Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weakly bound states in heterogeneous waveguides   We study the spectrum of the Helmholtz equation in a two-dimensional infinite
waveguide, containing a weak heterogeneity localized at an internal point, and
obeying Dirichlet boundary conditions at its border. We prove that, when the
heterogeneity corresponds to a locally denser material, the lowest eigenvalue
of the spectrum falls below the continuum threshold and a bound state appears,
localized at the heterogeneity. We devise a rigorous perturbation scheme and
derive the exact expression for the energy to third order in the heterogeneity.

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The categories of this paper are: chao-dyn
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The categories of this paper are: mtrl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
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The categories of this paper are: econ
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
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The categories of this paper are: adap-org
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The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph