Short-time Loschmidt gap in dynamical systems with critical chaos.

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,,eta)=f_{cl}(chi_{cl} identical witheta;{3-alpha}/) ; alpha is the order of singularity of the potential, eta is the spread of the initial phase-space density, and 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}/) 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.