Quantized Decay Charges in Non-Hermitian Networks Characterized by Directed Graphs

Abstract

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