Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Excitations of the One Dimensional Bose-Einstein Condensates in a Random
  Potential   We examine bosons hopping on a one-dimensional lattice in the presence of a
random potential at zero temperature. Bogoliubov excitations of the
Bose-Einstein condensate formed under such conditions are localized, with the
localization length diverging at low frequency as $\ell(\omega)\sim
1/\omega^\alpha$. We show that the well known result $\alpha=2$ applies only
for sufficiently weak random potential. As the random potential is increased
beyond a certain strength, $\alpha$ starts decreasing. At a critical strength
of the potential, when the system of bosons is at the transition from a
superfluid to an insulator, $\alpha=1$. This result is relevant for
understanding the behavior of the atomic Bose-Einstein condensates in the
presence of random potential, and of the disordered Josephson junction arrays.

23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
2
The categories of this paper are: math
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci