Theory of carrier motion in dynamically disordered systems

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Abstract
We present a quantum mechanical theory of the dynamics of a charge carrier or an electronic excitation in a condensed phase system, in which the solvent degrees of freedom that couple to the electronic excitation are characterized by a correlation time of arbitrary magnitude. We consider a charge carrier moving among active sites that are randomly distributed in space. The site energies undergo stochastic modulation with a finite correlation time, through the interactions with the solvent. A mode-coupling self-consistent equation is derived from which transport properties such as the ac conductivity, the mean-squared displacement, and the time-dependent probability that a carrier remains on the initial site are calculated. A metal–insulator transition is predicted in three dimensions, but not in one or two dimensions, in agreement with the scaling theory of Anderson localization. The present treatment allows the investigation of carrier dynamics even when there is no separation of time scales between the dynamics of carrier and solvent.