Title: Passivity constraints on the relations between transmission, reflection, and absorption eigenvalues Show Chinese title

Title: 传输、反射和吸收本征值之间的因果关系上的无源性约束

Abstract: 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. Show Chinese abstract

Abstract: 我们研究线性时不变系统中传输、反射和吸收本征值之间关系的被动性约束。 利用矩阵分析技术，我们推导出这些本征值允许组合的必要且充分条件。 我们的分析表明，允许的本征值组合集在本征值空间中形成一个由迹等式和一组线性不等式表征的凸多面体。 令人惊讶的是，我们发现这一物理问题与阿尔弗雷德·霍恩不等式之间存在直接联系，这是矩阵理论中的一个基本结果。 我们提供了具有不同输入端口数量系统的具体例子，展示了随着系统规模的增长，约束条件的复杂性不断增加。 我们将理论应用于分析一些重要现象的影响，包括开放和封闭通道、相干完美反射和无反射散射模式，以及相干完美吸收和相干零吸收。 我们的研究不仅提供了对波传输本征值上被动性约束的完整表征，还在基础波物理和高级矩阵理论之间建立了一个意想不到的桥梁，为它们交汇处的研究开辟了新的途径。 这些结果在光学、声学和介观物理等多个应用领域的被动波器件设计和优化中具有重要意义。