标题： 非厄米连续准周期系统中的局域化和迁移率边 显示英文标题

标题： Localization and mobility edges in non-Hermitian continuous quasiperiodic systems

摘要： 迁移边缘（ME）是安德森局域化系统中的一个基本概念，它标记了扩展态和局域态之间的能量界限。 尽管ME和局域化现象在非厄米（NH）准周期紧束缚模型中已被广泛研究，但它们仍局限于NH连续系统。 在此，我们研究了一维（1D）NH准周期连续系统的ME和局域化特性，该系统由一个具有虚矢势和不可通约单点势的薛定谔方程描述。 我们发现，ME位于实谱中，并介于局域态和扩展态之间。 此外，我们表明，在周期性边界条件下，能谱始终表现出一条代表高能扩展电子态的开曲线，这些态由非零整数绕数特征。 这种复杂的谱拓扑与在开放边界条件下观察到的非厄米皮肤效应（NHSE）密切相关，其中体带的本征态集中在边界处。 此外，我们分析了局域化相变的临界行为，并获得了伴随普遍临界指数$\nu \simeq 1/3$的临界势幅值。 我们的研究为探索NH准周期连续系统中的ME和局域化行为提供了有价值的启示。 显示英文摘要

摘要： The mobility edge (ME) is a fundamental concept in the Anderson localized systems, which marks the energy separating extended and localized states. Although the ME and localization phenomena have been extensively studied in non-Hermitian (NH) quasiperiodic tight-binding models, they remain limited to NH continuum systems. Here, we investigate the ME and localization properties of a one-dimensional (1D) NH quasiperiodic continuous system, which is described by a Schr{\"o}dinger equation with an imaginary vector potential and an incommensurable one-site potential. We find that the ME is located in the real spectrum and falls between the localized and extended states. Additionally, we show that under the periodic boundary condition, the energy spectrum always exhibits an open curve representing high-energy extended electronic states characterized by a non-zero integer winding number. This complex spectrum topology is closely connected with the non-Hermitian skin effect (NHSE) observed under open boundary conditions, where the eigenstates of the bulk bands accumulate at the boundaries. Furthermore, we analyze the critical behavior of the localization transition and obtain critical potential amplitude accompanied by the universal critical exponent $\nu \simeq 1/3$. Our study provides valuable inspiration for exploring MEs and localization behaviors in NH quasiperiodic continuous systems.