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

超导体的临界涨落，特别是动态涨落，仍然知之甚少。这与超流氦和非受挫磁系统的平衡和动力学临界特性形成对比。超导体的难点在于处理与序参量波动密切相关的热磁场波动。本项目的目的之一是纠正以前平衡波动的双环重整化群计算，并使用变分摄动理论来恢复纠正的双环结果。这将导致实验测量超导体的临界性质。另一个目标是，首次发展一种包括磁热波动效应在内的超导体动态临界现象理论。项目的两个部分是互补的，适合博士生。

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.