Zero modes in a system of Aharonov Bohm solenoids on the Lobachevsky plane
Abstract
We consider a spin 1/2 charged particle on the Lobachevsky plane subjected to a magnetic field corresponding to a discrete system of AharonovBohm solenoids. Let H^{+} and H^{} be the two components of the Pauli operator for spinup 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.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 February 2006
 DOI:
 10.1088/03054470/39/6/011
 arXiv:
 arXiv:mathph/0509001
 Bibcode:
 2006JPhA...39.1375G
 Keywords:

 Mathematical Physics;
 Mathematics  Mathematical Physics