Resistive Transition in a Superconducting Filament

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.