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Lower bounds on wave packet propagation by packing dimensions of spectral measures. (English) Zbl 0910.47059
Summary: We prove that, for any quantum evolution in \(\ell^2(\mathbb{Z}^D)\), 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.

MSC:
47N50 Applications of operator theory in the physical sciences
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
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