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On the spectrum of narrow Neumann waveguide with periodically distributed\delta\prime traps

Pavel Exner Andrii Khrabustovskyi

Spectral Theory and Operator Algebra mathscidoc:1910.43301

Journal of Physics A Mathematical General, 48, 2015.8
We analyze a family of singular Schrdinger operators describing a Neumann waveguide with a periodic array of singular traps of a delta\prime type. We show that in the limit when perpendicular size of the guide tends to zero and the delta\prime interactions are appropriately scaled, the first spectral gap is determined exclusively by geometric properties of the traps.
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@inproceedings{pavel2015on,
  title={On the spectrum of narrow Neumann waveguide with periodically distributed\delta\prime traps},
  author={Pavel Exner, and Andrii Khrabustovskyi},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020140348217128830},
  booktitle={Journal of Physics A Mathematical General},
  volume={48},
  year={2015},
}
Pavel Exner, and Andrii Khrabustovskyi. On the spectrum of narrow Neumann waveguide with periodically distributed\delta\prime traps. 2015. Vol. 48. In Journal of Physics A Mathematical General. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020140348217128830.
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