del Rio R., Jitomirskaya S., Last Y., Simon B.
What Is Localization?
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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 $\langle x(t)^{2}\rangle /t^{2-\delta}$ is unbounded 
for any $\delta >0$. We show that the recently discovered instability 
of localization under rank one perturbations is only a weak instability.