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Fluctuations in superconducting rings with two order parameters

Starting from the Ginzburg-Landau energy functional, we discuss how the presence of two order parameters and the coupling between them influence a superconducting ring in the fluctuative regime. Our method is exact, but requires numerical implementation. We also study approximations for which some analytic expressions can be obtained, and check their ranges of validity. We provide estimates for the temperature ranges where fluctuations are important, calculate the persistent current in magnesium diboride rings as a function of temperature and enclosed flux, and point out its additional dependence on the cross-section area of the ring. We find temperature regions in which fluctuations enhance the persistent currents and regions where they inhibit the persistent current. The presence of two order parameters that can fluctuate independently always leads to larger averages of the order parameters at Tc, but only for appropriate parameters this yields larger persistent current. In cases of very different material parameters for the two coupled condensates, the persistent current is inhibited.