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Convergence of resonances on thin branched quantum waveguides

Pavel Exner Olaf Post

TBD mathscidoc:1910.43075

Journal of Mathematical Physics, 48, (9), 092104, 2007.9
We prove an abstract criterion stating resolvent convergence in the case of operators acting in different Hilbert spaces. This result is then applied to the case of Laplacians on a family X of branched quantum waveguides. Combining it with an exterior complex scaling we show, in particular, that the resonances on X approximate those of the Laplacian with free boundary conditions on X0, the skeleton graph of X.
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@inproceedings{pavel2007convergence,
  title={Convergence of resonances on thin branched quantum waveguides},
  author={Pavel Exner, and Olaf Post},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020125049543183604},
  booktitle={Journal of Mathematical Physics},
  volume={48},
  number={9},
  pages={092104},
  year={2007},
}
Pavel Exner, and Olaf Post. Convergence of resonances on thin branched quantum waveguides. 2007. Vol. 48. In Journal of Mathematical Physics. pp.092104. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020125049543183604.
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