  We study numerically and analytically isolated interacting quantum systems
that are taken out of equilibrium instantaneously (quenched). The probability
of finding the initial state in time, the so-called fidelity, decays fastest
for systems described by full random matrices, where simultaneous many-body
interactions are implied. In the realm of realistic systems with two-body
interactions, the dynamics is slower and depends on the interplay between the
initial state and the Hamiltonian characterizing the system. The fastest
fidelity decay in this case is Gaussian and can persist until saturation. A
simple general picture, in which the fidelity plays a central role, is also
achieved for the short-time dynamics of few-body observables. It holds for
initial states that are eigenstates of the observables. We also discuss the
need to reassess analytical expressions that were previously proposed to
describe the evolution of the Shannon entropy. Our analyses are mainly
developed for initial states that can be prepared in experiments with cold
atoms in optical lattices.
