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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Bibliographic Details
Published inInventiones mathematicae Vol. 217; no. 2; pp. 603 - 701
Main Authors Goldstein, Michael, Schlag, Wilhelm, Voda, Mircea
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2019
Springer Nature B.V
Subjects
Mathematics
Mathematics and Statistics
Operators (mathematics)
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Summary: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