| Abstract: |
| In this paper, an efficient and accurate numerical method is proposed to compute the ground
state of spin-2 Bose-Einstein condensates (BECs) by using the normalized gradient flow (NGF)
or imaginary time method (ITM). The key idea is twofold. One is
to find the five projection or normalization conditions that are used in the projection step of NGF/ITM,
while the other one is to find a good initial data for the NGF/ITM.
Based on the relations between chemical
potentials and the two physical constrains given by the conservation of the totlal mass
and magnetization, these five projection or normalization conditions can be completely and
uniquely determined in the context of the back-Euler finite difference (BEFD) scheme
that discretized the NGF/ITM, which allows one to successfully extend the most
powerful and popular NGF/ITM to compute the ground state of spin-2 BECs.
Additionally, the structures and properties of the ground states in a spatial uniform system are
analysed so as to construct efficient initial data for NGF/ITM. Extensive numerical results on
ground states of spin-2 BECs with ferromagnetic/nematic/cyclic interaction and harmonic/optical
lattice potential in one/two dimensions are reported to show the efficiency of our method
and to demonstrate some interesting physical phenomena. |
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