Related Experiment Video
Updated: Jul 7, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
Published on: June 8, 2018
Fractional variant Planck's over 2pi scaling for quantum kicked rotors without Cantori
J Wang1, T S Monteiro, S Fishman
1Temasek Laboratories, National University of Singapore, 117542 Singapore.
Abstract:
Previous studies of quantum delta-kicked rotors have found momentum probability distributions with a typical width (localization length L) characterized by fractional variant Planck's over 2pi scaling; i.e., L approximately variant Planck's over 2pi;{2/3} in regimes and phase-space regions close to "golden-ratio" cantori. In contrast, in typical chaotic regimes, the scaling is integer, L approximately variant Planck's over 2pi;{-1}. Here we consider a generic variant of the kicked rotor, the random-pair-kicked particle, obtained by randomizing the phases every second kick; it has no Kol'mogorov-Arnol'd-Moser mixed-phase-space structures, such as golden-ratio cantori, at all. Our unexpected finding is that, over comparable phase-space regions, it also has fractional scaling, but L approximately variant Planck's over 2pi;{-2/3}. A semiclassical analysis indicates that the variant Planck's over 2pi;{2/3} scaling here is of quantum origin and is not a signature of classical cantori.
Related Concept Videos
Determination of Pi Terms
The theorem indicates that the number...
Time and frequency -Domain Interpretation of PI Control
Acting as a low-pass filter, the PI controller slows the system's response and extends settling times. This requires careful...
The Buckingham Pi Theorem
Calculation of First-Law Quantities II
Bernoulli's Equation
Equation of Rotational Dynamics