一维非互易准晶体中李雅普诺夫指数的非对称转移矩阵分析
Asymmetric transfer matrix analysis of Lyapunov exponents in one-dimensional non-reciprocal quasicrystals
AI总结：
本文提出非对称转移矩阵分析方法，用于研究一维非互易准晶体中由非厄米效应引起的双侧不同李雅普诺夫指数及迁移率边，并在三个非互易准晶体模型中验证了其有效性。
摘要：
李雅普诺夫指数作为局域态的指示量，通常被用于识别无序系统中的局域化转变。在非厄米准晶体中，由非互易跃迁引起的非厄米效应可能导致在局域化中心两侧出现两个不同的李雅普诺夫指数。基于这一观察，我们在此引入一种用于研究非互易准晶体局域化特性和迁移率边的综合方法，称为非对称转移矩阵分析。我们展示了该方法在三个具体场景中的应用：非互易Aubry-André模型、非互易非对角Aubry-André模型以及非互易镶嵌准晶体。这项工作可能为非厄米准晶体和无序系统的研究提供有价值的见解。
英文摘要：
The Lyapunov exponent, serving as an indicator of the localized state, is commonly utilized to identify localization transitions in disordered systems. In non-Hermitian quasicrystals, the non-Hermitian effect induced by non-reciprocal hopping can lead to the manifestation of two distinct Lyapunov exponents on opposite sides of the localization center. Building on this observation, we here introduce a comprehensive approach for examining the localization characteristics and mobility edges of non-reciprocal quasicrystals, referred to as asymmetric transfer matrix analysis. We demonstrate the application of this method to three specific scenarios: the non-reciprocal Aubry-André model, the non-reciprocal off-diagonal Aubry-André model, and the non-reciprocal mosaic quasicrystals. This work may contribute valuable insights to the investigation of non-Hermitian quasicrystal and disordered systems.
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