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

V. A. Geyler·P. Stovicek
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Abstract

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 flux carried by the solenoids.

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V. A. Geyler, P. Stovicek. 2005-09-01. Zero modes in a system of Aharonov--Bohm solenoids on the Lobachevsky plane. https://doi.org/10.1088/0305-4470%2F39%2F6%2F011

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