Delocalized Spectra of Landau Operators on Helical Surfaces

On a flat surface, the Landau operator, or quantum Hall Hamiltonian, has spectrum a discrete set of infinitely-degenerate Landau levels. We consider surfaces with asymptotically constant curvature away from a possibly non-compact submanifold, the helicoid being our main example. The Landau levels re...

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Bibliographic Details
Published in:Communications in mathematical physics 2022-11, Vol.395 (3), p.1211-1242
Main Authors: Kubota, Yosuke, Ludewig, Matthias, Thiang, Guo Chuan
Format: Article
Language:English
Subjects:
Classical and Quantum Gravitation
Complex Systems
Flat surfaces
Manifolds (mathematics)
Mathematical and Computational Physics
Mathematical Physics
Operators (mathematics)
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Theoretical
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Summary:On a flat surface, the Landau operator, or quantum Hall Hamiltonian, has spectrum a discrete set of infinitely-degenerate Landau levels. We consider surfaces with asymptotically constant curvature away from a possibly non-compact submanifold, the helicoid being our main example. The Landau levels remain isolated, provided the spectrum is considered in an appropriate Hilbert module over the Roe algebra of the surface delocalized away from the submanifold. Delocalized coarse indices may then be assigned to them. As an application, we prove that Landau operators on helical surfaces have no spectral gaps above the lowest Landau level.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-022-04452-4