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A regular version of Smilansky model

Diana Barseghyan Pavel Exner

TBD mathscidoc:1910.43173

Journal of Mathematical Physics, 55, (4), 042104, 2014.4
We discuss a modification of Smilansky model in which a singular potential channel is replaced by a regular, below unbounded potential which shrinks as it becomes deeper. We demonstrate that, similarly to the original model, such a system exhibits a spectral transition with respect to the coupling constant, and determine the critical value above which a new spectral branch opens. The result is generalized to situations with multiple potential channels.
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@inproceedings{diana2014a,
  title={A regular version of Smilansky model},
  author={Diana Barseghyan, and Pavel Exner},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020132304037248702},
  booktitle={Journal of Mathematical Physics},
  volume={55},
  number={4},
  pages={042104},
  year={2014},
}
Diana Barseghyan, and Pavel Exner. A regular version of Smilansky model. 2014. Vol. 55. In Journal of Mathematical Physics. pp.042104. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020132304037248702.
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