Strong resonant tunneling, level repulsion and spectral type for one-dimensional adiabatic quasi-periodic Schrödinger operators

DOI10.1016/j.ansens.2005.10.002zbMath1112.47038OpenAlexW2000028639MaRDI QIDQ3413462

Alexander Fedotov, Frédéric Klopp

Publication date: 7 December 2006

Published in: Annales Scientifiques de l’École Normale Supérieure (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=ASENS_2005_4_38_6_889_0

zbMATH Keywords

spectral gapsingular spectrumresonant tunnelingquasi-periodic Schrödinger operator

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Applications of operator theory in the physical sciences (47N50) Spectrum, resolvent (47A10) General theory of ordinary differential operators (47E05) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10)

Related Items (10)

Monodromization method in the theory of almost-periodic equations ⋮ Complex WKB method (one-dimensional linear problems on the complex plane) ⋮ Extended States for the Schrödinger Operator with Quasi-periodic Potential in Dimension Two ⋮ Energy splitting in dynamical tunneling ⋮ Multiscale analysis in momentum space for quasi-periodic potential in dimension two ⋮ An exact renormalization formula for the Maryland model ⋮ Adiabatic almost-periodic Schrödinger operators ⋮ Complex WKB method for adiabatic perturbations of a periodic Schrödinger operator ⋮ Difference equations in the complex plane: quasiclassical asymptotics and Berry phase ⋮ Extended states for polyharmonic operators with quasi-periodic potentials in dimension two

Cites Work

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• On the singular spectrum for adiabatic quasi-periodic Schrödinger operators on the real line
• Une méthode pour minorer les exposants de Lyapounov et quelques exemples montrant le caractère local d'un théorème d'Arnold et de Moser sur le tore de dimension 2
• A metal-insulator transition for the almost Mathieu model
• Almost periodic Schrödinger operators. II: The integrated density of states
• On subordinacy and analysis of the spectrum of one-dimensional Schrödinger operators
• Double wells
• Positive Lyapunov exponents for Schrödinger operators with quasi- periodic potentials
• Hill's operator with finitely many gaps
• The spectrum of Hill's equation
• The one-dimensional Schrödinger equation with a quasiperiodic potential
• Eigenfunctions, transfer matrices, and absolutely continuous spectrum of one-dimensional Schrödinger operators
• Anderson transitions for a family of almost periodic Schrödinger equations in the adiabatic case
• On the difference equations with periodic coefficients
• Instantons, double wells and large deviations
• Multiple wells in the semi-classical limit I
• Weakly resonant tunneling interactions for adiabatic quasi-periodic Schrödinger operators
• Hill’s surfaces and their theta functions
• A CHARACTERIZATION OF THE SPECTRUM OF HILL'S OPERATOR
• On the absolutely continuous spectrum of one-dimensional quasi-periodic Schrödinger operators in the adiabatic limit

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