  We study isolated quantum systems with two-body interactions after a quench.
In these systems, the energy shell is a Gaussian of width $\sigma$, and it
gives the maximum possible spreading of the energy distribution of the initial
states. When the distribution achieves this shape, the fidelity decay can be
Gaussian until saturation. This establishes a lower bound for the fidelity
decay in realistic systems. An ultimate bound for systems with many-body
interactions is also derived based on the analysis of full random matrices. We
find excellent agreement between numerical and analytical results. We also
provide the conditions under which the short-time dynamics of few-body
observables is controlled by $\sigma$. The analyses are developed for systems,
initial states, and observables accessible to experiments.
