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Approximations of singular vertex couplings in quantum graphs

Pavel Exner ONDEJ TUREK

TBD mathscidoc:1910.43068

Reviews in Mathematical Physics, 19, (06), 571-606, 2007.7
We discuss approximations of the vertex coupling on a star-shaped quantum graph of n edges in the singular case when the wave functions are not continuous at the vertex and no edge-permutation symmetry is present. It is shown that the CheonShigehara technique using interactions with nonlinearly scaled couplings yields a 2n-parameter family of boundary conditions in the sense of norm resolvent topology. Moreover, using graphs with additional edges, one can approximate the {n+1\choose 2}-parameter family of all time-reversal invariant couplings.
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@inproceedings{pavel2007approximations,
  title={Approximations of singular vertex couplings in quantum graphs},
  author={Pavel Exner, and ONDEJ TUREK},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020123837066870597},
  booktitle={Reviews in Mathematical Physics},
  volume={19},
  number={06},
  pages={571-606},
  year={2007},
}
Pavel Exner, and ONDEJ TUREK. Approximations of singular vertex couplings in quantum graphs. 2007. Vol. 19. In Reviews in Mathematical Physics. pp.571-606. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020123837066870597.
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