论文标题
伪透明探测的非舒适拓扑晶格中的鲁棒性与灵敏度
Robustness versus sensitivity in non-Hermitian topological lattices probed by pseudospectra
论文作者
论文摘要
储层计算是预测湍流的有力工具，其简单的架构具有处理大型系统的计算效率。然而，其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间，然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用，该系统模拟了湍流的若干特征。我们表明，使用径向基函数作为非线性投影器，即使只有部分观测并且不知道控制方程，也能稳健地捕捉复杂的系统非线性。最后，我们表明，当测量稀疏、不完整且带有噪声，甚至控制方程变得不准确时，我们的网络仍然可以产生相当准确的预测，从而为实际湍流系统的无模型预测铺平了道路。
Non-Hermitian topological systems simultaneously posses two antagonistic features: ultra sensitivity due to exceptional points and robustness of topological zero energy modes, and it is unclear which one prevails under different perturbations. We study that question by applying the pseudospectra theory on the prototypical non-Hermitian SSH (NHSSH) lattice. Topological modes are robust with respect to chiral perturbations and sensitive to parity-time (PT) symmetry preserving perturbations. In fact, the chiral symmetry exactly at the exceptional point leads to the suppression of its sensitivity, corresponding to a lower order exceptional point. However, counterintuitively, they are most sensitive with respect to unstructured perturbations, leaving the fingerprint of the pertinent higher order exceptional (HEP) point.
