  We study the Loschmidt echo F(t) for a class of dynamical systems showing
critical chaos. Using a kicked rotor with singular potential as a prototype
model, we found that the classical echo shows a gap (initial drop) 1-F_g where
F_g scales as F_g(\alpha, \epsilon, \eta)= f_cl(\chi_cl
equiv\eta^{3-\alpha}/\epsilon); \alpha is the order of singularity of the
potential, \eta is the spread of the initial phase space density and \epsilon
is the perturbation strength. Instead, the quantum echo gap is insensitive to
\alpha, described by a scaling law F_g = f_q(\chi_q = \eta^2/\epsilon) which
can be captured by a Random Matrix Theory modeling of critical systems. We
trace this quantum-classical discrepancy to strong diffraction effects that
dominate the dynamics.
