J. Bellissard, H. Schulz-Baldes
Subdiffusive quantum transport for $3D$-Hamiltonians 
with absolutely continuous spectra
(143K, postscript)

ABSTRACT.  Both in the $3D$ Anderson model at low disorder and 
in $3D$ quasicrystals, the local density of states is expected to be 
absolutely continuous, although the quantum transport is diffusive or 
subdiffusive respectively. By studying sums of $1D$ models with 
well-understood spectral and transport properties, we exhibit a $3D$ 
model with absolutely continuous spectrum for which the diffusion 
exponent characterizing the growth of the mean square displacement is 
only slightly bigger than imposed by Guarneri's lower bound.