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On the spectrum of a bent chain graph

Pierre Duclos Pavel Exner Ondej Turek

TBD mathscidoc:1910.43074

Journal of Physics A: Mathematical and Theoretical, 41, (41), 415206, 2008.9
We study Schrdinger operators on an infinite quantum graph of a chain form which consists of identical rings connected at the touching points by -couplings with a parameter\alpha\in {\bb R}. If the graph is' straight', ie periodic with respect to ring shifts, its Hamiltonian has a band spectrum with all the gaps open whenever 0. We consider a'bending'deformation of the chain consisting of changing one position at a single ring and show that it gives rise to eigenvalues in the open spectral gaps. We analyze dependence of these eigenvalues on the coupling and the'bending angle'as well as resonances of the system coming from the bending. We also discuss the behaviour of the eigenvalues and resonances at the edges of the spectral bands.
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@inproceedings{pierre2008on,
  title={On the spectrum of a bent chain graph},
  author={Pierre Duclos, Pavel Exner, and Ondej Turek},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020125032060156603},
  booktitle={Journal of Physics A: Mathematical and Theoretical},
  volume={41},
  number={41},
  pages={415206},
  year={2008},
}
Pierre Duclos, Pavel Exner, and Ondej Turek. On the spectrum of a bent chain graph. 2008. Vol. 41. In Journal of Physics A: Mathematical and Theoretical. pp.415206. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020125032060156603.
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