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Curvature-induced bound states in Robin waveguides and their asymptotical properties

Pavel Exner Alexander Minakov

TBD mathscidoc:1910.43131

Journal of Mathematical Physics, 55, (12), 122101, 2014.12
We analyze bound states of Robin Laplacian in infinite planar domains with a smooth boundary, in particular, their relations to the geometry of the latter. The domains considered have locally straight boundary being, for instance, locally deformed halfplanes or wedges, or infinite strips, alternatively they are the exterior of a bounded obstacle. In the situation when the Robin condition is strongly attractive, we derive a two-term asymptotic formula in which the next-to-leading term is determined by the extremum of the boundary curvature. We also discuss the non-asymptotic case of attractive boundary interaction and show that the discrete spectrum is nonempty if the domain is a local deformation of a halfplane or a wedge of angle less than , and it is void if the domain is concave.
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@inproceedings{pavel2014curvature-induced,
  title={Curvature-induced bound states in Robin waveguides and their asymptotical properties},
  author={Pavel Exner, and Alexander Minakov},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020130909840220660},
  booktitle={Journal of Mathematical Physics},
  volume={55},
  number={12},
  pages={122101},
  year={2014},
}
Pavel Exner, and Alexander Minakov. Curvature-induced bound states in Robin waveguides and their asymptotical properties. 2014. Vol. 55. In Journal of Mathematical Physics. pp.122101. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020130909840220660.
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