Current Dissipation in Thin Superconducting Wires: Accurate Numerical   Evaluation Using the String Method
  Current dissipation in thin superconducting wires is numerically evaluated by using the string method, within the framework of time-dependent Ginzburg-Landau equation with a Langevin noise term. The most probable transition pathway between two neighboring current-carrying metastable states, continuously linking the Langer-Ambegaokar saddle-point state to a state in which the order parameter vanishes somewhere, is found numerically. We also give a numerically accurate algorithm to evaluate the prefactors for the rate of current-reducing transitions. 
Tiezheng Qian, Weiqing Ren, Ping Sheng