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1 October 2001 Fractal dimensions and the phenomenon of intermittency in quantum dynamics
Jean-Marie Barbaroux, François Germinet, Serguei Tcheremchantsev
Duke Math. J. 110(1): 161-193 (1 October 2001). DOI: 10.1215/S0012-7094-01-11015-6

Abstract

We exhibit an intermittency phenomenon in quantum dynamics. More precisely, we derive new lower bounds for the moments of order $p$ associated to the state $\psi(t)=e^{-itH}\psi$ and averaged in time between zero and $T$. These lower bounds are expressed in terms of generalized fractal dimensions $D^\pm_{\mu_\psi}(1/(1+p/d))$ of the measure $\mu_\psi$ (where $d$ is the space dimension). This improves previous results obtained in terms of Hausdorff and Packing dimension.

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Jean-Marie Barbaroux. François Germinet. Serguei Tcheremchantsev. "Fractal dimensions and the phenomenon of intermittency in quantum dynamics." Duke Math. J. 110 (1) 161 - 193, 1 October 2001. https://doi.org/10.1215/S0012-7094-01-11015-6

Information

Published: 1 October 2001
First available in Project Euclid: 18 June 2004

zbMATH: 1012.81018
MathSciNet: MR1861091
Digital Object Identifier: 10.1215/S0012-7094-01-11015-6

Subjects:
Primary: 81Q99
Secondary: 28A80 , 35J10 , 35Q40

Rights: Copyright © 2001 Duke University Press

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Vol.110 • No. 1 • 1 October 2001
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