Quantum quenches in a three-dimensional system exhibiting Anderson localization

We theoretically study a quantum quench in fermionic lattice model that exhibits Anderson localization, in which a disorder potential is suddenly turned on in isolation from a thermal environment. We relate several physical observables of the system (including their temporal as well as sample-to sample fluctuations) to the statistical properties of the single-particle disordered wave functions and analyze their behavior as a function of disorder. In particular, we find a non-monotonic disorder dependence for sample-to-sample density fluctuations. We, furthermore, examine the equilibration of the system to generalized thermodynamic ensembles. We relate several of the observed features to the crossover from extended to localized behavior.