Zero modes in a system of Aharonov--Bohm solenoids on the Lobachevsky plane
Geyler, V. A. · Stovicek, P.
Original · EN
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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