Singular continuous Floquet operator for systems with increasing gaps.
type: Item
instance of: scholarly article
title: Singular continuous Floquet operator for systems with increasing gaps.
zbMATH Open document ID: 1043.47051
DOI: 10.1016/S0022-247X(02)00277-9
author: O. Bourget
published in: Journal of Mathematical Analysis and Applications
publication date: 2003-02-11T00:00:00Z
review text: The paper under review investigates the Hamiltonian \(H_0\) of a quantum mechanical harmonic oscillator that is periodically perturbed by a time-dependent potential of the form \[ V(t)=P_{\phi}\sum_{n\in{\mathbb Z}}\delta(t-nT), \] where \(P_{\phi}\) denotes the projection operator onto an arbitrary state vector \(\phi\). In [J. Stat. Phys. 59, 679--690 (1990; Zbl 0713.58044)], \textit{M. Combescure} showed that if \(\phi\) is cyclic with respect to \(H_0\) and if the oscillator frequency \(\omega\) is ``sufficiently irrational'' in the sense that \(\omega T/(2\pi)\) is a Diophantine number, the spectrum of the system's Floquet operator is purely singular continuous for all \(\kappa\in {\mathbb R\backslash \mathbb Z}\). The present paper generalizes this result by admitting a larger class of oscillator frequencies.
reviewed by: Bernd Kuckert
Mathematics Subject Classification ID: 47N50
Mathematics Subject Classification ID: 81Q10
Mathematics Subject Classification ID: 47B25
zbMATH DE Number: 1866729
zbMATH Keywords: Floquet operator
zbMATH Keywords: harmonic oscillator
zbMATH Keywords: spectral analysis
zbMATH Keywords: oscillator frequency
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1866729