Fractional $\hbar$-scaling for quantum kicked rotors without cantori

Wang, J.; Monteiro, T. S.; Fishman, S.; Keating, J. P.; Schubert, R.

Fractional $\hbar$-scaling for quantum kicked rotors without cantori

Authors

Description

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.
5 pages, 4 figures, Revtex, typos removed, further analysis added, authors adjusted