论文标题
基于Riemann Zeta功能的量子厅电阻率的现象学公式
Phenomenological formula for Quantum Hall resistivity based on the Riemann zeta function
论文作者
论文摘要
我们提出了一个由基本功能构建的公式，该公式捕获了整数量子霍尔效应的横向电阻率$ρ_{xy} $的许多详细特征。这只是一个现象学公式，从某种意义上说，它不是基于涉及电子景观中电子的特定物理模型的任何运输计算，因此，是否存在实现这种电阻率的物理模型仍然是一个悬而未决的问题。然而，由于该公式涉及Riemann Zeta函数及其非平凡的零发挥着核心作用，因此根据其考虑考虑Riemann假设的含义是很有趣的。
We propose a formula constructed out of elementary functions that captures many of the detailed features of the transverse resistivity $ρ_{xy}$ for the integer quantum Hall effect. It is merely a phenomenological formula in the sense that it is not based on any transport calculation for a specific class of physical models involving electrons in a disordered landscape, thus, whether a physical model exists which realizes this resistivity remains an open question. Nevertheless, since the formula involves the Riemann zeta function and its non-trivial zeros play a central role, it is amusing to consider the implications of the Riemann Hypothesis in light of it.
