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Leaky quantum graphs: approximations by point-interaction Hamiltonians

Pavel Exner K Nemcov

TBD mathscidoc:1910.43054

Journal of Physics A: Mathematical and General, 36, (40), 10173, 2003.9
We prove an approximation result showing how operators of the type (x ) in L^ 2 ({\bb R}^ 2), where is a graph, can be modelled in the strong resolvent sense by point-interaction Hamiltonians with an appropriate arrangement of the potentials. The result is illustrated on finding the spectral properties in cases when is a ring or a star. Furthermore, we use this method to indicate that scattering on an infinite curve which is locally close to a loop shape or has multiple bends may exhibit resonances due to quantum tunnelling or repeated reflections.
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@inproceedings{pavel2003leaky,
  title={Leaky quantum graphs: approximations by point-interaction Hamiltonians},
  author={Pavel Exner, and K Nemcov},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020123216295317583},
  booktitle={Journal of Physics A: Mathematical and General},
  volume={36},
  number={40},
  pages={10173},
  year={2003},
}
Pavel Exner, and K Nemcov. Leaky quantum graphs: approximations by point-interaction Hamiltonians. 2003. Vol. 36. In Journal of Physics A: Mathematical and General. pp.10173. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020123216295317583.
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