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Wigner-von Neumann perturbations of a periodic potential: spectral singularities in bands

Kurasov, Pavel LU and Naboko, Serguei (2007) In Mathematical Proceedings of the Cambridge Philosophical Society 142(1). p.161-183
Abstract
Wigner-von Neumann type perturbations of the periodic one-dimensional Schrodinger operator are considered. The asymptotics of the solution to the generalized eigenfunction equation is investigated. It is proven that a subordinated solution and therefore art embedded eigenvalue may occur at the points of the absolutely continuous spectrum satisfying a certain resonance (quantization) condition between the frequencies of the perturbation, the frequency of the background potential and the corresponding quasimomentum.
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Mathematical Proceedings of the Cambridge Philosophical Society
volume
142
issue
1
pages
161 - 183
publisher
Cambridge University Press
external identifiers
  • wos:000244596500015
  • scopus:33846973378
ISSN
1469-8064
DOI
10.1017/S0305004106009583
language
English
LU publication?
yes
id
7a3e6bba-5586-43e7-abdc-bbd804268411 (old id 674119)
date added to LUP
2007-12-13 17:49:32
date last changed
2017-02-12 04:15:13
@article{7a3e6bba-5586-43e7-abdc-bbd804268411,
  abstract     = {Wigner-von Neumann type perturbations of the periodic one-dimensional Schrodinger operator are considered. The asymptotics of the solution to the generalized eigenfunction equation is investigated. It is proven that a subordinated solution and therefore art embedded eigenvalue may occur at the points of the absolutely continuous spectrum satisfying a certain resonance (quantization) condition between the frequencies of the perturbation, the frequency of the background potential and the corresponding quasimomentum.},
  author       = {Kurasov, Pavel and Naboko, Serguei},
  issn         = {1469-8064},
  language     = {eng},
  number       = {1},
  pages        = {161--183},
  publisher    = {Cambridge University Press},
  series       = {Mathematical Proceedings of the Cambridge Philosophical Society},
  title        = {Wigner-von Neumann perturbations of a periodic potential: spectral singularities in bands},
  url          = {http://dx.doi.org/10.1017/S0305004106009583},
  volume       = {142},
  year         = {2007},
}