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arxiv: 1708.09711 · v1 · pith:DNRYMWGRnew · submitted 2017-08-31 · 🧮 math.SP · math-ph· math.MP

On the Spectrum of Multi-Frequency Quasiperiodic Schr\"odinger Operators with Large Coupling

classification 🧮 math.SP math-phmath.MP
keywords spectrumintervallargemulti-frequencyoperatorsquasiperiodicschranalytic
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We study multi-frequency quasiperiodic Schr\"{o}dinger operators on $\mathbb{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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