伪谱现象与非厄密特皮肤效应的起源
Pseudospectral phenomena and the origin of the non-Hermitian skin effect
AI总结：
研究揭示非厄密特皮肤效应源于谱不稳定性与非 reciprocity，而非拓扑性质，且拓扑性质反映在有限系统的奇异值谱中。
摘要：
非厄密特皮肤效应（NHSE），其特征是开放边界系统中本征态的宏观积累，通常归因于布洛赫哈密顿量的非平凡点隙拓扑。本文重新审视这一联系，表明非正常算子的本征谱对边界条件和扰动极为敏感，因此不构成稳定的拓扑信息编码对象。相反，拓扑性质反映在有限系统的奇异值谱中，并在半无限极限下对应由相应Toeplitz算子的索引所暗示的边界局域本征模。对于可独立调节点隙缠绕和非正常性的Hatano-Nelson梯子，本文证明NHSE可在无点隙缠绕时出现，反之亦然。这些结果表明NHSE源于谱不稳定性与非 reciprocity，而非拓扑，并且通常假设的谱缠绕与边界局域化关系依赖于平移不变性，因此并非普遍成立。
英文摘要：
The non-Hermitian skin effect (NHSE), characterized by a macroscopic accumulation of eigenstates at the edge of a system with open boundaries, is often ascribed to a non-trivial point-gap topology of the Bloch Hamiltonian. We revisit this connection and separate the question of the NHSE as a spectral reconstruction effect in clean systems from the question of stable topological protection. For a Hatano-Nelson ladder, where point-gap winding and non-normality can be varied independently, we demonstrate that, in a clean translationally invariant multiband setting, the NHSE can occur without point-gap winding and, conversely, that point-gap winding can persist without the NHSE. These results establish that in the clean case the connection between point-gap winding and the NHSE only holds in the scalar one-band case but, in general, not in the multiband case. Even more importantly, the eigenspectrum of non-normal operators is generically highly sensitive to boundary conditions and perturbations, and therefore does not constitute a stable object encoding topological information. Instead, topological properties are reflected in the splitting of the singular-value spectrum for finite systems and, in the semi-infinite limit, correspond to boundary-localized kernel modes implied by the index of the corresponding Toeplitz operator.
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