  Using supersymmetry techniques analytical expressions for 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) > are obtained, where H_epsilon=H_0+(sqrt{epsilon}/(2 pi)
)*V, and H_0 and H_epsilon are taken from the Gaussian unitary ensemble (GUE)
or the Gaussian orthogonal ensemble (GOE), respectively. As long as the
perturbation strength is small compared to the mean level spacing, a Gaussian
decay of the fidelity amplitude is observed, whereas for stronger perturbations
a change to a single-exponential decay takes place, in accordance with results
from literature. Close to the Heisenberg time tau=1, however, a partial revival
of the fidelity is found, which hitherto remained unnoticed. Random matrix
simulations have been performed for the three Gaussian ensembles. For the case
of the GOE and the GUE they are in perfect agreement with the analytical
results.
