I = Ic sin(φ) · V = (ℏ/2e) dφ/dt · DC & AC Josephson effects
DC Josephson effect: zero-voltage supercurrent I = I_c sin(φ) for |I| < I_c. AC Josephson effect: for V ≠ 0, phase evolves as dφ/dt = 2eV/ℏ, creating AC current at frequency f_J = 2eV/h ≈ 483.6 MHz/μV. The RCSJ model: ℏ/2eR · dφ/dt + I_c sin(φ) = I_bias (resistively & capacitively shunted junction).