Existence and nonexistence of wave operators for time-decaying harmonic oscillators

DOI10.1016/S0034-4877(20)30040-9zbMath1447.81190arXiv1810.12018OpenAlexW3102087385MaRDI QIDQ2194293

Masaki Kawamoto, Atsuhide Ishida

Publication date: 25 August 2020

Published in: Reports on Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1810.12018

zbMATH Keywords

scattering theoryharmonic oscillatortime-dependent magnetic fieldsnonexistence of wave operators

Mathematics Subject Classification ID

Scattering theory for PDEs (35P25) Electromagnetic interaction; quantum electrodynamics (81V10) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) (S)-matrix theory, etc. in quantum theory (81U20) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Related Items (7)

Strichartz estimates for Schrödinger operators with square potential with time-dependent coefficients ⋮ Nonexistence of wave operators via strong propagation estimates for Schrödinger operators with sub-quadratic repulsive potentials ⋮ Long-range scattering for a critical homogeneous type nonlinear Schrödinger equation with time-decaying harmonic potentials ⋮ Critical scattering in a time-dependent harmonic oscillator ⋮ Threshold between short and long-range potentials for non-local Schrödinger operators ⋮ Final state problem for nonlinear Schrödinger equations with time-decaying harmonic oscillators ⋮ Asymptotic behavior of solutions to a dissipative nonlinear Schrödinger equation with time-dependent harmonic potentials

Cites Work

• Schrödinger evolution equations with magnetic fields
• Non-existence of wave operators for Stark effect Hamiltonians
• On regularly varying solutions of second order linear differential equations
• Asymptotic Behavior of Solutions of Second Order Differential Equations with Integrable Coefficients
• EXISTENCE AND NON-EXISTENCE RESULTS FOR WAVE OPERATORS FOR PERTURBATIONS OF THE LAPLACIAN
• Non-Existence of Standard Wave Operators for Fractional Laplacian and Slowly Decaying Potentials
• The borderline of the short-range condition for the repulsive Hamiltonian

This page was built for publication: Existence and nonexistence of wave operators for time-decaying harmonic oscillators