Gaplessness of Landau Hamiltonians on Hyperbolic Half-planes via Coarse Geometry

Abstract

Abstract We use coarse index methods to prove that the Landau Hamiltonian on the hyperbolic half-plane, and even on much more general imperfect half-spaces, has no spectral gaps. Thus the edge states of hyperbolic quantum Hall Hamiltonians completely fill up the gaps between Landau levels, just like those of the Euclidean counterparts.

Locations

• Communications in Mathematical Physics - View - PDF
• arXiv (Cornell University) - View - PDF
• University of Regensburg Publication Server (University of Regensburg) - View - PDF
• Adelaide Research & Scholarship (AR&S) (University of Adelaide) - View - PDF
• DataCite API - View