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.
Citation
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
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