  Using supersymmetry calculations and random matrix simulations, we studied
the decay of the average of the fidelity amplitude f_epsilon(tau)=<psi(0)|
exp(2 pi i H_epsilon tau) exp(-2 pi i H_0 tau) |psi(0)>, where H_epsilon
differs from H_0 by a slight perturbation characterized by the parameter
epsilon. For strong perturbations a recovery of f_epsilon(tau) at the
Heisenberg time tau=1 is found. It is most pronounced for the Gaussian
symplectic ensemble, and least for the Gaussian orthogonal one. Using Dyson's
Brownian motion model for an eigenvalue crystal, the recovery is interpreted in
terms of a spectral analogue of the Debye-Waller factor known from solid state
physics, describing the decrease of X-ray and neutron diffraction peaks with
temperature due to lattice vibrations.
