We discuss the localization behavior of quantum particles in a one-dimensional Anderson model with self-affine random potentials, characterized by a Hurst exponent $H>0.$ 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.
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Russ et al. (2001) studied this question.
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