00-507 Jean-Marie Barbaroux, Francois Germinet, Serguei Tcheremchantsev

Fractal dimensions and the Phenomenon of Intermittency in Quantum Dynamics (revised version, september 2000) (512K, Postscript) Dec 21, 00

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Abstract. We exhibit an intermittency phenomenon in quantum dynamics. More precisely we derive new lower bounds for the moments of order {\it p} associated to the state $\psi(t)={\rm e}^{-itH}\psi$ and averaged in time between $0$ and {\it 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 {\it d} is the space dimension). This improves previous results, obtained in terms of Hausdorff and Packing dimension.

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