Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Derivation of the Bose-Hubbard model in the multiscale limit   In this paper we consider a one-dimensional non-linear Schroedinger equation
(NLSE) with a periodic potential. In the semiclassical limit we prove that the
stationary solutions of the Bose-Hubbard equation approximate the stationary
solutions of the (NLSE). In particular, in the limit of large nonlinearity
strength the stationary solutions turn out to be localized on a single lattice
site of the periodic potential; as a result the phase transition from
superfluid to Mott-insulator phase for Bose-Einstein condensates in a
one-dimensional periodic lattice is rigorously proved.

37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg