Proofs of some simplified characterizations of the ground states of   spin-1 Bose-Einstein condensates
  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. 
Liren Lin and I-Liang Chern
math-ph cond-mat.quant-gas math.AP math.MP