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Open quantum dots: resonances from perturbed symmetry and bound states in strong magnetic fields

Pierre Duclos Pavel Exner Bernhard Meller

TBD mathscidoc:1910.43064

Reports on Mathematical Physics, 47, (2), 253-267, 2001.4
We discuss the Nckel model of an open quantum dot, i.e. a straight hard-wall channel with a potential well. If this potential depends on the longitudinal variable only, there are embedded eigenvalues which turn into resonances if the symmetry is violated, either by applying a magnetic field or by deformation of the well. For a weak symmetry breaking we derive the perturbative expansion of these resonances. We also deduce a sufficient condition under which the discrete spectrum of such a system (without any symmetry) survives the presence of a strong magnetic field. It is satisfied, in particular, if the dot potential is purely attractive.
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@inproceedings{pierre2001open,
  title={Open quantum dots: resonances from perturbed symmetry and bound states in strong magnetic fields},
  author={Pierre Duclos, Pavel Exner, and Bernhard Meller},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020123726536367593},
  booktitle={Reports on Mathematical Physics},
  volume={47},
  number={2},
  pages={253-267},
  year={2001},
}
Pierre Duclos, Pavel Exner, and Bernhard Meller. Open quantum dots: resonances from perturbed symmetry and bound states in strong magnetic fields. 2001. Vol. 47. In Reports on Mathematical Physics. pp.253-267. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020123726536367593.
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