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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.13024 |
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Table of Contents:
- 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 ε^(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 ε^(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.