Adiabatic theorem and spectral concentration. I: Arbitrary order spectral concentration for the Stark effect in atomic physics

DOI10.1007/BF01206948zbMath0493.47009OpenAlexW1966529698MaRDI QIDQ1168570

Gheorghe Nenciu

Publication date: 1981

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

Full work available at URL: https://doi.org/10.1007/bf01206948

zbMATH Keywords

asymptotic expansionsinvariant subspacesadiabatic theoremspectral concentrationStark effectasymptotically invariant subspacesisolated bounded part of the spectrum subspace

Mathematics Subject Classification ID

Applications of operator algebras to the sciences (47L90) Spectrum, resolvent (47A10) Perturbation theory of linear operators (47A55) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Atomic physics (81V45) Asymptotic expansions of solutions to ordinary differential equations (34E05)

Related Items (22)

First-order relativistic corrections and spectral concentration ⋮ A Note on Exponential Estimates in Adiabatic Theory ⋮ Adiabatic Evolution and Shape Resonances ⋮ Imaginary parts of Stark–Wannier resonances ⋮ Existence of the spontaneous pair creation in the external field approximation of Q.E.D ⋮ Asymptotic transition probabilities ⋮ On asymptotic perturbation theory for quantum mechanics: Almost invariant subspaces and gauge invariant magnetic perturbation theory ⋮ Existence of the Stark-Wannier quantum resonances ⋮ Precise exponential estimates in adiabatic theory ⋮ Adiabatic theorems for dense point spectra ⋮ A note on spectral concentration for non-isolated eigenvalues ⋮ Stark Wannier ladders ⋮ Adiabatic approximation with exponential accuracy for many-body systems and quantum computation ⋮ Time development of exponentially small non-adiabatic transitions ⋮ An Adiabatic Theorem for Singularly Perturbed Hamiltonians ⋮ Adiabatic theorems and applications to the quantum Hall effect ⋮ Elementary exponential error estimates for the adiabatic approximation. ⋮ Linear adiabatic theory. Exponential estimates ⋮ Adiabatic expansions near eigenvalue crossings ⋮ Proof of the Landau-Zener formula in an adiabatic limit with small eigenvalue gaps ⋮ Shortcuts to adiabaticity: suppression of pair production in driven Dirac dynamics ⋮ Stark ladders of resonances: Wannier ladders and perturbation theory

Cites Work

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• Adiabatic invariance to all orders
• Dilation analyticity in constant electric field I. The two body problem
• Resonances in the Stark effect of atomic systems
• On the adiabatic limit for Dirac particles in external fields
• Perturbation des transformations autoadjointes dans l'espace de Hilbert
• On the adiabatic theorem of quantum mechanics
• Dynamics of Bloch electrons in time-dependent external electric fields: bounds for inter-band transitions
• Exponential decay in the Stark effect

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