Nondiffusive Quantum Transport in a Dynamically Disordered Medium

Abstract

For a dynamically disordered continuum it is found that the exact quantum mechanical mean square displacement $〈{x}^{2}(t)〉\ensuremath{\sim}{t}^{3}$, for $t\ensuremath{\rightarrow}\ensuremath{\infty}$. 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."