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Approximations by graphs and emergence of global structures

Pavel Exner Pavel Hejcik Petr Seba

TBD mathscidoc:1910.43183

arXiv preprint quant-ph/0508226, 2005.8
We study approximations of billiard systems by lattice graphs. It is demonstrated that under natural assumptions the graph wavefunctions approximate solutions of the Schroedinger equation with energy rescaled by the billiard dimension. As an example, we analyze a Sinai billiard with attached leads. The results illustrate emergence of global structures in large quantum graphs and offer interesting comparisons with patterns observed in complex networks of a different nature.
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@inproceedings{pavel2005approximations,
  title={Approximations by graphs and emergence of global structures},
  author={Pavel Exner, Pavel Hejcik, and Petr Seba},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020132605432197712},
  booktitle={arXiv preprint quant-ph/0508226},
  year={2005},
}
Pavel Exner, Pavel Hejcik, and Petr Seba. Approximations by graphs and emergence of global structures. 2005. In arXiv preprint quant-ph/0508226. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020132605432197712.
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