  While exponential decay is ubiquitous in Nature, deviations at both short and
long times are dictated by quantum mechanics. Non-exponential decay is known to
arise due to the possibility of reconstructing the initial state from the
decaying products. We discuss the quantum decay dynamics by tunneling of a
many-particle system, characterizing the long-time non-exponential behavior of
the non-escape and survival probabilities. The effects of contact interactions
and quantum statistics are described. It is found that whereas for
non-interacting bosons the long-time decay follows a power-law with an exponent
linear in the number of particles $\N$, the exponent becomes quadratic in $\N$
in the fermionic case. The same results apply to strongly interacting many-body
systems related by the generalized Bose-Fermi duality. The faster fermionic
decay can be traced back to the effective hard-core interactions between
particles, which are as well the decaying products, and exhibit spatial
anti-bunching which hinders the reconstruction of the initial unstable state.
The results are illustrated with a paradigmatic model of quantum decay from a
trap allowing leaks by tunneling, whose dynamics is described exactly by means
of an expansion in resonant states.
