Abstract
The contribution of thermal fluctuations to the conductivity of a narrow superconducting filament is examined. A Fokker-Planck equation based on time-dependent Ginzburg-Landau theory is used to describe the system. A variational solution of this equation yields an upper bound for the resistivity as a function of temperature in the limit of small electric field. The result is accurate above ${T}_{c}$ and appears to be a better estimate of the resistivity at and just below ${T}_{c}$ than that given by previous calculations.
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