99-344 J. Bellissard, H. Schulz-Baldes
Subdiffusive quantum transport for $3D$-Hamiltonians with absolutely continuous spectra (143K, postscript) Sep 19, 99
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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.

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