标题： 非厄米网络中由有向图表征的量化衰减电荷 显示英文标题

标题： Quantized decay charges in non-Hermitian networks characterized by directed graphs

摘要： 非厄米物理揭示了一个在厄米系统中不存在的奇特现象领域，其中非厄米皮肤效应（NHSE）展示了由非互易相互作用驱动的边界局域本征态。 在这里，我们引入了一类新的非厄米系统，表现出纯衰减模式：具有纯平滑指数衰减的本征态，没有传统NHSE典型的振荡波图案。 这些系统被建模为具有非互易跃迁的有向图，它们揭示了量化衰减电荷，定义为每个节点沿边的衰减常数之和，提供了一种新的拓扑不变量。 我们推导了这些模式的普遍条件，使得从一维环、具有复杂连通性的有向图到高维晶格都能实现灵活的配置。 使用微波谐振电路进行的实验验证确认了预测的纯衰减轮廓。 这一发现为光子学、信号处理等领域的潜在应用铺平了道路，利用非厄米网络独特的拓扑特性。 显示英文摘要

摘要： Non-Hermitian physics has unveiled a realm of exotic phenomena absent in Hermitian systems, with the non-Hermitian skin effect (NHSE) showcasing boundary-localized eigenstates driven by non-reciprocal interactions. Here, we introduce a new class of non-Hermitian systems exhibiting pure decay modes: eigenstates with pure, smooth exponential decay, devoid of the oscillatory wave patterns typical of traditional NHSE. Modeled as directed graphs with non-reciprocal hopping, these systems reveal quantized decay charges, defined as the sum of decay constants along edges at each node, offering a novel topological invariant. We derive universal conditions for these modes, enabling versatile configurations from one-dimensional rings, directed graphs with complicated connectivity, to higher-dimensional lattices. Experimental validation using microwave resonant circuits confirms the predicted pure decay profiles. This discovery paves the way for potential applications in photonics, signal processing, and beyond, harnessing the unique topological properties of non-Hermitian networks.