- 98-457 I. Guarneri, H. Schulz-Baldes.
- Lower bounds on wave packet propagation by packing dimensions of
Jun 20, 98
(auto. generated ps),
of related papers
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.