Fractal dimensions and the phenomenon of intermittency in quantum dynamics
Barbaroux, Jean-Marie ; Germinet, François ; Tcheremchantsev, Serguei
Duke Math. J., Tome 110 (2001) no. 1, p. 161-193 / Harvested from Project Euclid
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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.
Publié le : 2001-10-01
Classification:  81Q99,  28A80,  35J10,  35Q40 
@article{1087574815,
     author = {Barbaroux, Jean-Marie and Germinet, Fran\c cois and Tcheremchantsev, Serguei},
     title = {Fractal dimensions and the phenomenon of intermittency in quantum dynamics},
     journal = {Duke Math. J.},
     volume = {110},
     number = {1},
     year = {2001},
     pages = { 161-193},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1087574815}
}

Barbaroux, Jean-Marie; Germinet, François; Tcheremchantsev, Serguei. Fractal dimensions and the phenomenon of intermittency in quantum dynamics. Duke Math. J., Tome 110 (2001) no. 1, pp.  161-193. http://gdmltest.u-ga.fr/item/1087574815/