Fidelity Gap in Dynamical Systems with Critical Chaos*

We analyze the fidelity decay for a class of dynamical systems showing {\it critical chaos}, using a Kicked Rotor with singular kicking potential as a prototype model. We found that the classical fidelity shows a gap $F_g$ (initial drop of fidelity) which scales as $F_g(\alpha, \epsilon, \eta ) = f(\chi\equiv\frac{\eta^{3-\alpha}}{\epsilon})$ where $\alpha$ is the order of singularity of the non-analytical potential, $\eta$ is the characteristic spread of the initial phase space density and $\epsilon$ is the perturbation strength. Instead, the corresponding quantum fidelity gap is insensitive to $\alpha$ due to strong diffraction effects that dominate the quantum dynamics.