标题： 小能量边界态在有限尺寸马赛克Wannier-Stark晶格中的出现和扩展化 显示英文标题

标题： Low-Energy Boundary-State Emergence and Delocalization in Finite-sized Mosaic Wannier-Stark Lattices

摘要： 莫赛克沃纳尔斯特克晶格作为一种无无序系统，因其空间周期性斯特克势引起的非常规局域化行为而日益受到关注。在无限大小极限下，精确的谱分析揭示了一个几乎纯点谱。除了（M 1）孤立的扩展态外，没有真正的迁移率边缘，这些扩展态伴随着局域化长度发散的弱局域模式。受此谱结构的启发，我们研究了有限尺寸下的莫赛克沃纳尔斯特克模型。在这样的系统中，当系统长度与调制周期不共度时，由于边界残差会出现额外的低能边界局域态。这些态通过逆参与比率（IPR）和空间期望值有效地被区分和识别。为了探索它们对非厄米扰动的响应，引入了复数位点势来模拟增益和损耗。随着非厄米强度的增加，只有弱局域态经历渐进的去局域化，表现出从局域化到空间扩展的平滑交叉。 显示英文摘要

摘要： The mosaic Wannier Stark lattice has gained increasing prominence as a disorder free system exhibiting unconventional localization behavior induced by spatially periodic Stark potentials. In the infinite size limit, exact spectral analysis reveals an almost pure point spectrum. There is no true mobility edge, except for (M 1) isolated extended states, which are accompanied by weakly localized modes with diverging localization lengths. Motivated by this spectral structure, we investigate the mosaic Wannier Stark model under finite-size. In such systems, additional low energy boundary localized states emerge due to boundary residuals when the system length is not commensurate with the modulation period. These states are effectively distinguished and identified using the inverse participation ratio (IPR) and spatial expectation values. To explore their response to non-Hermitian perturbations, complex on site potentials are introduced to simulate gain and loss. As the non-Hermitian strength increases, only the weakly localized states undergo progressive delocalization, exhibiting a smooth crossover from localization to spatial extension.