Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Absolute continuity in periodic thin tubes and strongly coupled leaky
  wires   Using a perturbative argument, we show that in any finite region containing
the lowest transverse eigenmode, the spectrum of a periodically curved smooth
Dirichlet tube in two or three dimensions is absolutely continuous provided the
tube is sufficiently thin. In a similar way we demonstrate absolute continuity
at the bottom of the spectrum for generalized Schr\"odinger operators with a
sufficiently strongly attractive $\delta$ interaction supported by a periodic
curve in $\mathbb{R}^d, d=2,3$.

27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol