Collective Quantum Phase-Locking Picture for an Analogy Between Periodically Driven Josephson Oscillation and Quantum Hall Effects

In this report, a comparison between the phase-slippage picture of superconductive Josephson effect and the Quantum Hall effects is examined. Collective quantum phase-locking mechanism can be used to unify these two effects by considering the relative motion between the flux quanta and the electron as a common mechanism. From the phase-locking dynamics, the phase changes of the electron and the flux during their relative motion can be in integer ratios or fractional ratios. The Integer Quantum Hall Effect and the Fractional Quantum Hall Effect can thus be shown as collective quantum phase-locking dynamics, as for the rf-driven superconductive Josephson oscillation. The collective quantization, especially the fractional one, is discussed with the pure dynamical arguments. The chaotic behavior of the collective phase-locking is compared with the probabilistic behavior of traditional quantum mechanical quantization.