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Spectral and resonance properties of the Smilansky Hamiltonian

Pavel Exner Vladimir Lotoreichik Milo Tater

Spectral Theory and Operator Algebra mathscidoc:1910.43245

Physics Letters A, 381, (8), 756-761, 2017.2
We analyze the Hamiltonian proposed by Smilansky to describe irreversible dynamics in quantum graphs and studied further by Solomyak and others. We derive a weak-coupling asymptotics of the ground state and add new insights by finding the discrete spectrum numerically in the subcritical case. Furthermore, we show that the model then has a rich resonance structure.
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@inproceedings{pavel2017spectral,
  title={Spectral and resonance properties of the Smilansky Hamiltonian},
  author={Pavel Exner, Vladimir Lotoreichik, and Milo Tater},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020134553905493774},
  booktitle={Physics Letters A},
  volume={381},
  number={8},
  pages={756-761},
  year={2017},
}
Pavel Exner, Vladimir Lotoreichik, and Milo Tater. Spectral and resonance properties of the Smilansky Hamiltonian. 2017. Vol. 381. In Physics Letters A. pp.756-761. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020134553905493774.
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