论文标题
来自混乱和量子力学的拓扑维度？
Topological Dimensions from Disorder and Quantum Mechanics?
论文作者
论文摘要
我们最近表明，$ d = 3 $尺寸中的关键安德森电子有效地占据了红外（ir）缩放维度的空间区域$ d_ \ text {ir} \大约8/3 $。在这里，我们询问所涉及的维度子结构。我们将空间分配到相等量子出现概率的区域，以便包含一个区域的点具有相似的相关性，并计算每个区域的缩放尺寸$ d $。这使我们可以推断电子访问尺寸$ d $的概率密度$ p（d）$。我们发现$ p（d）$在$ d $非常接近2的峰值上达到了强大的峰值。实际上，我们的数据表明，$ p（d）$在间隔$ [d_ \ text {min}，d_ \ text {max}] \ of [4/3,8/3] $上的$ [d_ \ text {min}，d_ \ text {max}] $ and-limim-unim-limimume in Infline in Iff infins in Inffine n infin infins n infins，d_ \ text {min} $ d_ text {max}] \ of [4/3,8/3]后者援引量子力学和纯粹的混乱的组合可能导致拓扑维度的出现的可能性。尽管$ d_ \ text {ir} $是基于有效计数，其中$ p（d）$没有先验知识，但$ d_ \ text {ir} \ ge d_ \ d_ \ d_ \ text {max} $是随后形式主义的确切特征。强调了我们的结果与$ d_ \ text {ir} \近2 $的最新发现接近零量子染色体动力学模式。
We have recently shown that critical Anderson electron in $D=3$ dimensions effectively occupies a spatial region of infrared (IR) scaling dimension $d_\text{IR} \approx 8/3$. Here we inquire about the dimensional substructure involved. We partition space into regions of equal quantum occurrence probability, such that points comprising a region are of similar relevance, and calculate the IR scaling dimension $d$ of each. This allows us to infer the probability density $p(d)$ for dimension $d$ to be accessed by electron. We find that $p(d)$ has a strong peak at $d$ very close to 2. In fact, our data suggests that $p(d)$ is non-zero on the interval $[d_\text{min}, d_\text{max}] \approx [4/3,8/3]$ and may develop a discrete part ($δ$-function) at $d=2$ in infinite-volume limit. The latter invokes the possibility that combination of quantum mechanics and pure disorder can lead to emergence of topological dimensions. Although $d_\text{IR}$ is based on effective counting of which $p(d)$ has no a priori knowledge, $d_\text{IR} \ge d_\text{max}$ is an exact feature of the ensuing formalism. Possible connection of our results to recent findings of $d_\text{IR} \approx 2$ in Dirac near-zero modes of thermal quantum chromodynamics is emphasized.
