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Absolute Continuity of the Spectrum for Periodically Modulated Leaky Wires in {\mathbb{R}^{3}}

Pavel Exner Rupert L Frank

TBD mathscidoc:1910.43150

Annales Henri Poincare, 8, (2), 241-263, 2007.4
We consider a model of leaky quantum wires in three dimensions. The Hamiltonian is a singular perturbation of the Laplacian supported by a line with the coupling which is bounded and periodically modulated along the line. We demonstrate that such a system has a purely absolutely continuous spectrum and its negative part has band structure with an at most finite number of gaps. This result is extended also to the situation when there is an infinite number of the lines supporting the perturbations arranged periodically in one direction.
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@inproceedings{pavel2007absolute,
  title={Absolute Continuity of the Spectrum for Periodically Modulated Leaky Wires in {\mathbb{R}^{3}}},
  author={Pavel Exner, and Rupert L Frank},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020131551922450679},
  booktitle={Annales Henri Poincare},
  volume={8},
  number={2},
  pages={241-263},
  year={2007},
}
Pavel Exner, and Rupert L Frank. Absolute Continuity of the Spectrum for Periodically Modulated Leaky Wires in {\mathbb{R}^{3}}. 2007. Vol. 8. In Annales Henri Poincare. pp.241-263. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020131551922450679.
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