发表机构
Wuhan University of Technology（武汉理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究针对非互易SSH链，通过插入核与传输强度的关系，揭示了图路径结构决定传输主导行为，并给出弱插入下局域稳定增强的判据，为端口响应提供通道特定标准。
AI 中文摘要
非互易晶格为定向波传输提供了灵活的设置，这引发了增强的内部散射如何转化为固定外部端口之间传输的问题。我们针对具有交错增益和损耗的非互易Su-Schrieffer-Heeger（SSH）链，通过将参考依赖的插入核$K_p=VG_pV$与相干传输强度$T$联系起来，来解决这一问题。在固定的有限图上，强插入展开给出了一项正比于$\gamma^{1-d}$的贡献，其系数是长度为$d$的最短有向路径的带符号和。当该和不为零时，它独立于固定的对角损耗设定主导行为；当它抵消时，这些损耗可以进入第一个存活的更高阶项。对于固定的跨子晶格端点通道，在核幅值的每个非零可微驻点处，传输具有严格负斜率。在弱插入区域，参考系统系数$\chi=-\mathrm{Re}\\,\mathrm{Tr}[(G_{0p}Z)^2]$预测对称SSH端口的初始传输变化，并且$\chi>0$连同严格稳定的基线保证局域稳定增强。有限链计算和驱动动力学将这些结果与可观测响应联系起来，并区分渐近收敛与瞬态稳定。一个严格耗散的短链示例展示了无净功率增益的局域增强。总之，这些结果分离了图路径结构、相干端口响应和动力学建立，为解释内部散射提供了通道特定的标准。
英文摘要
Non-reciprocal lattices offer a flexible setting for directional wave transport, raising the question of how enhanced internal scattering translates into transmission between fixed external ports. We address this question for non-reciprocal Su--Schrieffer--Heeger (SSH) chains with staggered gain and loss by relating the reference-dependent insertion kernel $K_p=VG_pV$ to the coherent transmission intensity $T$. On a fixed finite graph, a strong-insertion expansion gives a contribution proportional to $γ^{1-d}$, whose coefficient is the signed sum of shortest directed paths of length $d$. When this sum is nonzero, it sets the leading behavior independently of fixed diagonal losses; when it cancels, those losses can enter the first surviving higher-order term. For a fixed cross-sublattice endpoint channel, transmission has a strictly negative slope at every nonzero differentiable stationary point of the kernel magnitude. In the weak-insertion regime, the reference-system coefficient $χ=-\mathrm{Re}\,\mathrm{Tr}[(G_{0p}Z)^2]$ predicts the initial transmission change for symmetric SSH ports, and $χ>0$ together with a strictly stable baseline guarantees local stable enhancement. Finite-chain calculations and driven dynamics connect these results to observable response and distinguish asymptotic convergence from transient settling. A strictly dissipative short-chain example exhibits local enhancement without net power gain. Together, these results separate graph-path structure, coherent port response, and dynamical establishment, providing channel-specific criteria for interpreting internal scattering.
