利用非线性动力学实现时间驱动的 Berry 阶段在经典系统中
Harnessing Nonlinear Dynamics for Time-Driven Berry Phase in Classical Systems
AI总结：
本文研究了经典非线性系统中时间驱动 Berry 阶段的积累，提出了一种无需改变内部或外部条件即可使 gauge 变量随时间自然演化的机制，并通过实验验证了频率依赖的 Berry 阶段理论预测。
摘要：
由两个球形颗粒组成的经典非线性系统中时间驱动 Berry 阶段的积累是本研究的核心。我们开发了一种基于扰动的模型，将系统的弹性特性映射到 Bloch 状态，并通过实验验证了频率依赖的 Berry 阶段的理论预测。我们的发现表明，Berry 阶段可以表现出平凡和非平凡值，受外部驱动力和静态预压缩的影响。我们的结果展示了丰富的振动模式，能够在不同频率下显示相同的 Berry 阶段特征，这与以前研究中识别的单一拓扑共振有显著不同。在高度非线性设置中出现多个非平凡 Berry 阶段，而更线性区域则表现出单一非平凡阶段。值得注意的是，本系统中 Berry 阶段的行为与基本量子力学概念如路径依赖的状态演化相似。本研究展示了经典机械系统模仿量子现象的潜力，为量子启发的拓扑计算开辟了新途径，并提供了通过时间驱动 Berry 阶段积累研究非线性介质拓扑性质的新视角。
英文摘要：
Phases arising from cyclic processes are fundamental in physics, bridging quantum and classical domains and providing deeper insights into the topology and dynamics of physical systems. This study investigates the accumulation of a time-driven Berry phase in a classical nonlinear system comprised of two spherical granules and introduces a method in which gauge variants naturally evolve over time without altering internal or external conditions. We develop a perturbation-based model to map the system's elastic characteristics to Bloch states and confirm the theoretical predictions of the frequency-dependent Berry phase through experiments. Our findings reveal that the Berry phase can exhibit trivial and nontrivial values, influenced by external driving forces and static precompression. Our results demonstrate a rich array of vibrational modes, capable of displaying identical Berry phase signatures across different frequencies-a significant departure from previous studies that identified a single topological resonance. Multiple nontrivial Berry phases emerge in highly nonlinear settings, whereas more linear regimes exhibit a singular nontrivial phase. Notably, the behavior of the Berry phase in our system mirrors fundamental quantum mechanics concepts, such as path-dependent state evolution. This study highlights the potential of classical mechanical systems to mimic quantum phenomena, opening new pathways for quantum-inspired topological computation and offering fresh perspectives on using time-driven Berry phase accumulation to investigate topological properties in nonlinear media.
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