Non-perturbative response: Chaos versus disorder

Quantized chaotic systems are generically characterized by two energy scales: the mean level spacing Δ, and the bandwidth Δ_b α ℏ. This implies that with respect to driving such systems have an adiabatic, a perturbative and a non-perturbative regimes. A 'strong' nonlinearity in the response, due to a quantal non-perturbative effect, is found for disordered systems that are described by random matrix theory models. Is there a similar effect for quantized chaotic systems? Theoretical arguments cannot exclude the existence of an analogous 'weak' version of the above-mentioned nonlinear response effect, but our numerics demonstrates an unexpected degree of semiclassical correspondence.