论文标题
从非Bloch带理论的定向扩增的简单公式
Simple formulas of directional amplification from non-Bloch band theory
论文作者
论文摘要
格林的功能是决定物理系统线性响应的基本数量。因此，非热系统的最新发展呼吁格林的非热带频段的功能公式。能量谱对边界条件的高灵敏度使这项任务变得复杂，这使得遗传公式的直接概括无效。在这里，基于非Bloch频带理论，我们获得了一维非富度频段的简单绿色功能公式。此外，在大尺寸的极限中，这些公式大大减少了找到简单代数方程的根。作为一种应用，我们的公式为定义数量，增益和方向性，定向放大的定义量提供了理想的公式。因此，我们的公式为设计方向放大器提供了有效的指南。
Green's functions are fundamental quantities that determine the linear responses of physical systems. The recent developments of non-Hermitian systems, therefore, call for Green's function formulas of non-Hermitian bands. This task is complicated by the high sensitivity of energy spectrums to boundary conditions, which invalidates the straightforward generalization of Hermitian formulas. Here, based on the non-Bloch band theory, we obtain simple Green's function formulas of general one-dimensional non-Hermitian bands. Furthermore, in the large-size limit, these formulas dramatically reduce to finding the roots of a simple algebraic equation. As an application, our formulation provides the desirable formulas for the defining quantities, the gain and directionality, of directional amplification. Thus, our formulas provide an efficient guide for designing directional amplifiers.
