On the Spectrum of Multi-Frequency Quasiperiodic Schrödinger Operators with Large Coupling

Michael Goldstein; Wilhelm Schlag; Mircea Voda

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arXiv · 1708.09711

On the Spectrum of Multi-Frequency Quasiperiodic Schrödinger Operators with Large Coupling

Michael Goldstein·Wilhelm Schlag·Mircea Voda

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Abstract

We study multi-frequency quasiperiodic Schrödinger 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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BibTeX RIS

Michael Goldstein, Wilhelm Schlag, Mircea Voda. 2017-08-31. On the Spectrum of Multi-Frequency Quasiperiodic Schrödinger Operators with Large Coupling. https://arxiv.org/abs/1708.09711

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