Magnetic transport in a straight parabolic channel

Pavel Exner Alain Joye H Kovarik

TBD mathscidoc:1910.43123

Journal of Physics A: Mathematical and General, 34, (45), 9733, 2001.11
We study a charged two-dimensional particle confined to a straight parabolic-potential channel and exposed to a homogeneous magnetic field under the influence of a potential perturbation W. If W is bounded and periodic along the channel, a perturbative argument yields the absolute continuity of the bottom of the spectrum. We show that it can have any finite number of open gaps provided that the confining potential is sufficiently strong. However, if W depends on the periodic variable only, we prove by the Thomas argument that the whole spectrum is absolutely continuous, irrespective of the size of the perturbation. On the other hand, if W is small and satisfies a weak localization condition in the the longitudinal direction, we prove by the Mourre method that a part of the absolutely continuous spectrum persists.
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@inproceedings{pavel2001magnetic,
  title={Magnetic transport in a straight parabolic channel},
  author={Pavel Exner, Alain Joye, and H Kovarik},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020130650543140652},
  booktitle={Journal of Physics A: Mathematical and General},
  volume={34},
  number={45},
  pages={9733},
  year={2001},
}
Pavel Exner, Alain Joye, and H Kovarik. Magnetic transport in a straight parabolic channel. 2001. Vol. 34. In Journal of Physics A: Mathematical and General. pp.9733. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020130650543140652.
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