分层洛伦兹镜模型：正常传输与一个通用的2/3均方律
Hierarchical Lorentz Mirror Model: Normal Transport and a Universal $2/3$ Mean--Variance Law
AI总结：
该研究提出分层洛伦兹镜模型，证明了正常传输并揭示了2/3均方律的通用性。
摘要：
洛伦兹镜模型提供了一个清晰的环境随机性研究宏观传输的设定。我们引入了一个分层版本，其左右交叉分布满足精确的递推关系。在维度d≥3的情况下，我们证明了正常传输：平均电导在所有长度尺度上都按截面/长度的比例缩放。一个由数值支持的高斯闭合预测，电导的方差与均值比收敛到通用值2/3（“2/3定律”）。我们在原始（非分层）洛伦兹镜模型中为d=3提供了2/3定律的数值证据，并推测它是一个正常传输的通用特征，由随机电流匹配引起。在边缘情况d=2时，我们的分层递推重现了已知的平均电导及其方差的缩放。一篇讨论论文背景和主要结果的视频可用：https://youtu.be/G1nqKd6MiXo
英文摘要：
The Lorentz mirror model provides a clean setting to study macroscopic transport generated solely by quenched environmental randomness. We introduce a hierarchical version whose distribution of left--right crossings satisfies an exact recursion. In dimensions $d\ge3$, we prove two-sided bounds that support normal transport: the mean conductance scales as (cross-section)/(length). A Gaussian closure, supported by numerics, predicts that the variance-to-mean ratio of the dimensionless conductance converges to the universal value $2/3$ for all $d\ge2$ (the ``$2/3$ law''). We provide numerical evidence for the $2/3$ law in the original (non-hierarchical) Lorentz mirror model in $d=3$, and conjecture that it is a universal signature of normal transport induced by random current matching. In the marginal case $d=2$, our hierarchical recursion reproduces the known scaling of the mean and variance of conductance. A YouTube video discussing the background and the main results of the paper is available: https://youtu.be/G1nqKd6MiXo
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
