Sfb 288 Differential Geometry and Quantum Physics

Abstract for Sfb Preprint No. 413

Subdiffusive quantum transport for $3D$-Hamiltonians with absolutely continuous spectra

J. Bellissard and H. Schulz-Baldes

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

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