Remarks on the relation between quantum dynamics and fractal spectra
type: Item
instance of: scholarly article
title: Remarks on the relation between quantum dynamics and fractal spectra
zbMATH Open document ID: 0893.47048
author: R. Montcho
author: Jean-Marie Barbaroux
author: Jean-Michel Combes
published in: Journal of Mathematical Analysis and Applications
publication date: 1998-08-24T00:00:00Z
review text: The large time behaviour of various solutions of Schrödinger equations is studied by means of certain local and global dimensions of the spectral measure. Their relation to Hausdorff and correlation dimensions are given. The correlation dimensions control the time-decay of correlation functions. Growth exponents for moments of position operators are considered in terms of information dimension. The stability of such exponents under rank one perturbations is discussed. For such perturbations the dynamics is invariant in weak sense.
Mathematics Subject Classification ID: 47N50
Mathematics Subject Classification ID: 81Q05
Mathematics Subject Classification ID: 81Q10
Mathematics Subject Classification ID: 81Q15
zbMATH DE Number: 1115573
zbMATH Keywords: growth exponents for moments of position operators
zbMATH Keywords: large time behaviour
zbMATH Keywords: solutions of Schrödinger equations
zbMATH Keywords: local and global dimensions
zbMATH Keywords: spectral measure
zbMATH Keywords: Hausdorff and correlation dimensions
zbMATH Keywords: information dimension
zbMATH Keywords: stability
zbMATH Keywords: rank one perturbations
reviewed by: Michael Demuth
MaRDI profile type: Publication
OpenAlex ID: W1970107326
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DOI: 10.1006/JMAA.1997.5571
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description: scientific article; zbMATH DE number 1115573