论文标题
量子问题的生物萨瓦特法律
Biot-Savart law in quantum matter
论文作者
论文摘要
我们研究了一类晶格系统的拓扑性质，它们的Bloch载体可以表示为辅助空间中两个独立的周期矢量函数（调子）的差异。我们确切地表明，每个循环作为退化线都会产生一个极化场，遵守生物 - 萨瓦特定律：退化线充当电流荷线，而极化场则对应于生成的磁场。在非平凡的拓扑系统上应用安培的圆形法律，我们发现两个bloch结彼此纠缠，形成一个链接，链接数为能量频段的Chern数值。此外，提出了两个晶格模型，一个扩展的QWZ模型和一个带有磁通量的准1D模型，以示例我们的方法的应用。在生物 - 萨瓦特定律的帮助下，泵送电荷作为Chern数量的动态度量是从准绝热过程中获得的。
We study the topological nature of a class of lattice systems, whose Bloch vector can be expressed as the difference of two independent periodic vector functions (knots) in an auxiliary space. We show exactly that each loop as a degeneracy line generates a polarization field, obeying the Biot-Savart law: The degeneracy line acts as a current-carrying wire, while the polarization field corresponds to the generated magnetic field. Applying the Ampere's circuital law on a nontrivial topological system, we find that two Bloch knots entangle with each other, forming a link with the linking number being the value of Chern number of the energy band. In addition, two lattice models, an extended QWZ model and a quasi-1D model with magnetic flux, are proposed to exemplify the application of our approach. In the aid of the Biot-Savart law, the pumping charge as a dynamic measure of Chern number is obtained numerically from quasi-adiabatic processes.
