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On the existence of bound states in asymmetric leaky wires

Pavel Exner Semjon Vugalter

Mathematical Physics mathscidoc:1910.43230

Journal of Mathematical Physics, 57, (2), 022104, 2016.2
We analyze spectral properties of a leaky wire model with a potential bias. It describes a two-dimensional quantum particle exposed to a potential consisting of two parts. One is an attractive -interaction supported by a non-straight, piecewise smooth curve L dividing the plane into two regions of which one, the interior, is convex. The other interaction component is a constant positive potential V0 in one of the regions. We show that in the critical case, V0 = 2, the discrete spectrum is non-void if and only if the bias is supported in the interior. We also analyze the non-critical situations, in particular, we show that in the subcritical case, V0 < 2, the system may have any finite number of bound states provided the angle between the asymptotes of L is small enough.
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@inproceedings{pavel2016on,
  title={On the existence of bound states in asymmetric leaky wires},
  author={Pavel Exner, and Semjon Vugalter},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020134025749210759},
  booktitle={Journal of Mathematical Physics},
  volume={57},
  number={2},
  pages={022104},
  year={2016},
}
Pavel Exner, and Semjon Vugalter. On the existence of bound states in asymmetric leaky wires. 2016. Vol. 57. In Journal of Mathematical Physics. pp.022104. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020134025749210759.
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