论文标题
金茨堡 - 兰道方程式在非紧密riemann表面
Ginzburg-Landau Equations on Non-compact Riemann Surfaces
论文作者
论文摘要
我们研究了恒定负曲率的非紧凑型Riemann表面上的线束上的金茨堡 - 兰道方程。我们证明存在严格少于恒定曲率（磁场）的溶液的存在。这些溶液是超导性的Abrikosov涡流晶格的非交通概括。猜想，它们是金茨堡 - 兰能（Ginzburg-Landau）能源的（本地）最小化。我们从基础黎曼表面的曲率方面获得了这些溶液及其能量的精确渐近膨胀。除其他事项外，我们的结果表明，金茨堡 - 陆方方程的量规翻译对称性的自发破坏。
We study the Ginzburg-Landau equations on line bundles over non-compact Riemann surfaces with constant negative curvature. We prove existence of solutions with energy strictly less than that of the constant curvature (magnetic field) one. These solutions are the non-commutative generalizations of the Abrikosov vortex lattice of superconductivity. Conjecturally, they are (local) minimizers of the Ginzburg-Landau energy. We obtain precise asymptotic expansions of these solutions and their energies in terms of the curvature of the underlying Riemann surface. Among other things, our result shows the spontaneous breaking of the gauge-translational symmetry of the Ginzburg-Landau equations.
