Quantum diffusion of a particle in a dynamically disordered continuum

Abstract

An exact quantum mechanical diffusive solution is derived for the motion of a particle in a dynamically disordered continuum described by a gaussian random potential with a local correlation in both space and time coordinates. This demonstrates the validity of the long-wavelength continuum limit as an approximate description of the motion of an electron in a tight binding lattice with on-site correlation of the gaussian site energies. Earlier doubts about this point arose from the fact that the only known solution for a dynamically disordered continuum showed nondiffusive behaviour, in contrast to the well-known diffusive behaviour in discrete lattices. A recent suggestion that the diffusive behaviour in a lattice is due to the momentum cut-off inherent to it is not supported by our results.