三维各向异性超导体第一临界场的涡旋密度模型
First critical field of highly anisotropic three-dimensional superconductors via a vortex density model
摘要：
分析了强磁场作用下$3$ d各向异性层状超导体的平均场模型。平均场模型的出现是因为劳伦斯-多尼亚赫能量在某些区域的$Gamma$极限。一个重新制定的问题的基础上凸对偶，使我们能够表征的第一个临界场$H_{c_1}$的层状超导体，领先的顺序。在以前的工作中，Alama-Bronsard-Sandier \cite{ABS}已经推导出了满足周期边界条件的构型的$H_{c_1}$的渐近值;在这种情况下，描述Lawrence-Doniach能量极小化的问题简化为$2$ d问题。在这项工作中，我们对待的物理情况下，没有任何周期性的假设，从而导致研究一个微妙的和本质上$3$ d非局部障碍问题首先由Baldo-Jerrard-Orlandi-Soner \cite{BJOS2}各向同性的金斯堡-朗道能量。我们利用平均场模型的特殊各向异性结构得到了$H_{c_1}$的一个特征。
英文摘要：
We analyze a mean field model for $3$d anisotropic superconductors with a layered structure, in the presence of a strong magnetic field. The mean field model arises as the $Gamma$-limit of the Lawrence-Doniach energy in certain regimes. A reformulation of the problem based on convex duality allows us to characterize the first critical field $H_{c_1}$ of the layered superconductor, up to leading order. In previous work, Alama-Bronsard-Sandier \cite{ABS} have derived the asymptotic value of $H_{c_1}$ for configurations satisfying periodic boundary conditions; in that setting describing minimizers of the Lawrence-Doniach energy reduces to a $2$d problem. In this work, we treat the physical case without any periodicity assumptions, and are thus led to studying a delicate and essentially $3$d non-local obstacle problem first derived by Baldo-Jerrard-Orlandi-Soner \cite{BJOS2} for the isotropic Ginzburg-Landau energy. We obtain a characterization of $H_{c_1}$ using the special anisotropic structure of the mean field model.
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