AI 中文总结
本文提出非厄米对称破缺的动量空间路径积分对偶表述，证明轨道拓扑决定量子化形式，并应用于有限非厄米晶格中布洛赫振荡的边界诱导谱跃迁。
AI 中文摘要
最近，利用坐标空间路径积分建立了非厄米对称破缺的量子-经典对应关系，从而在单个本征态层面上提供了谱跃迁的半经典理解。在此，我们通过构造相应的迹公式和量子化条件，在动量空间中发展其对偶表述。我们表明，单个本征值的实性或复性由相关的半经典轨道的对称性决定，这与坐标空间路径积分方法一致。此外，我们证明半经典轨道的拓扑决定了量子化条件的自然表述：对于相空间中可收缩的周期轨道，坐标空间和动量空间的表述是等价的；而对于不可收缩的轨道，沿缠绕方向的量子化条件仍然有效，但其对偶形式必须通过边界项进行修正。特别地，实空间缠绕轨道和布里渊区缠绕轨道分别自然地选择坐标空间和动量空间的量子化。作为一个非平凡的应用，我们研究了有限非厄米晶格中布洛赫振荡的边界诱导谱跃迁，其中跨越布里渊区缠绕的布洛赫振荡轨道保持相关对称性并产生实能级，而边界反射轨道形成对称相关的对并产生复共轭本征值。我们的工作完善了非厄米对称破缺的量子-经典对应框架，将其适用性扩展到更广泛的非厄米问题。
英文摘要
A quantum-classical correspondence for non-Hermitian symmetry breaking has recently been established using coordinate-space path integrals, providing a semiclassical understanding of spectral transitions at the level of individual eigenstates. Here we develop its dual formulation in momentum space by constructing the corresponding trace formula and quantization condition. We show that the real or complex nature of individual eigenvalues is determined by the symmetry properties of the associated semiclassical orbits, as in the coordinate-space path-integral approach. Moreover, we demonstrate that the topology of semiclassical orbits determines the natural formulation of the quantization condition: the coordinate- and momentum-space formulations are equivalent for contractible periodic orbits in phase space, whereas for noncontractible orbits, the quantization condition along the winding direction remains valid, but its dual form must be corrected by a boundary term. In particular, real-space-winding and Brillouin-zone-winding orbits naturally select coordinate- and momentum-space quantization, respectively. As a nontrivial application, we investigate the boundary-induced spectral transition of Bloch oscillations in a finite non-Hermitian lattice, where Bloch-oscillation orbits winding across the Brillouin zone preserve the relevant symmetry and yield real energy levels, whereas boundary-reflected orbits form symmetry-related pairs and give rise to complex-conjugate eigenvalues. Our work completes the quantum-classical correspondence framework for non-Hermitian symmetry breaking, extending its applicability to a broader class of non-Hermitian problems.
