On the hierarchical behavior of solutions of the Maryland equation in the semiclassical approximation

DOI10.1134/S0001434620110346zbMath1454.81067OpenAlexW3112993193MaRDI QIDQ2217293

Yanyan Li

Publication date: 29 December 2020

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0001434620110346

zbMATH Keywords

semiclassical approximationquasiperiodic Schrödinger equationhierarchical behavior of solutions

Mathematics Subject Classification ID

Hierarchical systems (93A13) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Discrete version of topics in analysis (39A12) Periodic and quasi-periodic flows and diffeomorphisms (37C55) Linear difference equations (39A06)

Related Items (2)

Complex WKB method (one-dimensional linear problems on the complex plane) ⋮ One-dimensional quasiperiodic operators: global theory, duality, and sharp analysis of small denominators

Cites Work

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• Almost periodic Schrödinger operators. IV. The Maryland model
• Universal hierarchical structure of quasiperiodic eigenfunctions
• Anderson localization for one-dimensional difference Schrödinger operator with quasiperiodic potential
• Quantum group and magnetic translations Bethe ansatz for the Asbel-Hofstadter problem
• An exact renormalization formula for the Maryland model
• Monodromization method in the theory of almost-periodic equations
• Analyse semi-classique pour l'équation de Harper (avec application à l'équation de Schrödinger avec champ magnétique)
• Complex WKB method for a difference Schrödinger equation with the potential being a trigonometric polynomial
• The Complex WKB Method for Difference Equations and Airy Functions
• Arithmetic Spectral Transitions for the Maryland Model

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