98-457 I. Guarneri, H. Schulz-Baldes.
Lower bounds on wave packet propagation by packing dimensions of spectral measures. (579K, postscript) Jun 20, 98
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Abstract. We prove that, for any quantum evolution in $\ell^2(\ZZ^D)$, there exist arbitrarily long time scales on which the $q$th moment of the position operator increases at least as fast as a power of time given by $q/D$ times the packing dimension of the spectral measure. Packing dimensions of measures and their connections to scaling exponents and box-counting dimensions are also discussed.

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