Josephson Junction

Josephson junction: two superconductors separated by a thin barrier. The RSJ (Resistively Shunted Junction) model gives: β_c d²φ/dt² + dφ/dt = I/I_c − sin(φ), equivalent to a damped pendulum or particle in a washboard potential U(φ) = −E_J(cos φ + (I/I_c)φ). Below the critical current (I < I_c), the phase particle is trapped in a well (zero voltage, supercurrent state). Above I_c, it runs downhill — finite voltage appears. The Stewart-McCumber parameter β_c controls underdamping (β_c ≫ 1 → hysteretic I-V curve). The voltage V = (ℏ/2e) dφ/dt — AC Josephson effect: phase winding generates oscillation at 483.6 GHz/mV.