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Approximations of quantum-graph vertex couplings by singularly scaled rank-one operators

Pavel Exner Stepan S Manko

TBD mathscidoc:1910.43160

Letters in Mathematical Physics, 104, (9), 1079-1094, 2014.9
We investigate approximations of the vertex coupling on a star-shaped graph by families of operators with singularly scaled rank-one interactions. We find a family of vertex couplings, generalizing the <i></i>-interaction on the line, and show that with a suitable choice of the parameters they can be approximated in this way in the norm-resolvent sense. We also analyze spectral properties of the involved operators and demonstrate the convergence of the corresponding on-shell scattering matrices.
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@inproceedings{pavel2014approximations,
  title={Approximations of quantum-graph vertex couplings by singularly scaled rank-one operators},
  author={Pavel Exner, and Stepan S Manko},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020131842298240689},
  booktitle={Letters in Mathematical Physics},
  volume={104},
  number={9},
  pages={1079-1094},
  year={2014},
}
Pavel Exner, and Stepan S Manko. Approximations of quantum-graph vertex couplings by singularly scaled rank-one operators. 2014. Vol. 104. In Letters in Mathematical Physics. pp.1079-1094. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020131842298240689.
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