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Aharonov and Bohm versus Welsh eigenvalues

Pavel Exner Sylwia Kondej

Mathematical Physics mathscidoc:1910.43242

Letters in mathematical physics, 108, (9), 2153-2167, 2018.9
We consider a class of two-dimensional Schrdinger operator with a singular interaction of the type and a fixed strength supported by an infinite family of concentric, equidistantly spaced circles, and discuss what happens below the essential spectrum when the system is amended by an AharonovBohm flux in the center. It is shown that if , there is a critical value such that the discrete spectrum has an accumulation point when , while for the number of eigenvalues is at most finite, in particular, the discrete spectrum is empty for any fixed and small enough.
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@inproceedings{pavel2018aharonov,
  title={Aharonov and Bohm versus Welsh eigenvalues},
  author={Pavel Exner, and Sylwia Kondej},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020134508289409771},
  booktitle={Letters in mathematical physics},
  volume={108},
  number={9},
  pages={2153-2167},
  year={2018},
}
Pavel Exner, and Sylwia Kondej. Aharonov and Bohm versus Welsh eigenvalues. 2018. Vol. 108. In Letters in mathematical physics. pp.2153-2167. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020134508289409771.
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