On the dense point and absolutely continuous spectrum for Hamiltonians with concentric shells

Pavel Exner Martin Fraas

TBD mathscidoc:1910.43144

Letters in Mathematical Physics, 82, (1), 25-37, 2007.10
We consider Schrdinger operators in dimension 2 with a singular interaction supported by an infinite family of concentric spheres, analogous to a system studied by Hempel and coauthors for regular potentials. The essential spectrum covers a half line determined by the appropriate one-dimensional comparison operator; it is dense pure point in the gaps of the latter. If the interaction is nontrivial and radially periodic, there are infinitely many absolutely continuous bands; in contrast to the regular case the lengths of the p.p. segments interlacing with the bands tend asymptotically to a positive constant in the high-energy limit.
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@inproceedings{pavel2007on,
  title={On the dense point and absolutely continuous spectrum for Hamiltonians with concentric  shells},
  author={Pavel Exner, and Martin Fraas},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020131403009296673},
  booktitle={Letters in Mathematical Physics},
  volume={82},
  number={1},
  pages={25-37},
  year={2007},
}
Pavel Exner, and Martin Fraas. On the dense point and absolutely continuous spectrum for Hamiltonians with concentric shells. 2007. Vol. 82. In Letters in Mathematical Physics. pp.25-37. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020131403009296673.
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