Cai Zhuo-Ting, Li Hai-Dong, Chen Wei
Nanjing University, National Laboratory of Solid State Microstructures, School of Physics, Jiangsu Physical Science Research Center, and Collaborative Innovation Center of Advanced Microstructures, Nanjing 210093, China.
Phys Rev Lett. 2025 Jun 20;134(24):240201. doi: 10.1103/vvrx-mljg.
Real-to-complex spectral transitions and the associated spontaneous symmetry breaking of eigenstates are central to non-Hermitian physics, yet a comprehensive and universal theory that precisely describes the underlying physical mechanisms for each individual state remains elusive. Here, we resolve the mystery by employing the complex path integral formalism and developing a generalized Gutzwiller trace formula. These methodologies enable us to establish a universal quantum-classical correspondence that precisely links the real or complex nature of individual energy levels to the symmetry properties of their corresponding semiclassical orbits. Specifically, in systems with a general η-pseudo-Hermitian symmetry, real energy levels are quantized along periodic orbits that preserve the corresponding classical S_{η} symmetry. In contrast, complex conjugate energy levels arise from semiclassical orbits that individually break the S_{η} symmetry but together form S_{η}-symmetric pairs. This framework provides a unified explanation for the spectral behaviors in various continuous non-Hermitian models and for the PT transition in two-level systems. Moreover, we demonstrate that the exceptional point is inherently a quantum phenomenon, as it cannot be described by a single classical orbit. Our Letter uncovers the physical mechanism of non-Hermitian symmetry breaking and introduces a new perspective with broad implications for the control and application of non-Hermitian phenomena.
实到复的光谱跃迁以及本征态相关的自发对称性破缺是非厄米物理的核心，但一个精确描述每个单独态潜在物理机制的全面通用理论仍然难以捉摸。在此，我们通过采用复路径积分形式并发展广义古兹维勒迹公式来解开这个谜团。这些方法使我们能够建立一种通用的量子 - 经典对应关系，精确地将单个能级的实或复性质与其相应半经典轨道的对称性质联系起来。具体而言，在具有一般η - 伪厄米对称性的系统中，实能级沿着保持相应经典(S_{η})对称性的周期轨道进行量子化。相反，复共轭能级源于各自打破(S_{η})对称性但共同形成(S_{η})对称对的半经典轨道。这个框架为各种连续非厄米模型中的光谱行为以及两能级系统中的PT跃迁提供了统一的解释。此外，我们证明例外点本质上是一种量子现象，因为它不能由单个经典轨道来描述。我们的论文揭示了非厄米对称性破缺的物理机制，并引入了一个具有广泛意义的新视角，对非厄米现象的控制和应用具有重要意义。
