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

TL;DR

This paper introduces a new class of non-Hermitian systems with pure decay eigenstates characterized by quantized decay charges, expanding the understanding of topological invariants in directed graph networks and confirmed through microwave circuit experiments.

Contribution

It presents the concept of quantized decay charges as a new topological invariant in non-Hermitian networks modeled by directed graphs, with universal conditions and experimental validation.

Findings

Discovery of pure decay eigenstates without oscillations.

Introduction of quantized decay charges as topological invariants.

Experimental confirmation using microwave resonant circuits.

Abstract

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