Time Scale of Intrinsic Resistive Fluctuations in Thin Superconducting Wires

A thermal-activation theory of intrinsic fluctuations in thin superconducting wires has been proposed by Langer and Ambegaokar (LA). Their fluctuation rate equals an exponential activation factor ${e}^{\ensuremath{-}\frac{\ensuremath{\Delta}F}{{k}_{B}T}}$ times a prefactor $\ensuremath{\Omega}$ which fixes the fluctuation time scale. Using a model based upon a time-dependent Ginzburg-Landau equation, we obtain a new estimate of $\ensuremath{\Omega}$ which is different in functional form from the LA estimate, and smaller than that estimate by more than 10 orders of magnitude for the conditions in recent experiments. To within corrections which are roughly of order unity, our expression is $\ensuremath{\Omega}=(\frac{L}{\ensuremath{\xi}})\frac{{(\frac{\ensuremath{\Delta}F}{{k}_{B}T})}^{\frac{1}{2}}}{\ensuremath{\tau}}$, where ($\frac{L}{\ensuremath{\xi}}$) is the length of the sample in units of the Ginzburg-Landau coherence length $\ensuremath{\xi}$, ${(\frac{\ensuremath{\Delta}F}{{k}_{B}T})}^{\frac{1}{2}}$ is a correction for overlap of fluctuations at different places along the wire, and $\ensuremath{\tau}\ensuremath{\approx}{10}^{\ensuremath{-}8}$ sec is the relaxation time in the Ginzburg-Landau equation. Although our specific expressions have been derived from a time-dependent Ginzburg-Landau theory, we expect from general physical arguments that they are relatively insensitive to the starting model.