Threshold fluctuations in a superconducting current-carrying bridge

We calculate the energy of threshold fluctuation $\delta F_{thr}$ which triggers the transition of a superconducting current-carrying bridge to the resistive state. We show that the dependence $\delta F_{thr}{\left(I\right)\propto I_{dep}\hslash (1-I/I_{dep})}^{5/4}/e$, found by Langer and Ambegaokar for a long bridge with length $L\gg \xi$, holds far below the critical temperature in both dirty and clean limits (here I _dep is the depairing current of the bridge and ξ is a coherence length). We also find that even a 'weak' local defect (leading to a small suppression of the critical current of the bridge $I_c\lesssim I_{dep}$) provides $\delta F_{thr}\propto I_c\hslash {(1-I/I_c)}^{3/2}/e$, typical for a short bridge with $L\ll \xi$ or a Josephson junction. (paper)