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(α, ϵ, η)= f_cl(χ_cl equivη^3-α/ϵ); α is the order of singularity of the potential, η is the spread of the initial phase space density and ϵ is the perturbation strength. Instead, the quantum echo gap is insensitive to α, described by a scaling law F_g

more »

... f_q(χ_q = η^2/ϵ) 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.