Consistent Langevin terms in the numeric treatment of superconducting wires

In order to take thermal fluctuations into account, Schmid added a Langevin term to the time-dependent Ginzburg-Landau equations. This addition was incorrect in two respects: (i) the size of this term contained a spurious factor and (ii) it ignored the influence of fluctuations of the electromagnetic potential A. For a 1D wire A can be gauged out of the problem and it might seem that its fluctuations are irrelevant. This is not the case, because the transformed order parameter does not behave as a “canonical” variable. In a recent study, based on the fluctuation-dissipation theorem, we investigated the influence that the fluctuations of A have on equilibrium and transport properties. It seems that this influence is strongest when the length of the wire is of the order of the coherence length. We also found the deviation from the Aslamazov-Larkin result near Tc and the influence of fluctuations and constrictions on phase slips. We have extended our formalism to the case of gapped superconductors, which obey a generalized form of the Ginzburg-Landau equations.