The quantum stability problem for some class of time-dependent Hamiltonians

DOI10.1016/0003-4916(88)90259-XzbMath0655.35076MaRDI QIDQ1109236

Monique Combescure

Publication date: 1988

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

zbMATH Keywords

perturbationsquantum dynamicsharmonic oscillatortime-dependent Schrödinger equationquantum stabilitySchrödinger hamiltoniansSuitable scaling

Mathematics Subject Classification ID

Perturbation theories for operators and differential equations in quantum theory (81Q15) Partial differential equations of mathematical physics and other areas of application (35Q99)

Related Items (11)

Quantum averaging. III. Time-dependent systems ⋮ Quasienergy operators and generalized squeezed states for systems of trapped ions ⋮ Stability of oscillators driven by ergodic processes ⋮ Julia sets in iterative KAM methods for eigenvalue problems ⋮ The physics and applications of strongly coupled Coulomb systems (plasmas) levitated in electrodynamic traps ⋮ Squeezed coherent states of motion for ions confined in quadrupole and octupole ion traps ⋮ Recurrent versus diffusive dynamics for a kicked quantum system ⋮ Upper quantum Lyapunov exponent and parametric oscillators ⋮ The WKB method and geometric instability for nonlinear Schrödinger equations on surfaces ⋮ Coherent and Squeezed States: Introductory Review of Basic Notions, Properties, and Generalizations ⋮ Quantum Nekhoroshev Theorem for Quasi-Periodic Floquet Hamiltonians

Cites Work

• Exact solutions of the nonlinear Schrödinger equation in time-dependent parabolic density profiles
• Existence of solutions for Schrödinger evolution equations
• Scattering theory for Schrödinger equation with potential periodic in time
• Schrödinger operators with magnetic fields. I: General interactions
• Schrödinger operators with singular potentials
• Stable and Random Motions in Dynamical Systems
• Pseudo‐differential operators
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