Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Two-body problem in periodic potentials   We investigate the problem of two atoms interacting via a short range s-wave
potential in the presence of a deep optical lattice of arbitrary dimension $D$.
Using a tight binding approach, we derive analytical results for the properties
of the bound state and the scattering amplitude. We show that the tunneling
through the barriers induces a dimensional crossover from a confined regime at
high energy to an anisotropic three dimensional regime at low energy. The
critical value of the scattering length needed to form a two-body bound state
shows a logaritmic dependence on the tunneling rate for D=1 and a power law for
$D>1$. For the special case D=1, we also compare our analytical predictions
with exact numerics, finding remarkably good agreement.

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The categories of this paper are: q-alg
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex