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Magnetoresonances on a lasso graph

Pavel Exner

TBD mathscidoc:1910.43077

Foundations of Physics, 27, (2), 171, 1997.2
We consider a charged spinless quantum particle confined to a graph consisting of a loop to which a halfline lead is attached; this system is placed into a homogeneous magnetic field perpendicular to the loop plane. We derive the reflection amplitude and show that there is an infinite ladder of resonances; analyzing the resonance pole trajectories, we show that half of them turn into true embedded eigenvalues provided the flux through the loop is an integer or half-integer multiple of the flux unit hc/e. We also describe a general method to solve the scattering problem on graphs of which the present model is a simple particular case. Finally, we discuss ways in which a state localized initially at the loop decays.
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@inproceedings{pavel1997magnetoresonances,
  title={Magnetoresonances on a lasso graph},
  author={Pavel Exner},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020125125857226606},
  booktitle={Foundations of Physics},
  volume={27},
  number={2},
  pages={171},
  year={1997},
}
Pavel Exner. Magnetoresonances on a lasso graph. 1997. Vol. 27. In Foundations of Physics. pp.171. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020125125857226606.
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