%0 Journal Article
%T Zero modes in a system of Aharonov--Bohm solenoids on the Lobachevsky plane
%A V. A. Geyler
%A P. Stovicek
%J Mathematics
%D 2005
%I arXiv
%R 10.1088/0305-4470/39/6/011
%X 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.
%U http://arxiv.org/abs/math-ph/0509001v1