将因果性规律直接嵌入传统散射矩阵,实现与实验数据的无缝对接。
Causality Sum Rules in Conventional Scattering Matrices
- 通过消除参考域引入的时间超前,定义域延迟矩阵恢复因果时间原点。
- 在解析性等假设下,矩阵成为舒尔函数,导出相干叠加与多通道损耗的约束边界。
- 适用于光子器件设计与测量,尤其适合关注插入损耗和延迟带宽权衡的研究者。
散射矩阵是描述光子与电磁器件的标准实验与计算工具。传统输入-输出矩阵显式包含无源性,但因果性求和规则通常需转换到辅助变量后才能表述。本文提出,通过消除参考域引入的时间超前,可直接在传统散射矩阵中写出因果性规则。利用各通道最早到达延迟,定义域延迟矩阵,在保持实频率无源性的前提下恢复因果时间原点。在显式解析性、透明性和正则性假设下,该矩阵成为舒尔函数,支持凯利-赫格洛茨构造。由此导出的投影与行列式界,约束了相干通道叠加及多通道总损耗。该框架重现了罗扎诺夫吸收体极限与球形多极求和规则,并将因果性边界扩展至可测物理量,包括插入损耗、抑制的奇异值通道,以及条件无损延迟-带宽权衡。本工作直接连接基础因果理论与实验可测散射数据。初始理论路径由量子引擎(Qiushi Engine)这一自主探索的AI科研系统提出,随后经作者验证、优化与深化,展示了人机协同科学发现的新范式。
原文摘要 · Abstract (English)
Scattering matrices are the standard experimental and computational description of photonic and electromagnetic devices. Passivity is explicit in the conventional incoming-outgoing matrix, whereas causality sum rules are usually formulated only after transforming the response into auxiliary variables. Here we show that these rules can be written directly in the conventional scattering matrix by removing the time advance introduced by the reference domain. Using the earliest-arrival delay of each channel, we define a domain-delayed matrix that preserves real-frequency passivity while restoring the causal time origin. Under explicit analyticity, transparency, and regularity assumptions, this matrix becomes a Schur function, enabling a Cayley-Herglotz construction. The resulting projected and determinant bounds constrain coherent channel superpositions and aggregate multichannel loss. The framework recovers Rozanov's absorber limit and spherical-multipole sum rules, while extending causality bounds to measurable quantities including insertion loss, suppressed singular-value channels, and conditional lossless delay-bandwidth trade-offs. Our work directly connects fundamental causality theory with experimentally accessible scattering data. The initial theoretical route is autonomously explored by Qiushi Engine, an AI research system for open-ended scientific discovery, and subsequently verified, refined, and developed by the authors, demonstrating a hybrid AI-human discovery workflow.
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