Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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.

30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an