  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.
