论文标题
通过拓扑矢量电势分类深色孤子
Classification of Dark Solitons via Topological Vector Potentials
论文作者
论文摘要
深色Soliton是物理系统中最有趣的非线性激发之一，在均匀背景上表现出空间局部的密度“ DIP”，并伴随着相位的相位跳跃。但是，深色孤子的拓扑特性远非充分理解。我们的调查首次揭示了非线性激发的矢量潜力，其线路积分使阶段的跳跃具有惊人的阶段。更重要的是，我们发现矢量电位字段具有类似于Lagrangian表示的Wess-Zumino项的拓扑结构。它可以诱导某些定期散布在复杂平面上的点状磁场，每个磁场都具有基本$π$的量化磁通量。然后，我们计算矢量电位场拓扑歧管的欧拉特征，并根据索引对所有已知的暗词进行分类。
Dark soliton is one of most interesting nonlinear excitations in physical systems, manifesting a spatially localized density "dip" on a uniform background accompanied with a phase jump across the dip. However, the topological properties of the dark solitons are far from fully understood. Our investigation for the first time uncover a vector potential underlying the nonlinear excitation whose line integral gives the striking phase jump. More importantly, we find that the vector potential field has a topological configuration in analogous to the Wess-Zumino term in a Lagrangian representation. It can induce some point-like magnetic fields scattered periodically on a complex plane, each of them has a quantized magnetic flux of elementary $π$. We then calculate the Euler characteristic of the topological manifold of the vector potential field and classify all known dark solitions according to the index.
