Statistical dynamical mean - field description of strongly correlated disordered electron - phonon systems ∗

Combining the self-consistent theory of localization and the dynamical mean-field theory, we present a theoretical approach capable of describing both self-trapping of charge carriers during the process of polaron formation and disorder-induced Anderson localization. By constructing random samples for the local density of states (LDOS) we analyze the distribution function for this quantity and demonstrate that the typical rather than the mean LDOS is a natural measure to distinguish between itinerant and localized states. Significant polaron effects on the mobility edge are found.