Floquet solutions for the Schrödinger equation with fast-oscillating quasi-periodic potentials

DOI10.3934/DCDS.2021047zbMath1482.37063OpenAlexW3138445712MaRDI QIDQ2042891

Yingte Sun

Publication date: 22 July 2021

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.2021047

zbMATH Keywords

reducibilityKAM theoryFloquet solutions

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Asymptotic properties of solutions to ordinary differential equations (34D05)

Cites Work

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• An extension of a result by Dinaburg and Sinai on quasi-periodic potentials
• Floquet solutions for the 1-dimensional quasi-periodic Schrödinger equation
• The one-dimensional Schrödinger equation with a quasiperiodic potential
• Anderson transitions for a family of almost periodic Schrödinger equations in the adiabatic case
• Periodic driving at high frequencies of an impurity in the isotropic XY chain
• Reducibility for a fast-driven linear Klein-Gordon Equation
• Forced vibrations via Nash-Moser iteration
• Reducibility of 1-d Schrödinger equation with time quasiperiodic unbounded perturbations. I
• Reducibility of Schrödinger equation at high frequencies
• A note on the extension of the Dinaburg–Sinai theorem to higher dimension

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