The theory of current transport in a narrow superconducting channel accounting for thermal fluctuations is revisited. The value of voltage appearing in the sample is found as the function of temperature (close to transition temperature $T-T_{mathrm{c}}$ $ll T_{mathrm{c}}$) and bias current $J<J_{mathrm{c}}$ ( $J_{mathrm{c}}$ is a value of critical current calculated in the framework of the BCS approximation, neglecting thermal fluctuations). It is shown that the careful analysis of vortex crossing of the stripe results in considerable increase of the activation energy.
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