Josephson Junction

RSJ Model: The junction phase φ obeys a "tilted washboard" potential: U(φ) = −E_J(cos φ + I/I_c·φ). When I < I_c, the phase particle is trapped in a well → zero DC voltage (supercurrent). When I > I_c, the particle rolls downhill → oscillating phase → finite voltage V = ħω_J/2e. The I-V curve shows hysteresis for underdamped junctions (large β_c): once running, the junction stays running even as current decreases below I_c.