We study time-dependent electrical properties of the Su-Schrieffer-Heeger (SSH) chain and coupled SSH chains on a substrate. Focusing on the midgap edge state dynamics we consider the abrupt transition from the normal to the SSH chain and determine characteristic timescale needed for topological states to develop. We have found that the midgap state is formed from the inside peaks of the normal chain density of states. For a ladderlike system we show that the edge SSH state vanishes in time or oscillates between neighboring sites. Moreover, for nonadiabatical time-dependent perturbations the midgap state can partially leak to other sites leading to induced topological states inside the trivial chain. We also analyze the mean-field correlation effects between the coupled chains revealing the induced Friedel oscillations in nontrivial chains.

中文翻译：

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耦合拓扑链中的边缘状态动力学

我们研究基质上Su-Schrieffer-Heeger（SSH）链和耦合SSH链的时变电学特性。关注中间间隙边缘状态动态，我们考虑从正常链到SSH链的突然过渡，并确定拓扑状态发展所需的特征时间尺度。我们发现中间间隙状态是由正常链状态密度的内部峰形成的。对于阶梯状系统，我们显示出边缘SSH状态随时间消失或在相邻站点之间振荡。此外，对于非绝热时间相关的扰动，中间能隙状态可能会部分泄漏到其他部位，从而导致琐碎链内的诱发拓扑状态。我们还分析了耦合链之间的平均场相关效应，揭示了非平凡链中的感应弗里德尔振荡。