Kubota, Yosuke and Ludewig, Matthias and Thiang, Guo Chuan (2022) Delocalized Spectra of Landau Operators on Helical Surfaces. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 395 (3). pp. 1211-1242. ISSN 0010-3616, 1432-0916
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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.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | QUANTIZED HALL CONDUCTANCE; SCHRODINGER-OPERATORS; INDEX; MODES; |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Bernd Ammann |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 08 Feb 2024 13:13 |
| Last Modified: | 08 Feb 2024 13:13 |
| URI: | https://pred.uni-regensburg.de/id/eprint/57845 |
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