具有不连续和快速振荡钉扎项的Ginzburg-Landau泛函。部分II：非零次情况
The Ginzburg-Landau functional with a discontinuous and rapidly oscillating pinning term. Part II: the non-zero degree case
摘要：
我们考虑极小的Ginzburg-Landau能量与一个不连续的和快速振荡的钉扎项，受狄利克雷边界条件的程度$d > 0$。钉扎项模拟了域中无限数量的小杂质。我们证明了对于含有杂质的强II型超导体，极小化子恰好有d个孤立的零点（涡旋）。这些涡旋是1度的，并且被杂质钉扎。在Bethuel、Brezis和Hélein研究的标准情况下，涡的宏观位置由涡/涡和涡/边界排斥效应决定。在某些特殊情况下，我们证明了它们的宏观位置趋于最小化Bethuel-Brezis-Hélein的重整化能量。此外，杂质影响涡旋的微观位置。我们的技术允许我们处理不同大小的杂质。在这种情况下，我们证明了最大的杂质的旋涡钉扎。
英文摘要：
We consider minimizers of a Ginzburg-Landau energy with a discontinuous and rapidly oscillating pinning term, subject to a Dirichlet boundary condition of degree $d > 0$. The pinning term models an unbounded number of small impurities in the domain. We prove that for strongly type II superconductor with impurities, minimizers have exactly d isolated zeros (vortices). These vortices are of degree 1 and pinned by the impurities. As in the standard case studied by Bethuel, Brezis and Hélein, the macroscopic location of vortices is governed by vortex/vortex and vortex/ boundary repelling effects. In some special cases we prove that their macroscopic location tends to minimize the renormalized energy of Bethuel-Brezis-Hélein. In addition, impurities affect the microscopic location of vortices. Our technics allows us to work with impurities having different size. In this situation we prove that vortices are pinned by the largest impurities.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
