  Motivated by neutron scattering experiments, we investigate the decay of the
fidelity with which a wave packet is reconstructed by a perfect time-reversal
operation performed after a phase space displacement. In the semiclassical
limit, we show that the decay rate is generically given by the Lyapunov
exponent of the classical dynamics. For small displacements, we additionally
show that, following a short-time Lyapunov decay, the decay freezes well above
the ergodic value because of quantum effects. Our analytical results are
corroborated by numerical simulations.
