Quantum-Classical Correspondence of Non-Hermitian Symmetry Breaking

• URL: http://arxiv.org/abs/2411.17398v1
• Date: Tue, 26 Nov 2024 12:57:39 GMT
• Title: Quantum-Classical Correspondence of Non-Hermitian Symmetry Breaking
• Authors: Zhuo-Ting Cai, Hai-Dong Li, Wei Chen,
• Abstract summary: Real-to-complex spectral transitions are central to non-Hermitian physics. Our work uncovers the physical mechanism of non-Hermitian symmetry breaking.
• Score: 5.181697052513637
• License:
• Abstract: Real-to-complex spectral transitions and the associated spontaneous symmetry breaking of eigenstates are central to non-Hermitian physics, yet their underlying physical mechanisms remain 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 $\eta$-pseudo-Hermitian symmetry, real energy levels are quantized along periodic orbits that preserve the corresponding classical $S_\eta$ symmetry. In contrast, complex conjugate energy levels arise from semiclassical orbits that individually break the $S_\eta$ symmetry but together form $S_\eta$-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. Our work 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.

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