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Large gaps in point-coupled periodic systems of manifolds

Jochen Brning Pavel Exner Vladimir A Geyler

TBD mathscidoc:1910.43060

Journal of Physics A: Mathematical and General, 36, (17), 4875, 2003.4
We study a free quantum motion on periodically structured manifolds composed of elementary two-dimensional'cells' connected either by linear segments or through points where the two cells touch. The general theory is illustrated with numerous examples in which the elementary components are spherical surfaces arranged into chains in a straight or zigzag way, or two-dimensional square lattice'carpets'. We show that the spectra of such systems have an infinite number of gaps and that the latter dominate the spectrum at high energies.
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@inproceedings{jochen2003large,
  title={Large gaps in point-coupled periodic systems of manifolds},
  author={Jochen Brning, Pavel Exner, and Vladimir A Geyler},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020123516285280589},
  booktitle={Journal of Physics A: Mathematical and General},
  volume={36},
  number={17},
  pages={4875},
  year={2003},
}
Jochen Brning, Pavel Exner, and Vladimir A Geyler. Large gaps in point-coupled periodic systems of manifolds. 2003. Vol. 36. In Journal of Physics A: Mathematical and General. pp.4875. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020123516285280589.
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