标题： 非线性 Hatano-Nelson 模型中的调制不稳定性与动力学增长阻塞 显示英文标题

标题： Modulational Instability and Dynamical Growth Blockade in the Nonlinear Hatano-Nelson Model

摘要： 哈塔诺-尼尔森模型是非厄米物理的基石，描述了一维晶格上的非对称跳跃动力学，这引发了方向性输运、非厄米拓扑和非厄米皮肤效应等迷人现象。 它在经典和量子系统中都得到了广泛研究，应用于凝聚态物理、光子学和冷原子气体中。 最近，哈塔诺-尼尔森模型的非线性扩展为探索非线性与非厄米效应之间的相互作用开辟了新途径。 特别是，在具有开放边界条件的晶格中，预测了位于晶格边缘或体内的非线性皮肤模式和孤子。 在本工作中，我们研究了具有周期性边界条件的哈塔诺-尼尔森模型的非线性扩展，并揭示了由非线性平面波的调制不稳定性引起的新型动态现象：增长阻塞。 这一现象的特点是规范增长的突然停止，如在线性哈塔诺-尼尔森模型中所观察到的，可以解释为由于晶格中自诱导无序引起的对流运动的停止。 显示英文摘要

摘要： The Hatano-Nelson model is a cornerstone of non-Hermitian physics, describing asymmetric hopping dynamics on a one-dimensional lattice, which gives rise to fascinating phenomena such as directional transport, non-Hermitian topology, and the non-Hermitian skin effect. It has been widely studied in both classical and quantum systems, with applications in condensed matter physics, photonics, and cold atomic gases. Recently, nonlinear extensions of the Hatano-Nelson model have opened a new avenue for exploring the interplay between nonlinearity and non-Hermitian effects. Particularly, in lattices with open boundary conditions, nonlinear skin modes and solitons, localized at the edge or within the bulk of the lattice, have been predicted. In this work, we examine the nonlinear extension of the Hatano-Nelson model with periodic boundary conditions and reveal a novel dynamical phenomenon arising from the modulational instability of nonlinear plane waves: growth blockade. This phenomenon is characterized by the abrupt halt of norm growth, as observed in the linear Hatano-Nelson model, and can be interpreted as a stopping of convective motion arising from self-induced disorder in the lattice.