Title: Competing edge and bulk localisation in non-reciprocal disordered systems Show Chinese title

Title: 非互易无序系统中的竞争边和体局域化

Abstract: We investigate the competing mechanisms of localisation in one-dimensional block disordered subwavelength resonator systems subject to non-reciprocal damping, induced by an imaginary gauge potential. Using a symmetrisation approach to enable the adaptation of tools from Hermitian systems, we derive the limiting spectral distribution of these systems as the number of blocks goes to infinity and characterise their spectral properties in terms of the spectral properties of their constituent blocks. By employing a transfer matrix approach, we then clarify, in terms of Lyapunov exponents, the competition between the edge localisation due to imaginary gauge potentials and the bulk localisation due to disorder. In particular, we demonstrate how the disorder acts as insulation against the non-Hermitian skin effect, preventing edge localisation for small imaginary gauge potentials. Show Chinese abstract

Abstract: 我们研究了在非互易阻尼（由虚数规范势引起）作用下，一维块无序亚波长谐振器系统中局域化的竞争机制。 通过一种对称化方法，以使从厄米系统中适应工具成为可能，我们推导出这些系统在块数趋于无穷大时的极限谱分布，并根据其组成部分块的谱特性来表征它们的谱特性。 通过采用转移矩阵方法，我们随后根据李雅普诺夫指数阐明了由于虚数规范势引起的边缘局域化与由于无序引起的体局域化之间的竞争。 特别是，我们展示了无序如何作为对抗非厄米皮肤效应的绝缘层，防止小虚数规范势下的边缘局域化。