RCSJ Josephson Junction: Tilted Washboard & Phase Portrait

A current-biased Josephson junction behaves exactly like a damped pendulum driven by a constant torque: its superconducting phase φ rolls down a "washboard" potential tilted by the bias current, resisted by the shunt resistance's damping. This simulator integrates that equation of motion — φ̈ + φ̇/Q + sin φ = i — directly in 2D, plotting the tilted washboard with the phase particle rolling along it, the (φ mod 2π, φ̇) phase portrait, and the resulting current–voltage curve. Sweep the bias current across the switching threshold i = 1 and back down to trace the hysteresis loop between the zero-voltage and running states, and change the quality factor Q to see how damping controls the gap between the switching current and the retrapping current i_r ≈ 4/(πQ).