  The most important law of radioactivity is that of the exponential decay. In
the realm of quantum mechanics, however, this decay law is neither rigorous nor
fundamental. The deviations from the exponential decay have been observed
experimentally at the early stage of a decay process, but there is little
evidence for non-exponential behavior at long times. Yet such long-term
non-exponentiality is expected theoretically to probe the non-resonant
background components of the initial wave function which preserve the
structural interference and the memory of how the state was created. In this
paper, we propose new observables that can be used for experimental
investigations of the post-exponential decay regime, including the decay of
threshold resonances, particle correlations in three-body decays, and
interference between near-lying resonances. While the specific examples
presented in this work pertain to atomic nuclei, the properties of
non-exponential decay are generic, i.e., they apply to other many-body open
quantum systems, such as hadrons, atoms, molecules, and nanostructures.
