论文标题
量子曲率的相关性和Chern数字的差异
Correlations of quantum curvature and variance of Chern numbers
论文作者
论文摘要
我们使用随机矩阵模型分析了复杂量子系统中量子曲率的相关函数，以提供通用相关函数的示例。我们表明，相关函数在较小的距离下作为距离的倒数。我们还定义和分析混合态的相关函数，表明它是有限的，但在小分离处是单数。蒙特 - 卡洛模拟支持两种相关性的通用形式上的缩放假设。我们将曲率的相关函数与Chern整数的方差联系起来，这些方差可以描述量化的霍尔电导。
We analyse the correlation function of the quantum curvature in complex quantum systems, using a random matrix model to provide an exemplar of a universal correlation function. We show that the correlation function diverges as the inverse of the distance at small separations. We also define and analyse a correlation function of mixed states, showing that it is finite but singular at small separations. A scaling hypothesis on a universal form for both types of correlations is supported by Monte-Carlo simulations. We relate the correlation function of the curvature to the variance of Chern integers which can describe quantised Hall conductance.
