Non diffusive quantum transport in a dynamically disordered medium

Abstract

For a dynamically disordered continuum it is found that the exact quantum mechanical mean square displacement <x2(t)>~t3, for t-->∞. 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."