传输、反射与吸收本征值之间关系的无源性约束
Passivity constraints on the relations between transmission, reflection, and absorption eigenvalues
AI总结：
本研究利用矩阵分析推导了线性时不变系统中传输、反射、吸收本征值组合的无源性充要条件，发现其与Alfred Horn不等式相关，为波器件设计及波物理与矩阵理论交叉研究提供了新方向。
摘要：
我们研究了线性时不变系统中传输、反射与吸收本征值之间关系的无源性约束。利用矩阵分析技术，我们推导得出了这些本征值可允许组合的充要条件。我们的分析表明，可允许的本征值组合集合在本征值空间中构成一个凸多面体，其特征为一个迹等式和一组线性不等式。令人惊讶的是，我们发现这一物理问题与矩阵理论中的基础结果——阿尔弗雷德·霍恩（Alfred Horn）不等式——之间存在直接联系。我们针对输入端口数量不同的系统给出了明确示例，证明了约束的复杂度会随着系统规模的增大而提升。我们将理论应用于分析重要现象的内涵，包括开放与闭合通道、相干完美反射与无反射散射模式、相干完美吸收与相干零吸收。我们的研究结果不仅完整刻画了波输运本征值的无源性约束，还在基础波动物理学与高等矩阵理论之间搭建了一座出人意料的桥梁，为二者交叉领域的研究开辟了新路径。这些结果对光学、声学和介观物理学中广泛应用的无源波器件的设计与优化具有重要意义。
英文摘要：
We investigate the passivity constraints on the relations between transmission, reflection, and absorption eigenvalues in linear time-invariant systems. Using techniques from matrix analysis, we derive necessary and sufficient conditions for the permissible combinations of these eigenvalues. Our analysis reveals that the set of allowable eigenvalue combinations forms a convex polyhedron in eigenvalue space, characterized by a trace equality and a set of linear inequalities. Surprisingly, we uncover a direct connection between this physical problem and Alfred Horn's inequalities, a fundamental result in matrix theory. We provide explicit examples for systems with varying numbers of input ports, demonstrating the increasing complexity of the constraints as system size grows. We apply our theory to analyze the implications of important phenomena, including open and closed channels, coherent perfect reflection and reflectionless scattering modes, and coherent perfect absorption and coherent zero absorption. Our findings not only offer a complete characterization of passivity constraints on wave transport eigenvalues but also establish an unexpected bridge between fundamental wave physics and advanced matrix theory, opening new avenues for research at their intersection. These results have significant implications for the design and optimization of passive wave devices across a wide range of applications in optics, acoustics, and mesoscopic physics.
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