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

TL;DR

This study reveals fractional ${ extstyle rac{2}{3}}$-scaling of localization length in a randomized quantum kicked rotor variant, indicating a quantum origin distinct from classical cantori effects.

Contribution

It demonstrates fractional ${ extstyle rac{2}{3}}$-scaling in a phase-space without classical cantori, challenging previous associations of such scaling with classical structures.

Findings

Localization length scales as ${ extstyle rac{2}{3}}$ power of ${ extstyle rac{1}{ ext{hbar}}}$

Fractional scaling observed in a non-cantori, randomized kicked rotor

Semiclassical analysis suggests quantum origin of the fractional scaling

Abstract

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.