Adiabatic theorems for dense point spectra
type: Item
instance of: scholarly article
title: Adiabatic theorems for dense point spectra
zbMATH Open document ID: 0711.35101
DOI: 10.1007/BF02096869
author: James S. Howland
author: B. Simon
author: J. E. Avron
published in: Communications in Mathematical Physics
publication date: 1990-01-01T00:00:00Z
review text: The time dependent Schrödinger equation in Hilbert space is considered for slow variations of the Hamiltonian. Adiabatic theorems are proven for two classes of operators: perturbations of Hamiltonians with dense point spectrum, and Hamiltonians with dense point spectrum whose eigenvalues and -vectors depend smoothly on time. The usual gap condition on the spectrum of the operator [see \textit{J. E. Avron}, \textit{R. Seiler} and \textit{L. G. Yaffe}, Commun. Math. Phys. 110, 33-49 (1987; Zbl 0626.58033)] is replaced in the first case by the requirement that the perturbation does not couple the eigenspaces to much; in the second case the eigenvectors are supposed to stay localized.
Mathematics Subject Classification ID: 35Q40
Mathematics Subject Classification ID: 35P05
Mathematics Subject Classification ID: 81Q05
Mathematics Subject Classification ID: 35G10
Mathematics Subject Classification ID: 35K25
zbMATH DE Number: 4169270
zbMATH Keywords: Schrödinger equation
zbMATH Keywords: Adiabatic theorems
zbMATH Keywords: Hamiltonians
zbMATH Keywords: dense point spectrum
reviewed by: Joachim Asch
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02096869
OpenAlex ID: W2021266296
description: scientific article; zbMATH DE number 4169270