What is Localization?

Abstract

We examine various issues relevant to localization in the Anderson model. We show there is more to localization than exponentially localized states by presenting an example with such states but where $〈x(t{)}^{2}〉{/t}^{2\ensuremath{-}\ensuremath{\delta}}$ is unbounded for any $\ensuremath{\delta}>0$. We show that the recently discovered instability of localization under rank one perturbations is only a weak instability.