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Anomalous electron trapping by magnetic flux tubes and electric current vortices

F Bentosela Pavel Exner VA Zagrebnov

TBD mathscidoc:1910.43274

191-196, 1999
We consider an electron with an anomalous magnetic moment, <i>g</i> &gt; &gt; 2, confined to a plane and interacting with a nonhomogeneous magnetic field <i>B</i>, and investigate the corresponding Pauli Hamiltonian. We prove a lower bound on the number of bound states for the case when <i>B</i> is of a compact support and the related flux is <i>N</i> + <i></i>, <i></i>(0, 1]. In particular, there are at least <i>N</i> + 1 bound states if <i>B</i> does not change sign. We also consider the situation where the magnetic field is due to a localized rotationally symmetric electric current vortex in the plane. In this case the flux is zero; there is a pair of bound states for a weak coupling, and higher orbital-momentum spin-down states appearing as the current strength increases.
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@inproceedings{f1999anomalous,
  title={Anomalous electron trapping by magnetic flux tubes and electric current vortices},
  author={F Bentosela, Pavel Exner, and VA Zagrebnov},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020135502275230803},
  pages={191-196},
  year={1999},
}
F Bentosela, Pavel Exner, and VA Zagrebnov. Anomalous electron trapping by magnetic flux tubes and electric current vortices. 1999. pp.191-196. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020135502275230803.
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