Effect of scattering on the dynamic localization of a particle in a time-dependent electric field

The theory of dynamic localization of a charged particle moving on a lattice under the influence of a time-dependent electric field developed in a previous paper is extended to include the effect of scattering of the particle by imperfections in the lattice. The description used to include scattering is that provided by the stochastic Liouville equation. Exact solutions for the mean-square displacement are obtained, and the average diffusion constant is calculated for a sinusoidal ac field. Scattering is found to play a dual role: It increases diffusion by preventing localization, and decreases it by increasing the amount of incoherence. Viewed another way, an alternating electric field is seen to result in an increase in the scattering rate in general and the appearance of singularities in the rate for specific values of the field magnitude and/or the field frequency. These singularities represent the phenomenon of dynamic localization and indicate the possibility of inducing anisotropy in isotropic materials through the application of strong time-varying electric fields.