On the spectrum of multi-frequency quasiperiodic Schrödinger operators with large coupling
We study multi-frequency quasiperiodic Schrödinger operators on Z . We prove that for a large real analytic potential satisfying certain restrictions the spectrum consists of a single interval. The result is a consequence of a criterion for the spectrum to contain an interval at a given location tha...
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Veröffentlicht in: | Inventiones mathematicae 2019-08, Vol.217 (2), p.603-701 |
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Hauptverfasser: | , , |
Format: | Artikel |
Sprache: | eng |
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Online-Zugang: | Volltext |
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Zusammenfassung: | We study multi-frequency quasiperiodic Schrödinger operators on
Z
. We prove that for a large real analytic potential satisfying certain restrictions the spectrum consists of a single interval. The result is a consequence of a criterion for the spectrum to contain an interval at a given location that we establish non-perturbatively in the regime of positive Lyapunov exponent. |
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ISSN: | 0020-9910 1432-1297 |
DOI: | 10.1007/s00222-019-00872-7 |