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We consider the notion of equilibration for an isolated quantum systemexhibiting Anderson localization. The system is assumed to be in a pure state,i.e., described by a wave-function undergoing unitary dynamics. We focus on thesimplest model of a 1D disordered chain and we analyse both the dynamics of aninitially localized state and the dynamics of quantum states drawn at randomfrom the ensemble corresponding to the minimum knowledge about the initialstate. While in the former case the site distribution remains confined in alimited portion of the chain, the site distribution of random pure statefluctuates around an equilibrium average that is delocalized over the entirechain. A clear connection between the equilibration observed when the system isinitialized in a fully localized state and the amplitude of dynamicalfluctuations of a typical random pure state is established.

Signatures of Anderson localization and delocalized random quantum states