  This work shows that dynamical features typical of full random matrices can
be observed also in the simple finite one-dimensional (1D) noninteracting
Anderson model with nearest neighbor couplings. In the thermodynamic limit, all
eigenstates of this model are exponentially localized in configuration space
for any infinitesimal onsite disorder strength $W$. But this is not the case
when the model is finite and the localization length is larger than the system
size $L$, which is a picture that can be experimentally investigated. We
analyze the degree of energy-level repulsion, the structure of the eigenstates,
and the time evolution of the finite 1D Anderson model as a function of the
parameter $\xi \propto (W^2 L)^{-1}$. As $\xi$ increases, all energy-level
statistics typical of random matrix theory are observed. The statistics are
reflected in the corresponding eigenstates and also in the dynamics. We show
that the probability in time to find a particle initially placed on the first
site of an open chain decays as fast as in full random matrices and much faster
that when the particle is initially placed far from the edges. We also see that
at long times, the presence of energy-level repulsion manifests in the form of
the correlation hole. In addition, our results demonstrate that the hole is not
exclusive to random matrix statistics, but emerges also for $W=0$, when it is
in fact deeper.
