Sfb 288 Differential Geometry and Quantum Physics

Abstract for Sfb Preprint No. 332

Lower bounds on wave packet propagation by packing dimensions of spectral measures

I. Guarneri and H. Schulz-Baldes

We prove that, for any quantum evolution in l2(ZD), 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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