Abstract: We study the stochastic dynamics of superconductive-resistive switching in hysteretic current-biased superconducting nanowires undergoing phase-slip fluctuations. We evaluate the mean switching time using the master-equation formalism, and hence obtain the distribution of switching currents. We find that as the temperature is reduced this distribution initially broadens; only at lower temperatures does it show the narrowing with cooling naively expected for phase slips that are thermally activated. We also find that although several phase-slip events are generally necessary to induce switching, there is an experimentally accessible regime of temperatures and currents for which just one single phase-slip event is sufficient to induce switching, via the local heating it causes.

Abstract: Eilenberger's transportlike equations for a superconductor of type II can be simplified very much in the dirty limit. In this limit a diffusionlike equation is derived which is the generalization of the de Gennes-Maki theory for dirty superconductors to arbitrary values of the order parameter.