Reducibility of Schrödinger equation at high frequencies

DOI10.1063/1.5125120zbMath1452.81107OpenAlexW3037946137MaRDI QIDQ5136161

Yingte Sun

Publication date: 25 November 2020

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

Full work available at URL: https://doi.org/10.1063/1.5125120

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05)

Related Items (2)

Reducibility for a linear wave equation with Sobolev smooth fast-driven potential ⋮ Floquet solutions for the Schrödinger equation with fast-oscillating quasi-periodic potentials

Cites Work

• Unnamed Item
• Unnamed Item
• On time dependent Schrödinger equations: global well-posedness and growth of Sobolev norms
• Reducibility of 1-d Schrödinger equation with time quasiperiodic unbounded perturbations. II
• KAM for the quantum harmonic oscillator
• On reducibility of Schrödinger equations with quasiperiodic in time potentials
• Schrödinger operator with a nonlocal potential whose absolutely continuous and point spectra coexist
• Unified theory of nuclear reactions
• Pure point spectrum of the Floquet Hamiltonian for the quantum harmonic oscillator under time quasi-periodic perturbations
• Existence and completeness of the wave operators in scattering theory with momentum-dependent potentials
• Nearly integrable infinite-dimensional Hamiltonian systems
• Reducibility of first order linear operators on tori via Moser's theorem
• Reducibility of the quantum harmonic oscillator in \(d\)-dimensions with polynomial time-dependent perturbation
• On reducibility of 1d wave equation with quasiperiodic in time potentials
• Periodic driving at high frequencies of an impurity in the isotropic XY chain
• On reducibility of quantum harmonic oscillator on \(\mathbb{R}^d\) with quasiperiodic in time potential
• Reducibility for a fast-driven linear Klein-Gordon Equation
• Lower bounds on the growth of Sobolev norms in some linear time dependent Schrödinger equations
• Reducibility of non-resonant transport equation on \({\mathbb {T}}^d\) with unbounded perturbations
• Reducibility for wave equations of finitely smooth potential with periodic boundary conditions
• Forced vibrations via Nash-Moser iteration
• Spectrum for quantum duffing oscillator and small-divisor equation with large-variable coefficient
• Reducibility of 1-d Schrödinger equation with time quasiperiodic unbounded perturbations. I
• Reducibility of 1-d Schrödinger equation with unbounded time quasiperiodic perturbations. III
• Reducibility of 1D quantum harmonic oscillator perturbed by a quasiperiodic potential with logarithmic decay
• A Reducibility Result for a Class of Linear Wave Equations on ${\mathbb T}^d$
• Time quasi-periodic unbounded perturbations of Schrödinger operators and KAM methods

This page was built for publication: Reducibility of Schrödinger equation at high frequencies