Sensitivity to initial conditions of the wave-packet dynamics in diluted Anderson chains

We study the one-electron wave-packet dynamics in the one-dimensional diluted Anderson model which is composed of two interpenetrating chains with pure and random on-site potentials, respectively. This model presents extended states at a particular resonance energy. Starting with one electron fully localized at the site closer to the chain center, we solve the set of coupled motion equations and calculate the time evolution of the wave-packet width. We report on a long-time memory effect which is reflected by distinct asymptotic dynamics governing the wave-function spread for electrons initially localized at random or pure sites. This anomalous behavior is discussed under the light of the Bloch character of the extended resonant state.