Localization in self-affine energy landscapes

Stefanie Russ, Jan W. Kantelhardt, Armin Bunde, Shlomo Havlin

Research output: Contribution to journalArticlepeer-review

36 Scopus citations


We discuss the localization behavior of quantum particles in a one-dimensional Anderson model with self-affine random potentials, characterized by a Hurst exponent (formula presented) Depending on H and energy E, a new type of “strong” localization 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 calculations. Finally, we consider a somewhat related model where the variance of the potential fluctuations is kept fixed for all system sizes L and a transition between localized and apparently extended states has been reported.

Original languageEnglish
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number13
StatePublished - 2001


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