  We consider $N$ non-interacting fermions prepared in the ground state of a 1D
confining potential and submitted to an instantaneous quench consisting in
releasing the trapping potential. We show that the quantum return probability
of finding the fermions in their initial state at a later time falls off as a
power law in the long-time regime, with a universal exponent depending only on
$N$ and on whether the free fermions expand over the full line or over a
half-line. In both geometries the amplitudes of this power-law decay are
expressed in terms of finite determinants of moments of the one-body
bound-state wavefunctions in the potential. These amplitudes are worked out
explicitly for the harmonic and square-well potentials. At large fermion
numbers they obey scaling laws involving the Fermi energy of the initial state.
The use of the Selberg-Mehta integrals stemming from random matrix theory has
been instrumental in the derivation of these results.
