- 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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