Efficient numerical methods for computing ground states of spin-1 Bose–Einstein condensates based on their characterizations

In this paper, we propose efficient numerical methods for computing ground states of spin-1 Bose–Einstein condensates (BECs) with/without the Ioffe–Pritchard magnetic field B ( x ) . When B ( x ) ≠ 0 , a numerical method is introduced to compute the ground states and it is also applied to study properties of ground states. Numerical results suggest that the densities of m F = ± 1 components in ground states are identical for any nonzero B ( x ) . In particular, if B ( x ) ≡ B ≠ 0 is a constant, the ground states satisfy the single-mode approximation. When B ( x ) ≡ 0 , efficient and simpler numerical methods are presented to solve the ground states of spin-1 BECs based on their ferromagnetic/antiferromagnetic characterizations. Numerical simulations show that our methods are more efficient than those in the literature. In addition, some conjectures are made from our numerical observations.