论文标题
关于拓扑缺陷晶格的能量
On the energy of topological defect lattices
论文作者
论文摘要
由于对数函数是在两个维度上的泊松方程的解决方案，因此它作为库仑相互作用在二维中是库仑相互作用，在II型超导体中的abrikosov通量线之间的相互作用，或弹性介质中的线条缺陷之间的相互作用等等。因此，由于其多种应用，与对数相互作用的线路相互作用的晶格是一项强烈研究的主题。自1990年代后期以来，泊松方程的解决方案以无限总和的形式知道。在本文中，我们就jacobi theta函数提出了一种以封闭形式的替代分析解决方案。
Since the logarithm function is the solution of Poisson's equation in two dimensions, it appears as the Coulomb interaction in two dimensions, the interaction between Abrikosov flux lines in a type II superconductor, or between line defects in elastic media, and so on. Lattices of lines interacting logarithmically are, therefore, a subject of intense research due to their manifold applications. The solution of the Poisson equation for such lattices is known in the form of an infinite sum since the late 1990's. In this article we present an alternative analytical solution, in closed form, in terms of the Jacobi theta function.
