从无序和量子力学的拓维度?
Ivan Horváth1,2, Peter Markoš3
1Nuclear Physics Institute CAS, 25068 Řež near Prague, Czech Republic.
Entropy (Basel, Switzerland)
|November 24, 2023
概括
研究人员在3D空间中探索了关键安德森电子的维度亚结构. 研究结果显示,概率密度在二维附近达到峰值,这表明量子力学和混乱中出现的整数维度.
科学领域:
- 凝聚物质物理学 凝聚物质物理学
- 量子力学就是量子力学.
- 无序的系统是无序的系统.
背景情况:
- 在3D空间中,关键的安德森电子实际上占据了一个具有近8/3的红外 (IR) 缩放维度 (dIR) 的区域.
- 了解维子结构和相关维度的分布对于描述电子在无序系统中的行为至关重要.
研究的目的:
- 在3D中研究关键安德森电子的维度亚结构.
- 为了确定电子访问的缩放维度"d"的概率密度函数,p(d).
- 探索从量子力学和混乱中整数维的潜在出现.
主要方法:
- 将3D空间的空间划分为具有相同量子发生概率的区域.
- 计算每个分区区域的IR缩放维度"d".
- 根据计算的尺寸推断概率密度p (d) 的推断.
主要成果:
- 概率密度p(d) 在维度d=2.2附近呈现出强烈的峰值.
- 在 [dmin,dmax] ≈ [4/3, 8/3] 间隔中,p (d) 是非零的.
- 在无限体积极限中,在d=2时可能出现一个离散元件 (delta函数).
结论:
- 这项研究表明,量子力学和混乱可以导致整数 (拓) 维度的出现.
- 访问维度的上限 (dmax ≈ 8/3) 与有效的红外扩展维度 (dIR) 相一致.
- 这些发现和最近对dIR ≈ 2在迪拉克热量子色态学近零模式的观测之间存在潜在的联系.
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