Attempt to Describe Phase Slips by Means of an Adiabatic Approximation

As a plausibility test for the feasibility of extension of the quasiclassical Keldysh–Usadel technique to slowly varying situations, we assess the influence of the time-derivative term in the time-dependent Ginzburg–Landau equation. We consider cases in which the superconducting state in a nanowire varies slowly, either because the voltage applied on it is small, or because most of phase drift takes place next to the boundaries. An approximation without this time derivative can describe the superconducting state away from phase slips, but is unable to predict the value or the existence of a critical voltage at which evolution becomes non-stationary.