Localization in self-affine energy landscapes - art. no. 134209

We discuss the localization behavior of quantum particles in a one-dimensio nal Anderson model with self-af fine random potentials, characterized by a Hurst exponent H>0. Depending on H and energy E, a new type of "strong" loc alization can occur, where all states are localized in a way different from the regular Anderson localized states. Using scaling arguments, we derive an analytical expression for the phase diagram and test it by numerical cal culations. Finally, we consider a somewhat related model where the variance of the potential fluctuations is kept fixed for all system sizes L and a t ransition between localized and apparently extended states has been reporte d.