横向$\u0001PT$-对称散射系统中的无阈值动力学不稳定性：连续谱中束缚态的隐藏作用
Thresholdless dynamical instability in transverse $\mathcal{PT}$-symmetric scattering systems: The hidden role of bound states in the continuum
- School of Education, Jiangsu Open University（江苏开放大学教育学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文揭示了横向$\u0001PT$-对称散射系统中由对称保护的连续谱束缚态驱动的无阈值动力学不稳定性，阐明了微扰作用机制并通过模型验证，建立了相关器件的稳定性判据与设计原则。
AI中文摘要：
横向宇称-时间（$\u0001PT$）对称系统的稳态散射特性已被广泛研究，但其动力学稳定性——这是任何稳态描述的前提——在很大程度上仍未被探索。本文揭示了这类系统中由对称保护的连续谱束缚态（BICs）驱动的无阈值动力学不稳定性。在无增益和损耗的情况下，横向几何结构的上下镜像对称性通常会保护一个BIC，它表现为复波数平面实轴上S矩阵极点与零点的聚结。厄米对称破缺微扰会将极点移至下半平面，将BIC转化为具有费米黄金规则衰变宽度的共振态。相反，反厄米$\u0001PT$-对称微扰会反转二阶能量偏移的符号，将极点推至上半平面，并产生随时间增长的束缚态，满足$\text{Im}E=\u0003^{2}\u0004_{V}/2+O(\u0003^{3})$，其中$\u0003$为增益-损耗强度，$\u0004_{V}$为BIC与连续谱的黄金规则耦合强度。因此，只要$\u0004_{V}>0$，不稳定性就会在任意小的$\u0003$下出现。我们在一个三格点侧耦合模型中证实了这一机制——该模型尽管具有幺正散射矩阵但仍不稳定，还在一个四格点菱形模型中验证了该机制，其中横向和纵向的增益-损耗排布分别产生零阈值和有限阈值。这些结果为稳定的$\u0001PT$-对称散射器件建立了微观稳定性判据和设计原则。
英文摘要：
The stationary scattering properties of transverse parity-time ($\mathcal{PT}$) symmetric systems have been extensively studied, yet their dynamical stability, a prerequisite for any stationary description, remains largely unexplored. Here we uncover a thresholdless dynamical instability in such systems, driven by symmetry-protected bound states in the continuum (BICs). Without gain and loss, the up-down mirror symmetry of the transverse geometry generically protects a BIC, which manifests as the coalescence of an $S$-matrix pole and zero on the real axis of the complex wave-number plane. A Hermitian symmetry-breaking perturbation shifts the poles into the lower half-plane, converting the BIC into a resonance with a Fermi-golden-rule decay width. An anti-Hermitian $\mathcal{PT}$-symmetric perturbation instead reverses the sign of the second-order energy shift, driving the poles into the upper half-plane and producing a time-growing bound state with $\operatorname{Im}E=γ^{2}Γ_{V}/2+O(γ^{3})$, where $γ$ is the gain-loss strength and $Γ_{V}$ is the golden-rule coupling of the BIC to the continuum. The instability therefore sets in at arbitrarily small $γ$ whenever $Γ_{V}>0$. We confirm this mechanism in a three-site side-coupled model that is unstable despite possessing a unitary scattering matrix, and in a four-site rhombic model where transverse and longitudinal gain-loss placements yield vanishing and finite thresholds, respectively. These results establish a microscopic stability criterion and a design principle for stable $\mathcal{PT}$-symmetric scattering devices.
