Zero modes in a system of Aharonov–Bohm solenoids on the Lobachevsky plane

@article{Geyler2005ZeroMI,
  title={Zero modes in a system of Aharonov–Bohm solenoids on the Lobachevsky plane},
  author={Vladimir A. Geyler and Pavel {\vS}ťov{\'i}{\vc}ek},
  journal={Journal of Physics A},
  year={2005},
  volume={39},
  pages={1375-1384}
}
We consider a spin 1/2 charged particle on the Lobachevsky plane subjected to a magnetic field corresponding to a discrete system of Aharonov–Bohm solenoids. Let H+ and H− be the two components of the Pauli operator for spin-up and -down, respectively. We show that neither H+ nor H− has a zero mode if the number of solenoids is finite. On the other hand, a construction is described of an infinite periodic system of solenoids for which either H+ or H− has zero modes depending on the value of the… 
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