Anderson localization is a general phenomenon that applies to a variety of disordered physical systems. Recently, a manifestation of Anderson localization for wave packets launched with a finite average velocity was proposed, the quantum boomerang effect (QBE). This phenomenon predicts that the disorder-averaged center of mass of a particle initially moves ballistically, then makes a U-turn, and finally slowly returns to its initial position. The QBE has been predicted to take place in several Hermitian models with Anderson localization and has been experimentally observed in the paradigmatic quantum kicked rotor model. In this paper, we investigate the emergence of the QBE in non-Hermitian systems and clarify the importance of symmetries of the Hamiltonian and the initial state. We generalize the analytical arguments available in the literature and show that even in the case of complex spectrum a boomeranglike behavior can appear in a non-Hermitian system. We confirm our analytical results through a careful numerical investigation of the dynamics for several non-Hermitian models. We find that non-Hermiticity leads to the breakdown of the dynamical relation, though the QBE is preserved. This paper opens avenues for future investigations in Anderson localized systems. The models studied here may be implemented using cold atoms in optical lattices.

中文翻译：

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非厄米系统中的稳健量子回旋镖效应

安德森局部化是一种普遍现象，适用于各种无序的物理系统。最近，提出了以有限平均速度发射的波包的安德森定位表现，即量子回旋镖效应（QBE）。这种现象预示着一个粒子的无序平均质心最初是弹道运动，然后掉头，最后慢慢回到它的初始位置。QBE 已被预测在几个安德森定位的 Hermitian 模型中发生，并已在典型的量子踢转子模型中进行了实验观察。在本文中，我们研究了非厄米系统中 QBE 的出现，并阐明了哈密顿量和初始状态对称性的重要性。我们概括了文献中可用的分析论证，并表明即使在复杂光谱的情况下，类似回旋镖的行为也可能出现在非厄米系统中。我们通过对几个非厄米特模型的动力学进行仔细的数值研究来确认我们的分析结果。我们发现非 Hermicity 导致动态关系的崩溃，尽管 QBE 被保留了。本文为安德森本地化系统的未来研究开辟了道路。这里研究的模型可以使用光学晶格中的冷原子来实现。我们发现非 Hermicity 导致动态关系的崩溃，尽管 QBE 被保留了。本文为安德森本地化系统的未来研究开辟了道路。这里研究的模型可以使用光学晶格中的冷原子来实现。我们发现非 Hermicity 导致动态关系的崩溃，尽管 QBE 被保留了。本文为安德森本地化系统的未来研究开辟了道路。这里研究的模型可以使用光学晶格中的冷原子来实现。