Geometric coupling thresholds in a two-dimensional strip

D Borisov Pavel Exner R Gadylshin

TBD mathscidoc:1910.43039

Journal of Mathematical Physics, 43, (12), 6265-6278, 2002.12
We consider the Laplacian in a strip R(0,d) with the boundary condition which is Dirichlet except at the segment of a length 2a of one of the boundaries where it is switched to Neumann. This operator is known to have a non-empty and simple discrete spectrum for any a>0. There is a sequence 0<a1<a2< of critical values at which new eigenvalues emerge from the continuum when the Neumann window expands. We find the asymptotic behavior of these eigenvalues around the thresholds showing that the gap is in the leading order proportional to (aan)2 with an explicit coefficient expressed in terms of the corresponding threshold-energy resonance eigenfunction.
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@inproceedings{d2002geometric,
  title={Geometric coupling thresholds in a two-dimensional strip},
  author={D Borisov, Pavel Exner, and R Gadylshin},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020122716099621568},
  booktitle={Journal of Mathematical Physics},
  volume={43},
  number={12},
  pages={6265-6278},
  year={2002},
}
D Borisov, Pavel Exner, and R Gadylshin. Geometric coupling thresholds in a two-dimensional strip. 2002. Vol. 43. In Journal of Mathematical Physics. pp.6265-6278. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020122716099621568.
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