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Non-Weyl resonance asymptotics for quantum graphs in a magnetic field

Pavel Exner Ji Lipovsk

TBD mathscidoc:1910.43136

Physics Letters A, 375, (4), 805-807, 2011.1
We study asymptotical behaviour of resonances for a quantum graph consisting of a finite internal part and external leads placed into a magnetic field, in particular, the question whether their number follows the Weyl law. We prove that the presence of a magnetic field cannot change a non-Weyl asymptotics into a Weyl one and vice versa. On the other hand, we present examples demonstrating that for some non-Weyl graphs the effective size of the graph, and therefore the resonance asymptotics, can be affected by the magnetic field.
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@inproceedings{pavel2011non-weyl,
  title={Non-Weyl resonance asymptotics for quantum graphs in a magnetic field},
  author={Pavel Exner, and Ji Lipovsk},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020131033544388665},
  booktitle={Physics Letters A},
  volume={375},
  number={4},
  pages={805-807},
  year={2011},
}
Pavel Exner, and Ji Lipovsk. Non-Weyl resonance asymptotics for quantum graphs in a magnetic field. 2011. Vol. 375. In Physics Letters A. pp.805-807. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020131033544388665.
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