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