Interplay of Anderson localization and quench dynamics

TL;DR

This paper investigates how a quantum quench in a disordered fermionic lattice affects localization, momentum distribution, and fluctuations, revealing nonmonotonic behavior of fluctuations with disorder strength.

Contribution

It provides a detailed analysis of post-quench dynamics in disordered systems, highlighting the impact of localization on equilibration and fluctuations, which is a novel insight.

Findings

Disorder influences the overlap between momentum states and eigenstates.

Disorder prevents local density from reaching a steady state.

Fluctuations peak at intermediate disorder levels.

Abstract

In the context of an isolated three-dimensional noninteracting fermionic lattice system, we study the effects of a sudden quantum quench between a disorder-free situation and one in which disorder results in a mobility edge and associated Anderson localization. Salient post-quench features hinge upon the overlap between momentum states and post-quench eigenstates and whether these latter states are extended or localized. We find that the post-quench momentum distribution directly reflects these overlaps. For the local density, we show that disorder generically prevents the equilibration of quantum expectation values to a steady state and that the persistent fluctuations have a nonmonotonic dependence on the strength of disorder. We identify two distinct types of fluctuations, namely, temporal fluctuations describing the time-dependent fluctuations of the local density around its time average and sample-to-sample fluctuations characterizing the variations of these time averages from one realization of disorder to another. We demonstrate that both of these fluctuations vanish for extremely extended as well as extremely localized states, peaking at some intermediate value.