Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spontaneous symmetry breaking in coupled Bose-Einstein condensates   We study a system of two hardcore bosonic Hubbard models weakly coupled with
each other by tunneling. Assuming that the single uncoupled model exhibits
off-diagonal long-range order, we prove that the coupled system exhibits
spontaneous symmetry breaking (SSB) in the infinite volume limit, in the sense
that the two subsystems maintain a definite relative U(1) phase when the
tunneling is turned off. Although SSB of the U(1) phase is never observable in
a single system, SSB of the relative U(1) phase is physically meaningful and
observable by interference experiments. The present theorem is made possible by
the rigorous theory of low-lying states and SSB in quantum antiferromagnets
developed over the years.

12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga