Singular continuous spectrum for singular potentials

DOI10.1007/s00220-016-2823-4zbMath1422.47036arXiv1604.04907OpenAlexW3101424298MaRDI QIDQ521986

Fan Yang, Svetlana Ya. Jitomirskaya

Publication date: 12 April 2017

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

Full work available at URL: https://arxiv.org/abs/1604.04907

zbMATH Keywords

Schrödinger operatorLyapunov exponentsingular continuous spectrumalmost Mathieu operatorMaryland model

Mathematics Subject Classification ID

Applications of operator theory in the physical sciences (47N50) Spectrum, resolvent (47A10) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Schrödinger operator, Schrödinger equation (35J10) Discrete version of topics in analysis (39A12) Linear difference operators (47B39)

Related Items (11)

Full measure reducibility and localization for quasiperiodic Jacobi operators: a topological criterion ⋮ Continuous quasiperiodic Schrödinger operators with Gordon type potentials ⋮ Arithmetic phase transitions for mosaic Maryland model ⋮ Singular continuous spectrum and generic full spectral/packing dimension for unbounded quasiperiodic Schrödinger operators ⋮ Spectral dimension for \(\beta\)-almost periodic singular Jacobi operators and the extended Harper's model ⋮ Second phase transition line ⋮ Absence of eigenvalues for quasiperiodic Schrödinger type operators ⋮ Localization for quasiperiodic operators with unbounded monotone potentials ⋮ 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

• Almost localization and almost reducibility
• Operators with singular continuous spectrum. III: Almost periodic Schrödinger operators
• Sharp phase transitions for the almost Mathieu operator
• Universal hierarchical structure of quasiperiodic eigenfunctions
• Trace class perturbations and the absence of absolutely continuous spectra
• Metal-insulator transition for the almost Mathieu operator
• The Ten Martini problem
• Dynamics and spectral theory of quasi-periodic Schrödinger-type operators
• Arithmetic Spectral Transitions for the Maryland Model
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