Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Zeroes of the spectral density of the periodic Schroedinger operator
  with Wigner-von Neumann potential   We consider the Schroedinger operator L_{\alpha} on the half-line with a
periodic background potential and the Wigner-von Neumann potential of Coulomb
type: csin(2\omega x+d)/(x+1). It is known that the continuous spectrum of the
operator L_{\alpha} has the same band-gap structure as the free periodic
operator, whereas in each band of the absolutely continuous spectrum there
exist two points (so-called critical or resonance) where the operator
L_{\alpha} has a subordinate solution, which can be either an eigenvalue or a
`half-bound' state. The phenomenon of an embedded eigenvalue is unstable under
the change of the boundary condition as well as under the local change of the
potential, in other words, it is not generic. We prove that in the general case
the spectral density of the operator L_{\alpha} has power-like zeroes at
critical points (i.e., the absolutely continuous spectrum has pseudogaps). This
phenomenon is stable in the above-mentioned sense.

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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: adap-org
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The categories of this paper are: cond-mat
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The categories of this paper are: cmp-lg
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-th
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The categories of this paper are: q-bio
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The categories of this paper are: q-fin
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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: solv-int
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The categories of this paper are: q-alg
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-th
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The categories of this paper are: quant-ph