MPEJ Volume 5, No.1, 16pp
Received: June 19, 1998, Accepted: Jan 6, 1999
I. Guarneri, H. Schulz-Baldes
Lower bounds on wave packet propagation by packing dimensions
of spectral measures
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.