K-格上三维镜像模型中的路由与记忆
Routing and memory in the three-dimensional mirror model on K-lattice
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中文总结 AI 辅助
本研究通过数值实验分离三维K-格镜像模型中的透射通道位置与路由，发现物理透射亏缺及邻近通道抑制，并解析重复顶点贡献，为严格证明提供估计，但未建立无限体积离域化相。
中文摘要 AI 辅助
我们研究了与三维曼哈顿镜像模型（也称为K-格）中离域化相关的数值可观测量。我们的主要实验将透射边界通道的位置与它们之间的路由分离开来。我们推导出一个精确的条件比较，该比较保留了所有透射和反射孔径集合，并发现相对于该比较，物理透射存在统计上显著的亏缺。邻近的透射通道相对于具有相同基数的均匀子集也被抑制。第二个实验通过返回年龄解析了重复顶点的贡献。带符号旧记忆余项的平方范数与测量范围内的平方根倒数衰减一致。环形实验量化了持续减小的连续损耗，而最初显现的历史依赖性未能在独立重复中复现。最后，一个周期配置具有连通的辅助接触图，但仅有有限的路由循环。这些结果确定了对反射路由和自适应选择的重复访问代价的估计，这可能有助于严格的证明。它们并未建立无限体积的离域化相。
英文摘要
We study numerical observables relevant to delocalization in the three-dimensional Manhattan mirror model, also known as the K-lattice. Our principal experiment separates the locations of transmitting boundary channels from the routing between them. We derive an exact conditional comparison that preserves all transmission and reflection aperture sets, and find a statistically resolved deficit of physical transmission relative to this comparison. Nearby transmitting channels are themselves suppressed relative to a uniform subset with the same cardinality. A second experiment resolves the contribution of repeated vertices by their return age. The squared norm of the signed old-memory remainder is consistent with an inverse-square-root decay over the measured range. Annular experiments quantify decreasing continuation losses, while an initially apparent history dependence fails independent replication. Finally, a periodic configuration has a connected auxiliary contact graph but only finite routing cycles. These results identify estimates on reflection routing and adaptively selected revisit charges that may assist a rigorous proof. They do not establish an infinite-volume delocalized phase.
发表机构
- ESSEC（ESSEC商学院）
- Polytechnic Institute of Paris（巴黎理工学院）
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