  Previous studies of quantum delta-kicked rotors have found momentum
probability distributions with a typical width (localization length $L$)
characterized by fractional $\hbar$-scaling, ie $L \sim \hbar^{2/3}$ in regimes
and phase-space regions close to `golden-ratio' cantori. In contrast, in
typical chaotic regimes, the scaling is integer, $L \sim \hbar^{-1}$. Here we
consider a generic variant of the kicked rotor, the random-pair-kicked particle
(RP-KP), obtained by randomizing the phases every second kick; it has no KAM
mixed phase-space structures, like golden-ratio cantori, at all. Our unexpected
finding is that, over comparable phase-space regions, it also has fractional
scaling, but $L \sim \hbar^{-2/3}$. A semiclassical analysis indicates that the
$\hbar^{2/3}$ scaling here is of quantum origin and is not a signature of
classical cantori.
