Scholarlink

<p>Non-Hermitian systems can have peculiar degeneracies of eigenstates called exceptional points (EPs). An EP of <i>n</i> degenerate states is said to have order <i>n</i>, and higher-order EPs (HEPs) with <i>n</i> ≥&#xa0;3 exhibit intrinsic order-scaling responses potential for applications. However, traditional eigenvalue-based searches for HEPs are facing fundamental limitations in terms of complexity and implementation. Here, we propose a design for HEPs based on a simple property for matrices termed nilpotence and concise inductive procedure. The nilpotence guarantees a HEP with specified order and helps divide the problem. Our inductive routine can repeatedly double EP order starting from known designs, such as a well-known 2&#xa0;×&#xa0;2 parity-time-symmetric Hamiltonian. By applying our framework, we systematically design reciprocal photonic cavity systems operating at HEPs with up to <i>n</i>&#xa0;=&#xa0;14 and find their unconventionally chiral, transparent, and enhanced responses. Our work pushes the investigation and application of HEPs to previously unexplored regimes in various physical systems.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Higher-order exceptional points unveiled by nilpotence and mathematical induction

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年5月5日

查看全文
  • Kenta Takata,
  • Adam Mock,
  • Masaya Notomi,
  • Akihiko Shinya

摘要

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 ≥ 3 exhibit intrinsic order-scaling responses potential for applications. However, traditional eigenvalue-based searches for HEPs are facing fundamental limitations in terms of complexity and implementation. Here, we propose a design for HEPs based on a simple property for matrices termed nilpotence and concise inductive procedure. The nilpotence guarantees a HEP with specified order and helps divide the problem. Our inductive routine can repeatedly double EP order starting from known designs, such as a well-known 2 × 2 parity-time-symmetric Hamiltonian. By applying our framework, we systematically design reciprocal photonic cavity systems operating at HEPs with up to n = 14 and find their unconventionally chiral, transparent, and enhanced responses. Our work pushes the investigation and application of HEPs to previously unexplored regimes in various physical systems.