同步诱导行走液滴模型中的贝尔不等式违背
Synchronization induces Bell violations in a model of walking droplets
浏览论文内容
中文总结 AI 辅助
该研究通过类洛伦兹模型，证实行走液滴的波介导同步机制可产生贝尔不等式违背，为导航波系统的经典纠缠提供了动力学框架。
中文摘要 AI 辅助
我们考虑一个简化的类洛伦兹模型，该模型描述两个行走液滴通过相互的波场发生相互作用，并研究这种经典波粒系统中强二体关联的出现。耦合的非线性动力学存在两个不变同步流形，分别对应关联态和反关联态，在这两个流形内，液滴表现出同步的混沌间歇性。采用受贝尔实验启发的测量方案，我们从长时间动力学中计算位置关联，并确定CHSH-Bell参数S超过2的参数区域，这对应贝尔不等式的违背。我们进一步引入一种分离两个子系统的程序，从而确保它们之间不存在波介导的信号传递。在这种分离后改变测量设置，使我们能够执行动态贝尔测试，其中违背现象持续存在。我们的结果表明，非线性确定性动力学可通过波介导的同步机制产生贝尔不等式违背；此外，这些违背可基于波形受测量设置影响的理由得到解释。因此，我们为导航波系统中经典纠缠的出现提供了一个一致的动力学框架。
英文摘要
We consider a reduced Lorenz-like model that describes two walking droplets interacting through their mutual wave field, and investigate the emergence of strong bipartite correlations in this classical wave-particle system. The coupled nonlinear dynamics admit two invariant synchronization manifolds associated with correlated and anticorrelated states, within which the droplets display synchronized chaotic intermittency. Employing measurement protocols inspired by Bell experiments, we compute position correlations from the long-time dynamics and identify parameter regimes for which the CHSH-Bell parameter $S$ exceeds 2, corresponding to violations of Bell's Inequality. We further introduce a procedure for isolating the two subsystems, thereby ensuring the absence of wave-mediated signaling between them. Changing measurement settings following this isolation allows us to execute dynamic Bell tests in which violations persist. Our results demonstrate that nonlinear deterministic dynamics can produce Bell violations through wave-mediated synchronization mechanisms; moreover, these violations may be rationalized on the grounds that the wave form is influenced by the measurement settings. We thus provide a consistent dynamical framework for the appearance of classical entanglement in pilot-wave systems.
