Anomalous electron trapping by localized magnetic fields

Francois Bentosela RM Cavalcanti Pavel Exner VA Zagrebnov

TBD mathscidoc:1910.43111

Journal of Physics A: Mathematical and General, 32, (16), 3029, 1999.4
We consider an electron with an anomalous magnetic moment g> 2 confined to a plane and interacting with a non-zero magnetic field B perpendicular to the plane. We show that if B has compact support and the magnetic flux in natural units is, the corresponding Pauli Hamiltonian has at least bound states, without making any assumptions about the field profile. Furthermore, in the zero-flux case there is a pair of bound states with opposite spin orientations. Using a Birman-Schwinger technique, we extend the last claim to a weak rotationally symmetric field with, thus correcting a recent result. Finally, we show that under mild regularity assumptions existence of the bound states can also be proved for non-symmetric fields with tails.
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@inproceedings{francois1999anomalous,
  title={Anomalous electron trapping by localized magnetic fields},
  author={Francois Bentosela, RM Cavalcanti, Pavel Exner, and VA Zagrebnov},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020130226604044640},
  booktitle={Journal of Physics A: Mathematical and General},
  volume={32},
  number={16},
  pages={3029},
  year={1999},
}
Francois Bentosela, RM Cavalcanti, Pavel Exner, and VA Zagrebnov. Anomalous electron trapping by localized magnetic fields. 1999. Vol. 32. In Journal of Physics A: Mathematical and General. pp.3029. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020130226604044640.
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