Anderson localization for the almost Mathieu equation: A nonperturbative proof

DOI10.1007/BF02099736zbMath0830.34072OpenAlexW2028518198MaRDI QIDQ1344511

Svetlana Ya. Jitomirskaya

Publication date: 14 January 1996

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02099736

zbMATH Keywords

pure point spectrumalmost Mathieu operator

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40)

Related Items

Discrete magnetic Laplacian, Operators with singular continuous spectrum. III: Almost periodic Schrödinger operators, Anderson localization for the almost Mathieu equation. II: Point spectrum for \(\lambda > 2\), Special nonuniform lattice (snul) orthogonal polynomials on discrete dense sets of points, Duality and singular continuous spectrum in the almost Mathieu equation, Singular continuous spectrum is generic, Discrete one-dimensional quasi-periodic Schrödinger operators with pure point spectrum, Localization and regularity of the integrated density of states for Schrödinger operators on \(\mathbb{Z}^d\) with \(C^2\)-cosine like quasi-periodic potential, Spectral theory of the multi-frequency quasi-periodic operator with a Gevrey type perturbation, Schrödinger operators with dynamically defined potentials, Quantitative inductive estimates for Green's functions of non-self-adjoint matrices, One-dimensional quasiperiodic operators: global theory, duality, and sharp analysis of small denominators, Localization in one-dimensional quasi-periodic nonlinear systems, Reducibility of one-dimensional quasi-periodic Schrödinger equations, Dimensional Hausdorff Properties of Singular Continuous Spectra, STRONG DYNAMICAL LOCALIZATION FOR THE ALMOST MATHIEU MODEL, Large deviations of the Lyapunov exponent and localization for the 1D Anderson model, Anderson localization for multi-frequency quasi-periodic operators on \(\mathbb{Z}^d\), Measurable enumeration of eigenelements, The arithmetic version of the frequency transition conjecture: new proof and generalization, Dimensional Hausdorff Properties of Singular Continuous Spectra

Cites Work

• Unnamed Item
• Unnamed Item
• Purely absolutely continuous spectrum for almost Mathieu operators
• Localization for a class of one dimensional quasi-periodic Schrödinger operators
• On the measure of the spectrum for the almost Mathieu operator
• Almost periodic Schrödinger operators. II: The integrated density of states
• A new proof of localization in the Anderson tight binding model
• Constructive proof of localization in the Anderson tight binding model
• A relation between a.c. spectrum of ergodic Jacobi matrices and the spectra of periodic approximants
• Anderson localization for one-dimensional difference Schrödinger operator with quasiperiodic potential
• The positivity of the Lyapunov exponent and the absence of the absolutely continuous spectrum for the almost-Mathieu equation
• Absence of localisation in the almost Mathieu equation