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Avoided crossings in mesoscopic systems: Electron propagation on a nonuniform magnetic cylinder

Pavel Exner Alain Joye

TBD mathscidoc:1910.43203

Journal of Mathematical Physics, 42, (10), 4707-4738, 2001.10
We consider an electron constrained to move on a surface with revolution symmetry in the presence of a constant magnetic field B parallel to the surface axis. Depending on B and the surface geometry the transverse part of the spectrum typically exhibits many crossings which change to avoided crossings if a weak symmetry breaking interaction is introduced. We study the effect of such perturbations on the quantum propagation. This problem admits a natural reformulation to which tools from molecular dynamics can be applied. In turn, this leads to the study of a perturbation theory for the time dependent BornOppenheimer approximation.
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@inproceedings{pavel2001avoided,
  title={Avoided crossings in mesoscopic systems: Electron propagation on a nonuniform magnetic cylinder},
  author={Pavel Exner, and Alain Joye},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020133232466397732},
  booktitle={Journal of Mathematical Physics},
  volume={42},
  number={10},
  pages={4707-4738},
  year={2001},
}
Pavel Exner, and Alain Joye. Avoided crossings in mesoscopic systems: Electron propagation on a nonuniform magnetic cylinder. 2001. Vol. 42. In Journal of Mathematical Physics. pp.4707-4738. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020133232466397732.
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