Bounded Sobolev norms for Klein-Gordon equations under non-resonant perturbation

DOI10.1063/1.4903255zbMath1312.82011OpenAlexW2084670774MaRDI QIDQ2939197

Zheng Han, Daoyuan Fang, Wei-Min Wang

Publication date: 19 January 2015

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

Full work available at URL: https://doi.org/10.1063/1.4903255

zbMATH Keywords

Klein-Gordon equationSobolev normAnderson localization

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) PDEs in connection with quantum mechanics (35Q40) Schrödinger operator, Schrödinger equation (35J10)

Related Items (5)

On a heavy quantum particle ⋮ The stability of Sobolev norms for the linear wave equation with unbounded perturbations ⋮ Point spectrum of the Floquet Hamiltonian for Klein-Gordon equation under quasi-periodic perturbations ⋮ Reducibility, Lyapunov exponent, pure point spectra property for quasi-periodic wave operator ⋮ Reducibility for a fast-driven linear Klein-Gordon Equation

Cites Work

• On growth of Sobolev norms in linear Schrödinger equations with time dependent Gevrey potential
• Bounded Sobolev norms for linear Schrödinger equations under resonant perturbations
• Pure point spectrum of the Floquet Hamiltonian for the quantum harmonic oscillator under time quasi-periodic perturbations
• Anderson localization for time quasi-periodic random Schrödinger and wave equations
• On growth of Sobolev norms in linear Schrödinger equations with smooth time dependent potential
• Stationary scattering theory for time-dependent Hamiltonians
• Logarithmic Bounds on Sobolev Norms for Time Dependent Linear Schrödinger Equations
• Green's Function Estimates for Lattice Schrodinger Operators and Applications. (AM-158)
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