Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Discrete bright solitons in Bose-Einstein condensates and dimensional
  reduction in quantum field theory   We first review the derivation of an effective one-dimensional (1D) discrete
nonpolynomial Schr\"odinger equation from the continuous 3D Gross-Pitaevskii
equation with transverse harmonic confinement and axial periodic potential.
Then we study the bright solitons obtained from this discrete nonpolynomial
equation showing that they give rise to the collapse of the condensate above a
critical attractive strength. We also investigate the dimensional reduction of
a bosonic quantum field theory, deriving an effective 1D nonpolynomial
Heisenberg equation from the 3D Heisenberg equation of the continuous bosonic
field operator under the action of transverse harmonic confinement. Moreover,
by taking into account the presence of an axial periodic potential we find a
generalized Bose-Hubbard model which reduces to the familiar 1D Bose-Hubbard
Hamiltonian only if a strong inequality is satisfied. Remarkably, in the
absence of axial periodic potential our 1D nonpolynomial Heisenberg equation
gives the generalized Lieb-Liniger theory we obtained some years ago.

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The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci