Duke Mathematical Journal

Fractal dimensions and the phenomenon of intermittency in quantum dynamics

Jean-Marie Barbaroux,François Germinet, and Serguei Tcheremchantsev

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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.

Article information

Duke Math. J. Volume 110, Number 1 (2001), 161-193.

First available: 18 June 2004

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Zentralblatt MATH identifier

Primary: 81Q99: None of the above, but in this section
Secondary: 28A80: Fractals [See also 37Fxx] 35J10: Schrödinger operator [See also 35Pxx] 35Q40: PDEs in connection with quantum mechanics


Barbaroux, Jean-Marie; Germinet, François; Tcheremchantsev, Serguei. Fractal dimensions and the phenomenon of intermittency in quantum dynamics. Duke Mathematical Journal 110 (2001), no. 1, 161--193. doi:10.1215/S0012-7094-01-11015-6. http://projecteuclid.org/euclid.dmj/1087574815.

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