Zero modes in a system of Aharonov--Bohm solenoids on the Lobachevsky plane
Mathematical Physics
2009-11-11 v1 math.MP
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 and be the two components of the Pauli operator for spin up and down, respectively. We show that neither nor 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 or has zero modes depending on the value of the flux carried by the solenoids.
Cite
@article{arxiv.math-ph/0509001,
title = {Zero modes in a system of Aharonov--Bohm solenoids on the Lobachevsky plane},
author = {V. A. Geyler and P. Stovicek},
journal= {arXiv preprint arXiv:math-ph/0509001},
year = {2009}
}