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
Hauptverfasser: Goldstein, Michael, Schlag, Wilhelm, Voda, Mircea
Format: Artikel
Sprache:eng
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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.
ISSN:0020-9910
1432-1297
DOI:10.1007/s00222-019-00872-7