Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Soft quantum waveguides in three dimensions   We discuss a three-dimensional soft quantum waveguide, in other words,
Schr\"odinger operator in $\R^3$ with an attractive potential supported by an
infinite tube and keeping its transverse profile fixed. We show that if the
tube is asymptotically straight, the distance between its ends is unbounded,
and its twist satisfies the so-called Tang condition, the esential spectrum is
not affected by smooth bends. Furthermore, we derive a sufficient condition,
expressed in terms of the tube geometry, for the discrete spectrum of such an
operator to be nonempty.

21
The categories of this paper are: adap-org
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The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
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The categories of this paper are: q-alg
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The categories of this paper are: acc-phys
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The categories of this paper are: atom-ph
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The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex