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 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.
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.