标题： 精确动力学和非厄米锯齿形格劳伯福克晶格中的布洛赫振荡 显示英文标题

标题： Exact Dynamics and Bloch Oscillations in a Non Hermitian Zigzag Glauber Fock Lattice

摘要： 一维非厄米锯齿波导阵列的离散动力学被理论研究。 该系统的特点是左右最近邻跃迁不平衡，且在两个跃迁方向上具有互易的次近邻相互作用。 不平衡跃迁幅度与波导结构之间的相互作用导致了非厄米布洛赫振荡，在特定位置能量传输会根据左右跃迁项的相对强度被放大或耗散。 我们证明，通过应用适当的非么正变换，原始系统可以映射到一个等效的互易波导，其具有厄米动力学。 这种变换使我们能够推导出一个闭合形式的解析解，并将其与系统的数值解进行比较。 显示英文摘要

摘要： The discrete dynamics of a one-dimensional non-hermitian zigzag waveguide array is studied theoretically. This system is characterized by unbalanced left/right nearest-neighbor hopping and reciprocal second-neighbor interactions in both hopping directions. The interplay between the unbalanced hopping amplitudes and the waveguide setup results in Non-Hermitian Bloch oscillations, where energy transport is either amplified or dissipated at specific locations, depending on the relative strengths of the left and right hopping terms. We demonstrate that by applying an appropriate non-unitary transformation, the original system can be mapped into an equivalent reciprocalwaveguide with Hermitian dynamics. This transformation allows us to derive a closed-form analytic solution, which is then compared with the numerical solution of the system.