On the absolutely continuous spectrum of one-dimensional quasi-periodic Schrödinger operators in the adiabatic limit

DOI10.1090/S0002-9947-05-03961-9zbMath1101.34069OpenAlexW1689150727MaRDI QIDQ5461393

Frédéric Klopp, Alexander Fedotov

Publication date: 26 July 2005

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-05-03961-9

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Spectrum, resolvent (47A10) General theory of ordinary differential operators (47E05) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Singular perturbations, turning point theory, WKB methods for ordinary differential equations (34E20) Singular perturbation problems for ordinary differential equations in the complex domain (complex WKB, turning points, steepest descent) (34M60)

Related Items

Monodromization method in the theory of almost-periodic equations, On the singular spectrum for adiabatic quasiperiodic Schrödinger operators, Spectral characteristics of Schrödinger operators generated by product systems, Complex WKB method (one-dimensional linear problems on the complex plane), Extended States for the Schrödinger Operator with Quasi-periodic Potential in Dimension Two, Multiscale analysis in momentum space for quasi-periodic potential in dimension two, Adiabatic almost-periodic Schrödinger operators, Complex WKB method for adiabatic perturbations of a periodic Schrödinger operator, WKB asymptotics of meromorphic solutions to difference equations, Strong resonant tunneling, level repulsion and spectral type for one-dimensional adiabatic quasi-periodic Schrödinger operators, Extended states for polyharmonic operators with quasi-periodic potentials in dimension two

Cites Work

• A metal-insulator transition for the almost Mathieu model
• Floquet solutions for the 1-dimensional quasi-periodic Schrödinger equation
• The spectrum of Hill's equation
• Anderson transitions for a family of almost periodic Schrödinger equations in the adiabatic case
• Reducibility or nonuniform hyperbolicity for quasiperiodic Schrödinger cocycles
• A CHARACTERIZATION OF THE SPECTRUM OF HILL'S OPERATOR
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