Nondiffusive Quantum Transport in a Dynamically Disordered Medium

For a dynamically disordered continuum it is found that the exact quantum mechanical mean square displacement $〈x^2\mathrm{}\left(t\right)\mathrm{}〉\sim t^3$, for $t\to \infty$. A Gaussian white-noise spectrum is assumed for the random potential. The result differs qualitatively from the diffusive behavior well known for the one-band lattice Hamiltonian, and is understandable in terms of the momentum cutoff inherent in the lattice, simulating a "momentum bath."