Adiabatic theorems for dense point spectra

DOI10.1007/BF02096869zbMath0711.35101OpenAlexW2021266296MaRDI QIDQ923256

James S. Howland, Barry Simon, Joseph E. Avron

Publication date: 1990

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

Full work available at URL: https://doi.org/10.1007/bf02096869

zbMATH Keywords

Schrödinger equationHamiltoniansdense point spectrumAdiabatic theorems

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) PDEs in connection with quantum mechanics (35Q40) Initial value problems for linear higher-order PDEs (35G10) Higher-order parabolic equations (35K25)

Related Items (9)

General adiabatic evolution with a gap condition ⋮ Derivation of Kubo's formula for disordered systems at zero temperature ⋮ A nonlinear quantum adiabatic approximation ⋮ Tosio Kato's work on non-relativistic quantum mechanics. I ⋮ An Adiabatic Theorem for Singularly Perturbed Hamiltonians ⋮ A STRONG OPERATOR TOPOLOGY ADIABATIC THEOREM ⋮ Linear adiabatic theory. Exponential estimates ⋮ Tosio Kato’s work on non-relativistic quantum mechanics, Part 2 ⋮ Adiabatic evolution for systems with infinitely many eigenvalue crossings

Cites Work

• Unnamed Item
• Adiabatic theorems and applications to the quantum Hall effect
• Pure point spectrum for discrete almost periodic Schrödinger operators
• Almost periodic Schrödinger operators. IV. The Maryland model
• Perturbation theory of dense point spectra
• Adiabatic theorem and spectral concentration. I: Arbitrary order spectral concentration for the Stark effect in atomic physics
• Singular continuous spectrum under rank one perturbations and localization for random hamiltonians

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