WEAKLY REGULAR FLOQUET HAMILTONIANS WITH PURE POINT SPECTRUM

DOI10.1142/S0129055X02001363zbMath1037.81038arXivmath-ph/0103041MaRDI QIDQ4420444

Pierre Duclos, Michel Vittot, O. Lev, Pavel Šťovíček

Publication date: 17 August 2003

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

Full work available at URL: https://arxiv.org/abs/math-ph/0103041

zbMATH Keywords

perturbation theoryKAM theorypure point spectrumsmall divisorsFloquet Hamiltonian

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Applications of operator theory in the physical sciences (47N50) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Groups and algebras in quantum theory and relations with integrable systems (81R12) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40)

Related Items (13)

Growth of Sobolev norms in 1-d quantum harmonic oscillator with polynomial time quasi-periodic perturbation ⋮ Reducibility of the quantum harmonic oscillator in \(d\)-dimensions with polynomial time-dependent perturbation ⋮ Reducibility of 1D quantum harmonic oscillator with decaying conditions on the derivative of perturbation potentials ⋮ Reducibility of 1-d Schrödinger equation with time quasiperiodic unbounded perturbations. I ⋮ Almost reducibility and oscillatory growth of Sobolev norms ⋮ Point spectrum of the Floquet Hamiltonian for Klein-Gordon equation under quasi-periodic perturbations ⋮ Quasi-periodic solutions for two-level systems ⋮ ON THE STABILITY OF PERIODICALLY TIME-DEPENDENT QUANTUM SYSTEMS ⋮ Almost periodic orbits and stability for quantum time-dependent Hamiltonians ⋮ 1-d quantum harmonic oscillator with time quasi-periodic quadratic perturbation: reducibility and growth of Sobolev norms ⋮ On a semiclassical formula for non-diagonal matrix elements ⋮ Reducibility of 1-d Schrödinger equation with unbounded time quasiperiodic perturbations. III ⋮ Reducibility of 1-d Schrödinger equation with time quasiperiodic unbounded perturbations. II

Cites Work

• The imbedding problem for Riemannian manifolds
• Scattering theory for Schrödinger equation with potential periodic in time
• Floquet spectrum for two-level systems in quasiperiodic time-dependent fields
• Absence of absolutely continuous spectrum of Floquet operators
• Floquet Hamiltonians with pure point spectrum
• Scattering theory for Hamiltonians periodic in time
• How and Why to Solve the Operator Equation AX −XB = Y
• Superconvergent Perturbation Method in Quantum Mechanics

This page was built for publication: WEAKLY REGULAR FLOQUET HAMILTONIANS WITH PURE POINT SPECTRUM