论文标题
Yang-Mills-higgs在复杂线束上运行：$γ$ - convergence和伦敦方程式
The Yang-Mills-Higgs functional on complex line bundles: $Γ$-convergence and the London equation
论文作者
论文摘要
我们将Abelian Yang-Mills-higgs在非自我双重缩放中的功能上，在封闭的Riemannian dimension $ n \ geq 3 $的封闭的Riemannian歧管上。该功能是金茨堡 - 兰道模型的自然概括，以实现非欧几里得环境的超导性。我们证明，在耦合参数的对数重新缩放的功能上，在强烈排斥的极限中证明了$γ$ - 连接的结果。作为推论，我们证明了最小剂的能量集中在尺寸$ n-2 $的面积最小化表面上，而最小化器的曲率则收敛于伦敦方程的溶液。
We consider the Abelian Yang-Mills-Higgs functional, in the non-self dual scaling, on a complex line bundle over a closed Riemannian manifold of dimension $n\geq 3$. This functional is the natural generalisation of the Ginzburg-Landau model for superconductivity to the non-Euclidean setting. We prove a $Γ$-convergence result, in the strongly repulsive limit, on the functional rescaled by the logarithm of the coupling parameter. As a corollary, we prove that the energy of minimisers concentrates on an area-minimising surface of dimension $n-2$, while the curvature of minimisers converges to a solution of the London equation.
