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Inverse scattering problem for quantum graph vertices

Taksu Cheon Pavel Exner Ondej Turek

TBD mathscidoc:1910.43201

Physical Review A, 83, (6), 062715, 2011.6
We demonstrate how the inverse scattering problem of a quantum star graph can be solved by means of diagonalization of the Hermitian unitary matrix when the vertex coupling is of the scale-invariant (or Flp-Tsutsui) form. This enables the construction of quantum graphs with desired properties in a tailor-made fashion. The procedure is illustrated on the example of quantum vertices with equal transmission probabilities.
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@inproceedings{taksu2011inverse,
  title={Inverse scattering problem for quantum graph vertices},
  author={Taksu Cheon, Pavel Exner, and Ondej Turek},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020133133706427730},
  booktitle={Physical Review A},
  volume={83},
  number={6},
  pages={062715},
  year={2011},
}
Taksu Cheon, Pavel Exner, and Ondej Turek. Inverse scattering problem for quantum graph vertices. 2011. Vol. 83. In Physical Review A. pp.062715. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020133133706427730.
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