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Quantum networks modelled by graphs

Pavel Exner Olaf Post

TBD mathscidoc:1910.43170

AIP Conference Proceedings, 998, (1), 1-17, 2008.4
Quantum networks are often modelled using Schrdinger operators on metric graphs. To give meaning to such models one has to know how to interpret the boundary conditions which match the wave functions at the graph vertices. In this article we give a survey, technically not too heavy, of several recent results which serve this purpose. Specifically, we consider approximations by means of fat graphsin other words, suitable families of shrinking manifoldsand discuss convergence of the spectra and resonances in such a setting.
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@inproceedings{pavel2008quantum,
  title={Quantum networks modelled by graphs},
  author={Pavel Exner, and Olaf Post},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020132154062042699},
  booktitle={AIP Conference Proceedings},
  volume={998},
  number={1},
  pages={1-17},
  year={2008},
}
Pavel Exner, and Olaf Post. Quantum networks modelled by graphs. 2008. Vol. 998. In AIP Conference Proceedings. pp.1-17. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020132154062042699.
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