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On the bound states of magnetic Laplacians on wedges

Pavel Exner Vladimir Lotoreichik Axel Prez-Obiol

Mathematical Physics mathscidoc:1910.43172

Reports on Mathematical Physics, 82, (2), 161-185, 2018.10
This paper is mainly inspired by the conjecture about the existence of bound states for magnetic Neumann Laplacians on planar wedges of any aperture <i></i> (0, <i></i>). So far, a proof was only obtained for apertures <i></i> 0.511. The conviction in the validity of this conjecture for apertures <i></i> 0.511<i></i> mainly relied on numerical computations. In this paper we succeed to prove the existence of bound states for any aperture <i></i> 0.583 using a variational argument with suitably chosen test functions. Employing some more involved test functions and combining a variational argument with computer assistance, we extend this interval up to any aperture <i></i> 0.595<i></i>. Moreover, we analyse the same question for closely related problems concerning magnetic Robin Laplacians on wedges and for magnetic Schrdinger operators in the plane with <i></i>-interactions supported on broken lines.
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@inproceedings{pavel2018on,
  title={On the bound states of magnetic Laplacians on wedges},
  author={Pavel Exner, Vladimir Lotoreichik, and Axel Prez-Obiol},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020132247438446701},
  booktitle={Reports on Mathematical Physics},
  volume={82},
  number={2},
  pages={161-185},
  year={2018},
}
Pavel Exner, Vladimir Lotoreichik, and Axel Prez-Obiol. On the bound states of magnetic Laplacians on wedges. 2018. Vol. 82. In Reports on Mathematical Physics. pp.161-185. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020132247438446701.
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