Semi-Classical Collective Quantum Phase-Locking Picture for a Macroscopic Quantization Analogy Between Periodically Driven Josephson Oscillation and Quantum Hall Effects

This report proposes a semi-classical quantization scheme for the Macroscopic quantum dynamics

of driven ac Josephson effect. A discussion is made for linking the classical resonance to the Macroscopic

quantum dynamics of Josephson oscillation of the phase difference across the junction. A collective

quantum phase locking dynamics, with integer or fractional winding numbers, is proposed to unify the

Shapiro steps as a mechanism of semiclassical quantization from ac Josephson relation.

Collective quantum phase-locking mechanism can be used to model the quantized Hall effects by considering the

relative motion between the magnetic flux quanta and the flowing electrons as a common quantization mechanism. From the

phase-locking dynamics, the collective phase changes of the electron and the magnetic 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 Macroscopic quantum phase-locking dynamics, the same as for the rf-driven

superconductive Josephson oscillation.