发表机构
Higher Teachers Training College, University of Bamenda; Promotion Centre of Research for Technological Advancement and Sustainable Development (PCR-TASD); Quantum Materials and Computing Group (QMaCG); Université des Sciences et Techniques de Masuku; Laboratoire d’Optique, Laser et Applications; Département de Physique; Faculté des Sciences; Unité de Recherche en Physique; Unité de Recherche de Matière Condensée, d’Électronique et de Traitement de Signal (URMACETS); University of Dschang（巴门达大学高等教师培训学院; 技术进步与可持续发展研究促进中心; 量子材料与计算小组; 马苏库科学技术大学; 光学、激光及应用实验室; 物理系；理学院; 物理学研究单元; 凝聚态物质、电子与信号处理研究单元; 杜尚格大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出经典可观测量融合作为判别性诊断，通过非厄米伊辛链演示其识别奇异点，区分二重点，并验证了与量子结果的对应及实验可行性。
AI 中文摘要
奇异点（EPs）通常通过本征矢量的融合来识别，这在缺乏哈密顿量谱的经典平台中是无法实现的。我们引入经典可观测量融合作为一种诊断方法，直接从物理构型中识别奇异点，并在一个已知的具有耦合$J$和交错虚场$\gamma$的非厄米伊辛链中演示该方法，选择该模型是为了与已建立的量子结果进行可验证性比较。海森堡动力学的平均场约化产生了平衡分支，这些分支组织成两个对称相关的族，它们在奇异点超曲面$|\gamma|=|J|$边界处的融合表现出特征性的$\sqrt{J^2-\gamma^2}$支点结构和两叶黎曼拓扑。至关重要的是，在$\gamma=0,\eta=0$处的简并被证明是一个二重点，不产生可观测量融合，从而确立了该诊断具有判别性而非仅仅是提示性。精确的Jordan-Wigner和Bogoliubov-de Gennes处理确认了在相同阈值处的本征矢量融合，并提出了一种耦合增益-损耗电路实现方案，确立了经典可观测量作为非厄米临界性的实验可访问特征。
英文摘要
Exceptional points (EPs) are conventionally identified through eigenvector coalescence, inaccessible in classical platforms lacking a Hamiltonian spectrum. We introduce classical observable coalescence as a diagnostic identifying EPs directly from physical configurations, and demonstrate it in a known non-Hermitian Ising chain with coupling $J$ and staggered imaginary field $γ$, chosen for verifiability against established quantum results. A mean-field reduction of the Heisenberg dynamics yields equilibrium branches organising into two symmetry-related families whose fusion at the boundary of the EP supersurface $|γ|=|J|$ exhibits the characteristic $\sqrt{J^2-γ^2}$ branch-point structure and two-sheeted Riemann topology. Crucially, the degeneracy at $γ=0,η=0 $ is shown to be a diabolic point, producing no observable coalescence, establishing the diagnostic as discriminating rather than merely suggestive. An exact Jordan-Wigner and Bogoliubov-de Gennes treatment confirms eigenvector coalescence at the same threshold, and a coupled gain-loss circuit realisation is proposed, establishing classical observables as experimentally accessible signatures of non-Hermitian criticality.
Comments23 pages, 9 figures
