Stability of quantum motion in regular systems: a uniform semiclassical approach

We study the stability of quantum motion of classically regular systems in presence of small perturbations. Onthe base of a uniform semiclassical theory we derive the fidelity decay which displays a quite complexbehaviour, from Gaussian to power law decay $t^{-\alpha}$ with $1 \le \alpha \le 2$. Semiclassical estimates are given for the time scales separating the different decaying regions and numerical results are presented which confirm our theoretical predictions.