Renormalization group analysis of superconductors at zero field: statics and dynamics

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Critical fluctuations in superconductors are still poorly understood, in particular for dynamical fluctuations. This is in contrast to both equilibrium and dynamical critical properties of superfluid helium and non-frustrated magnetic systems. The difficulty in superconductors lies in the treatment of the thermal magnetic field fluctuations, which are strongly coupled to the fluctuations of the order parameter. One of the aims of the present project is to correct previous two-loop renormalization group calculations of equilibrium fluctuations, and to use Variational Perturbation Theory to resume the corrected two-loop result. This will lead to experimentally measurable critical properties of superconductors. The other aim is to develop, for the first time, a theory of dynamic critical phenomena in superconductors that includes the effect of magnetic thermal fluctuations. Both parts of the project are complementary and appropriate for a PhD student.