Higher order corrections to electrical conductivity due to the fluctuation of the superconducting order parameter in the paraconducting region are studied systematically. Use is made of a perturbation expansion in powers of independent fluctuations. When δ≫ε0, where δ is a pair breaking energy and ε0(=(8/π)(T-Tc)) is the relaxation rate of the order parameter, it is shown that the deviation from the mean field theory can be described by use of the renormalized fluctuation propagator, which is consistent with the idea of the dynamical scaling theory. When δ≪ε0, on the other hand, the conductivity diverges more strongly than that expected from the analysis of the static properties, and in this case the above idea appears to be not applicable. In particular the most divergent series are summed up for small δ, and it is shown that the anomalous term still diverges but with a weaker δ-1 dependence. Fluctuation effects on other transports coefficients are also studied.
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Takayama et al. (1971) studied this question.