  We extend the results of two of our papers [Phys. Rev. A 94, 041603R (2016)
and Phys. Rev. B 97, 060303R (2018)] that touch upon the intimately connected
topics of quantum chaos and thermalization. In the first, we argued that when
the initial state of isolated lattice many-body quantum systems is chaotic, the
power-law decay of the survival probability is caused by the bounds in the
spectrum, and thus anticipates thermalization. In the current work, we provide
stronger numerical support for the onset of these algebraic behaviors. In the
second paper, we demonstrated that the correlation hole, which is a direct
signature of quantum chaos revealed by the evolution of the survival
probability at times beyond the power-law decay, appears also for other
observables. In the present work, we investigate the correlation hole in the
chaotic regime and in the vicinity of a many-body localized phase for the spin
density imbalance, which is an observable studied experimentally.
