Theory of Remaining Exceptional Points from Nongeneric Splitting in Non-Hermitian Systems

TL;DR

This paper investigates the fundamental properties of remaining exceptional points in non-Hermitian systems, revealing their origins and characteristics through graph theory and topology, with implications for sensing and photonic applications.

Contribution

It provides a theoretical framework for understanding remaining EPs in high-order exceptional points, combining graph theory and topology to analyze their number and splitting behavior.

Findings

Remaining EPs are fundamental eigenvalue points in perturbed HOEP systems.

The number and splitting order of remaining EPs are characterized mathematically.

Framework enables potential applications in sensing and photonic device design.

Abstract

In non-Hermitian physics, high-order exceptional points(HOEPs) with eigenvalues and eigenvectors coalesce are known for their enhanced sensitivity to perturbations. Typically, they exhibit eigenvalue splitting that scales as {\epsilon}^(1/n), which is referred to as the generic response. However, under certain conditions, a nongeneric response of HOEPs occurs where the splitting follows a lower order {\epsilon}^(1/m) (m<n). A nongeneric response of HOEPs with a lower order splitting lead to the remaining EPs. While the presence of these remaining EPs is acknowledged, a thorough elucidation of their fundamental properties has yet to be achieved. In this work, we demonstrate those unsplit eigenvalue points must constitute remaining EPs in a perturbed n-orders HOEPs system. Combining graph theory and topological analysis, the number and splitting order of the remaining EPs is studied. This framework not only resolves a fundamental challenge in HOEPs but also paves the way for exploiting remaining EPs in applications such as anisotropic sensing and the design of Dirac exceptional points.