Spectra of soft ring graphs

Pavel Exner M Tater

TBD mathscidoc:1910.43121

Waves in Random Media, 14, (1), S47-60, 2004.1
We discuss a ring-shaped soft quantum wire modelled by interaction supported by the ring with a generally nonconstant coupling strength. We derive the condition which determines the discrete spectrum of such systems, and analyse the dependence of the eigenvalues and eigenfunctions on the coupling and ring geometry. In particular, we illustrate that a random component in the coupling leads to a localization. The discrete spectrum is also investigated in the situation when the ring is placed into a homogeneous magnetic field or threaded by an AharonovBohm flux and the system exhibits persistent currents.
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@inproceedings{pavel2004spectra,
  title={Spectra of soft ring graphs},
  author={Pavel Exner, and M Tater},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020130617118357650},
  booktitle={Waves in Random Media},
  volume={14},
  number={1},
  pages={S47-60},
  year={2004},
}
Pavel Exner, and M Tater. Spectra of soft ring graphs. 2004. Vol. 14. In Waves in Random Media. pp.S47-60. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020130617118357650.
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