AI 中文总结
本研究提出普适非微扰激活模式原理，将实复谱阈值转化为模式选择问题，应用于三类问题得到闭式阈值、新关联及无拓扑相变的激活切换等结果。
AI 中文摘要
实复谱跃迁标志着非厄米系统中放大效应的起始，但其阈值常被视为特定模型的量。本文提出一种普适的非微扰激活模式原理，适用于各类非厄米系统的实复阈值。核心观点是：跃迁起始时仅存在一个小希尔伯特子空间被“激活”，可通过频谱失谐与模式级投影非厄米耦合的竞争变分确定。该结果为任意大“扰动”给出了闭式异常激活条件，而非微扰估计。将该框架应用于三类不同示例问题，确定了：(i) 任意系统尺寸下临界非厄米趋肤放大的闭式阈值；(ii) 杂质隧穿阈值与异常点切换的新关联；(iii) 无基础拓扑相变的激活通道切换。综上，本研究将实复跃迁重新定义为与特定对称性无关的普适模式选择问题。
英文摘要
Real-to-complex spectral transitions mark the onset of amplification in non-Hermitian systems, but their thresholds are often treated as model-specific quantities. Here we develop a general, non-perturbative activated-mode principle that governs the real-to-complex threshold across broad classes of non-Hermitian systems. A central insight is that only a small Hilbert subspace is ``activated" at the transition onset, which can be variationally determined through the competition between spectral detuning and mode-level projected non-Hermitian couplings. The result is a closed-form exceptional-activation condition for arbitrarily large ``disturbances", rather than a perturbative estimate. We apply our framework to three contrasting illustrative problems, establishing (i) a closed-form threshold for critical non-Hermitian skin amplification at \emph{all} system sizes; (ii) a new link between impurity tunneling threshold and exceptional point switching; and (iii) activation channel switching without underlying topological phase transition. Overall, our findings recast real-to-complex transitions as generic mode-selection problems independent of any specific symmetry.
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