  We identify a border between regular and chaotic quantum dynamics. The border
is characterized by a power law decrease in the overlap between a state evolved
under chaotic dynamics and the same state evolved under a slightly perturbed
dynamics. For example, the overlap decay for the quantum kicked top is well
fitted with $[1+(q-1) (t/\tau)^2]^{1/(1-q)}$ (with the nonextensive entropic
index $q$ and $\tau$ depending on perturbation strength) in the region
preceding the emergence of quantum interference effects. This region
corresponds to the edge of chaos for the classical map from which the quantum
chaotic dynamics is derived.
