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High-energy asymptotics of the spectrum of a periodic square lattice quantum graph

Pavel Exner Ondej Turek

TBD mathscidoc:1910.43210

Journal of Physics A: Mathematical and Theoretical, 43, (47), 474024, 2010.11
We investigate a periodic quantum graph in the form of a square lattice with a general self-adjoint coupling at the vertices. We analyse the spectrum's high-energy behaviour. Depending on the coupling type, bands and gaps have different asymptotics. Bands may be flat even if the edges are coupled, and non-flat band widths may behave like\mathcal O (n^ j),\, j= 1, 0,-1,-2,-3, as the band index n. The gaps may be of asymptotically constant width or linearly growing with the latter case being generic.
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@inproceedings{pavel2010high-energy,
  title={High-energy asymptotics of the spectrum of a periodic square lattice quantum graph},
  author={Pavel Exner, and Ondej Turek},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020133433549416739},
  booktitle={Journal of Physics A: Mathematical and Theoretical},
  volume={43},
  number={47},
  pages={474024},
  year={2010},
}
Pavel Exner, and Ondej Turek. High-energy asymptotics of the spectrum of a periodic square lattice quantum graph. 2010. Vol. 43. In Journal of Physics A: Mathematical and Theoretical. pp.474024. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020133433549416739.
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