Pure point spectrum for the Maryland model: a constructive proof

DOI10.1017/etds.2019.50zbMath1456.37053arXiv1909.12336OpenAlexW3102174417WikidataQ127392189 ScholiaQ127392189MaRDI QIDQ5139074

Fan Yang, Svetlana Ya. Jitomirskaya

Publication date: 4 December 2020

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1909.12336

zbMATH Keywords

Anderson localizationDiophantine frequenciesquasiperiodic operators

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Random dynamical systems aspects of multiplicative ergodic theory, Lyapunov exponents (37H15) Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25)

Related Items (9)

On the spectrum of a non-self-adjoint quasiperiodic operator ⋮ Arithmetic phase transitions for mosaic Maryland model ⋮ Exact mobility edges for 1D quasiperiodic models ⋮ One-dimensional quasiperiodic operators: global theory, duality, and sharp analysis of small denominators ⋮ All couplings localization for quasiperiodic operators with monotone potentials ⋮ Anderson localization for a generalized Maryland model with potentials given by skew shifts ⋮ Perturbative diagonalization for Maryland-type quasiperiodic operators with flat pieces ⋮ Convergence of perturbation series for unbounded monotone quasiperiodic operators ⋮ Anderson localization for long-range operators with singular potentials

Cites Work

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• An exactly solvable model of a multidimensional incommensurate structure
• Almost periodic Schrödinger operators. IV. The Maryland model
• On the multiplicative ergodic theorem for uniquely ergodic systems
• Universal hierarchical structure of quasiperiodic eigenfunctions
• Localization for a family of one-dimensional quasiperiodic operators of magnetic origin
• Metal-insulator transition for the almost Mathieu operator
• An exact renormalization formula for the Maryland model
• Anderson localization for the almost Mathieu operator in the exponential regime
• The Ten Martini problem
• Dynamical Bounds for Quasiperiodic Schrödinger Operators with Rough Potentials
• Arithmetic Spectral Transitions for the Maryland Model
• Shnol’s theorem and the spectrum of long range operators

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