论文标题
在二维Riemannian歧管上具有拓扑诱导的自由不连续性的分数涡流之间的重新归一化能量
Renormalized energy between fractional vortices with topologically induced free discontinuities on 2-dimensional Riemannian manifolds
论文作者
论文摘要
在没有边界的二维Riemannian歧管上，我们考虑了由两个术语总和给出的功能家族的变化极限：Ginzburg-landau和外围项。我们的缩放范围允许通过订单参数描述低能量状态，该参数可能具有有限的（可能是）通过线路不连续性（字符串缺陷）连接的（可能是）有限分数的有限点奇异性（涡旋状缺陷）。我们的主要结果是紧凑性和$γ$ - convergence定理，它显示了粗粒子的限制能量如何取决于歧管在驱动涡流和字符串缺陷之间相互作用时的几何形状。
On a two-dimensional Riemannian manifold without boundary we consider the variational limit of a family of functionals given by the sum of two terms: a Ginzburg-Landau and a perimeter term. Our scaling allows low-energy states to be described by an order parameter which can have finitely many point singularities (vortex-like defects) of (possibly) fractional-degree connected by line discontinuities (string defects) of finite length. Our main result is a compactness and $Γ$-convergence theorem which shows how the coarse grained limit energy depends on the geometry of the manifold in driving the interaction between vortices and string defects.
