  We study isolated finite interacting quantum systems after an instantaneous
perturbation and show three scenarios in which the probability for finding the
initial state later in time (fidelity) decays nonexponentially, often all the
way to saturation. The decays analyzed involve Gaussian, Bessel of the first
kind, and cosine squared functions. The Gaussian behavior emerges in systems
with two-body interactions in the limit of strong perturbation. The Bessel
function, associated with the evolution under full random matrices, is obtained
with surprisingly sparse random matrices. The cosine squared behavior,
established by the energy-time uncertainty relation, is approached after a
local perturbation in space.
