Phase particle in a tilted washboard: superconducting tunnel junction dynamics
A Josephson junction is described by the RSJ model: beta*phi_ddot + phi_dot = I/Ic - sin(phi), equivalent to a particle in a washboard potential U(phi) = -cos(phi) - I*phi. Below the critical current Ic the particle is trapped (zero voltage, superconducting). Above Ic it rolls freely (finite voltage). Thermal fluctuations cause stochastic switching — the basis of SQUID magnetometers and superconducting qubits.