Low-voltage dynamical properties of superconducting weak links

An extended-resistively-shunted-junction model is described to account for some nonequilibrium effects in superconducting weak links. The theory is based on a one-dimensional linearized time-dependent Ginzburg-Landau equation subject to rigid-boundary conditions. An analytical solution has been obtained by WKB approximation in the low-voltage region, and it can be used to calculate the complete position and time dependence of the supercurrent and pair densities. The supercurrent contains a cosφ term which appears in good agreement with experimental results. The pair density also contains a similar cosφ term. Several length- and temperature-dependent effects are predicted. It is shown that this model gives a quantitative description of the phase-slip process at the center of the weak link.