论文标题
从关键的非铁皮皮肤效应中进行通用的竞争光谱缩放
Universal competitive spectral scaling from the critical non-Hermitian skin effect
论文作者
论文摘要
最近，人们发现某些非炎性系统可以在不同的系统尺寸上表现出定性的不同属性，例如，在小尺寸上是无间隙的，并且具有大尺寸$ L $的拓扑边缘模式。这种戏剧性的系统尺寸敏感性被称为关键的非铁皮皮肤效应（CNHSE），并且由于两个或多个非省水泵送通道之间的竞争而发生。在这项工作中，我们严格地在一般的多组分CNHSE CNHSE模型ANSATZ中严格开发了依赖大小的普遍性布里群区（GBZ）的概念，并发现GBZ表现出通用$ A+B^{1/（L+1）} $缩放行为。特别是，我们在模型参数方面提供了缩放率$ b $的分析估计，并通过两个范式模型证明了它们良好的经验拟合，即带有偏移的Hatano-Nelson模型以及拓扑结合的链模型和偏移。我们还提供了关键尺寸$ L_C $的分析结果，在此下方CNHSE缩放率被冷冻。 CNHSE代表了将不同通道的散装对应断裂并置的结果，并且可以在非铁材料的超材料和电路阵列中很容易证明。
Recently, it was discovered that certain non-Hermitian systems can exhibit qualitative different properties at different system sizes, such as being gapless at small sizes and having topological edge modes at large sizes $L$. This dramatic system size sensitivity is known as the critical non-Hermitian skin effect (cNHSE), and occurs due to the competition between two or more non-Hermitian pumping channels. In this work, we rigorously develop the notion of a size-dependent generalized Brillouin zone (GBZ) in a general multi-component cNHSE model ansatz, and found that the GBZ exhibits a universal $a+b^{1/(L+1)}$ scaling behavior. In particular, we provided analytical estimates of the scaling rate $b$ in terms of model parameters, and demonstrated their good empirical fit with two paradigmatic models, the coupled Hatano-Nelson model with offset, and the topologically coupled chain model with offset. We also provided analytic result for the critical size $L_c$, below which cNHSE scaling is frozen. The cNHSE represents the result of juxtaposing different channels for bulk-boundary correspondence breaking, and can be readily demonstrated in non-Hermitian metamaterials and circuit arrays.
