Fractional Quantization Interpretation for the Phase-Locking dynamics of driven-Superconductive Josephson ac effect

This report proposes a quantization interpretation on the Macroscopic quantum dynamics of driven ac Jesephson effect. A discussion is made to compare the so-called classical resonance and the Macroscopic dynamics of 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 quantization. The proposed fractional quantization of macroscopic quantum phase locking may provide a new unifying thinking on the Quantized Hall Effects including IQHE and FQHE.