one/two/three dimensions are reported to show the efficiency of our method and to demonstrate interesting physical phenomena.
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