Zero modes in a system of Aharonov-Bohm solenoids on the Lobachevsky planeReport as inadecuate



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


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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.



Author: V. A. Geyler; P. Stovicek

Source: https://archive.org/







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