Spectral gaps of almost Mathieu operators in the exponential regime

DOI10.4171/JFG/15zbMath1410.47003arXiv1311.0658MaRDI QIDQ2344486

Wencai Liu, Xiao Ping Yuan

Publication date: 15 May 2015

Published in: Journal of Fractal Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1311.0658

zbMATH Keywords

reducibilityalmost Mathieu operatorAubry dualityten Martini problem

Mathematics Subject Classification ID

Ergodic theory of linear operators (47A35) Spectrum, resolvent (47A10)

Related Items (7)

Quantitative reducibility of Gevrey quasi-periodic cocycles and its applications ⋮ Almost Mathieu operators with completely resonant phases ⋮ Central spectral gaps of the almost Mathieu operator ⋮ Polynomial decay of the gap length for \(C^k\) quasi-periodic Schrödinger operators and spectral application ⋮ Anderson localization for the completely resonant phases ⋮ Hölder continuity of the spectral measures for one-dimensional Schrödinger operator in exponential regime ⋮ Exponential decay of the lengths of the spectral gaps for the extended Harper's model with a Liouvillean frequency

Cites Work

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• Almost periodic Schrödinger operators. II: The integrated density of states
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• Sharp phase transitions for the almost Mathieu operator
• The Ten Martini problem
• Reducibility or nonuniform hyperbolicity for quasiperiodic Schrödinger cocycles
• Absolute continuity of the integrated density of states for the almost Mathieu operator with non-critical coupling
• Singular continuous spectrum for a class of almost periodic Jacobi matrices
• Analysis of the spectrum of a particle on a triangular lattice with two magnetic fluxes by algebraic and numerical methods
• Green's Function Estimates for Lattice Schrodinger Operators and Applications. (AM-158)

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