Anomalous localization in a nonuniformly disordered medium

Disordered systems with a spatial dependent mean free path (due to, e.g., an external field) are studied. Such nonuniformity in the medium leads to anomalous localization behavior. The distribution function for the resistance of a 1D sample with length L, with power-law dependence of the mean free path l on the coordinate x, lx±, is presented. Transition from localized behavior (lnL) to delocalized (ln is not a normally distributed quantity) takes place through the power localization (lnlnL). Extensions of the model to higher dimensions, as well as to the case where dissipation is present, are discussed.