very handy because it enables us to determine $\langle Y_2\rangle_{p_0}$ at any time $t$ without previously computing everything that happened before $t$. Additionally, the temporal behavior of $\langle Y_2\rangle_{p_0}$ (which is still dependent on the disorder) can be simulated quite efficiently, i.e. without the statistical error attached to the average over initial conditions and over single trajectories. Thus the matrix approach gives a useful numerical tool of investigating the problem of dynamical localization, the tool which will be continuously used in the present paper. A nice consequence is that we are able to examine the temporal behavior of $\langle Y_2\rangle_{p_0}$ as averaged over initial conditions and trajectories in a fixed disorder realization and compare it to the disorder-averaged behavior to evaluate the inter-sample differences, as is done in Fig. \[fig:Y2p0av\].

Fig. \[fig:Y2p0av\] shows the behavior of $\langle Y_2\rangle_{p_0}$ in three different realizations of the random potential together with the result $\langle Y_2 \rangle_{p_0, \tau}$ as following from averaging over 100 such realizations. The pronounced plateau of $\langle Y_2 \rangle_{p_0, \tau}$ between $t \simeq 10^2$ and $10^9$ corresponds to the dynamical localization and up to now was only considered after applying the disorder average. We see that up to the crossover 