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Proofs of some simplified characterizations of the ground states of spin-1 Bose-Einstein condensates

Liren Lin and I-Liang Chern

arXiv:1102.0832 [math-ph] 4 Feb 2011

We justify some characterizations of the ground states of spin-1 Bose-Einstein condensates exhibited from numerical simulations. For ferromagnetic systems, we show the validity of the single-mode approximation (SMA). For an antiferromagnetic system with nonzero magnetization, we prove the vanishing of the $m_F=0$ component. In the end of the paper some remaining degenerate situations are also discussed. The proofs of the main results are all based on a simple observation, that a redistribution of masses among different components will reduce the kinetic energy.

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