Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.00623 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916023570006016 |
|---|---|
| author | Takata, Kenta Mock, Adam Notomi, Masaya Shinya, Akihiko |
| author_facet | Takata, Kenta Mock, Adam Notomi, Masaya Shinya, Akihiko |
| contents | Non-Hermitian systems can have peculiar degeneracies of eigenstates called exceptional points (EPs). An EP of $n$ degenerate states is said to have order $n$, and higher-order EPs (HEPs) with $n \ge 3$ exhibit intrinsic order-scaling responses potentially applied to superior sensing and state control. However, traditional eigenvalue-based searches for HEPs are facing fundamental limitations in terms of complexity and implementation. Here, we propose a design paradigm for HEPs based on a simple property for matrices termed nilpotence and concise inductive procedure. The nilpotence guarantees a HEP with desired order and helps divide the problem. Our inductive scheme repeatedly extends a system and doubles its EP order, starting with a known design. Based on the nilpotence, we systematically design photonic cavity arrays operating at chiral, passive, and active HEPs with $n = 3, 6, 7$ and show their peculiar directional radiation, induced transparency, and enhanced transmittance and spontaneous emission, respectively. We inductively find lattice systems with diverging EP order originating from a well-known $2 \times 2$ parity-time-symmetric Hamiltonian. We also extend the active HEP system with $n = 7$ to another with $n = 14$ and have further magnified responses. Our work pushes the investigation and application of HEPs to previously unexplored regimes in various physical systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_00623 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Higher-order exceptional points unveiled by nilpotence and mathematical induction Takata, Kenta Mock, Adam Notomi, Masaya Shinya, Akihiko Optics Non-Hermitian systems can have peculiar degeneracies of eigenstates called exceptional points (EPs). An EP of $n$ degenerate states is said to have order $n$, and higher-order EPs (HEPs) with $n \ge 3$ exhibit intrinsic order-scaling responses potentially applied to superior sensing and state control. However, traditional eigenvalue-based searches for HEPs are facing fundamental limitations in terms of complexity and implementation. Here, we propose a design paradigm for HEPs based on a simple property for matrices termed nilpotence and concise inductive procedure. The nilpotence guarantees a HEP with desired order and helps divide the problem. Our inductive scheme repeatedly extends a system and doubles its EP order, starting with a known design. Based on the nilpotence, we systematically design photonic cavity arrays operating at chiral, passive, and active HEPs with $n = 3, 6, 7$ and show their peculiar directional radiation, induced transparency, and enhanced transmittance and spontaneous emission, respectively. We inductively find lattice systems with diverging EP order originating from a well-known $2 \times 2$ parity-time-symmetric Hamiltonian. We also extend the active HEP system with $n = 7$ to another with $n = 14$ and have further magnified responses. Our work pushes the investigation and application of HEPs to previously unexplored regimes in various physical systems. |
| title | Higher-order exceptional points unveiled by nilpotence and mathematical induction |
| topic | Optics |
| url | https://arxiv.org/abs/2510.00623 |