论文标题
在存在无序的情况下，非铁质拓扑与定向放大之间的对应关系
Correspondence between non-Hermitian topology and directional amplification in the presence of disorder
论文作者
论文摘要
为了使非热（NH）拓扑作用与实际应用有关，有必要研究无序系统。在没有障碍的情况下，当与非平凡的NH动态矩阵相关时，具有工程非本地耗散的某些驱动驱动腔阵列显示出定向放大。在这项工作中，我们从分析上表明，即使存在障碍，NH拓扑与定向放大之间的对应关系也存在。当将具有非平凡拓扑的系统接近特殊点时，为任意强大的现场疾病保留了完美的非股展（通过消失的反向增益量化）。对于有界疾病，我们为散射矩阵元素的概率分布提供了简单的边界。这些界限表明，与非平凡的NH拓扑相关的基本特征，即，端到端前向（反向）增益随着系统大小的指数增长（被抑制）在无序系统中保留。腔阵列中的NH拓扑结构很强，因此可以用于实际应用。
In order for non-Hermitian (NH) topological effects to be relevant for practical applications, it is necessary to study disordered systems. In the absence of disorder, certain driven-dissipative cavity arrays with engineered non-local dissipation display directional amplification when associated with a non-trivial winding number of the NH dynamic matrix. In this work, we show analytically that the correspondence between NH topology and directional amplification holds even in the presence of disorder. When a system with non-trivial topology is tuned close to the exceptional point, perfect non-reciprocity (quantified by a vanishing reverse gain) is preserved for arbitrarily strong on-site disorder. For bounded disorder, we derive simple bounds for the probability distribution of the scattering matrix elements. These bounds show that the essential features associated with non-trivial NH topology, namely that the end-to-end forward (reverse) gain grows (is suppressed) exponentially with system size, are preserved in disordered systems. NH topology in cavity arrays is robust and can thus be exploited for practical applications.
