标题： 弱耦合非互易链中的尺寸依赖性表面效应转变 显示英文标题

标题： Size-Dependent Skin Effect Transitions in Weakly Coupled Non-Reciprocal Chains

摘要： 非厄米系统表现出其厄米对应物所没有的独特边界现象，最显著的是非厄米皮肤效应（NHSE）。在本工作中，我们研究了一个由两个耦合的非互易链组成的晶格模型，重点关注系统尺寸、链间耦合和谱拓扑之间的相互作用。通过分析和数值方法，我们系统地检查了在周期性和开边界条件下复能谱和谱绕数的演变。我们的结果揭示了多种尺寸依赖的局域化转变，包括$W=0$区域中同时双极皮肤效应（CBSE）的出现和不稳定性，以及随着系统尺寸增大，这些效应过渡到单极和传统双极NHSE。值得注意的是，我们证明了这些尺寸依赖的行为甚至在弱耦合区域之外仍然存在，突显了它们在具有复杂谱结构的非厄米系统中的普遍性。这项研究为控制皮肤效应的机制提供了新的见解，并为在合成晶格中工程非厄米拓扑相提供了实用指南。 显示英文摘要

摘要： Non-Hermitian systems exhibit unique boundary phenomena absent in their Hermitian counterparts, most notably the non-Hermitian skin effect (NHSE). In this work, we explore a lattice model consisting of two coupled non-reciprocal chains, focusing on the interplay between system size, inter-chain coupling, and spectral topology. Using both analytical and numerical approaches, we systematically examine the evolution of the complex energy spectra and spectral winding numbers under periodic and open boundary conditions. Our results uncover a variety of size-dependent localization transitions, including the emergence and instability of concurrent bipolar skin effects (CBSE) in the $W=0$ region, and their crossover to unipolar and conventional bipolar NHSE as the system size increases. Notably, we demonstrate that these size-dependent behaviors persist even beyond the weak-coupling regime, highlighting their universality in non-Hermitian systems with complex spectral structures. This study provides new insights into the mechanisms governing skin effects and offers practical guidelines for engineering non-Hermitian topological phases in synthetic lattices.