Gaplessness of Landau Hamiltonians on Hyperbolic Half-planes via Coarse Geometry
Matthias Ludewig, Guo Chuan Thiang
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.
Topics & Concepts
Hyperbolic geometryLandau quantizationEuclidean geometryHamiltonian (control theory)Ultraparallel theoremGeometryHyperbolic trianglePhysicsMathematicsEnhanced Data Rates for GSM EvolutionHyperbolic spaceMathematical physicsQuantum mechanicsDifferential geometryMathematical optimizationMagnetic fieldComputer scienceTelecommunicationsAdvanced Operator Algebra ResearchNoncommutative and Quantum Gravity TheoriesAlgebraic structures and combinatorial models