Upper bounds on the spectral gaps of quasi-periodic Schrödinger operators with Liouville frequencies

Abstract

We prove that the size of the spectral gaps of weakly coupled quasi-periodic Schrödinger operators with Liouville frequencies decays exponentially. As an application, we obtain the homogeneity of the spectrum.

JST to appear

References in corpus (6)

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• Universal reflective-hierarchical structure of quasiperiodic eigenfunctions and sharp spectral transition in phase
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Cited by in corpus (7)

• Quantitative inductive estimates for Green's functions of non-self-adjoint matrices
• On the abominable properties of the almost Mathieu operator with well approximated frequencies
• Almost Mathieu operators with completely resonant phases
• Exponential Decay of the lengths of Spectral Gaps for Extended Harper's Model with Liouvillean Frequency
• Polynomial decay of the gap length for C^k quasi-periodic Schrodinger operators and spectral application
• Hölder continuity of the integrated density of states for Extended Harper's Model with Liouville frequency
• Quantitative reducibility of Gevrey quasi-periodic cocycles and its applications