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Cantor spectra of magnetic chain graphs

Pavel Exner Daniel Vaata

Spectral Theory and Operator Algebra mathscidoc:1910.43244

Journal of Physics A: Mathematical and Theoretical, 50, (16), 165201, 2017.3
We demonstrate a one-dimensional magnetic system can exhibit a Cantor-type spectrum using an example of a chain graph with coupling at the vertices exposed to a magnetic field perpendicular to the graph plane and varying along the chain. If the field grows linearly with an irrational slope, measured in terms of the flux through the loops of the chain, we demonstrate the character of the spectrum relating it to the almost Mathieu operator.
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@inproceedings{pavel2017cantor,
  title={Cantor spectra of magnetic chain graphs},
  author={Pavel Exner, and Daniel Vaata},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020134538207342773},
  booktitle={Journal of Physics A: Mathematical and Theoretical},
  volume={50},
  number={16},
  pages={165201},
  year={2017},
}
Pavel Exner, and Daniel Vaata. Cantor spectra of magnetic chain graphs. 2017. Vol. 50. In Journal of Physics A: Mathematical and Theoretical. pp.165201. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020134538207342773.
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