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(α,ϵ,η)=f_cl(χ_cl≡η^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=f_q(χ_q=η²/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.