Symmetry-breaking dynamical phase transitions (DPTs) abound in the fluctuations of nonequilibrium systems. Here we show that the spectral features of a particular class of DPTs exhibit the fingerprints of the recently discovered time-crystal phase of matter. Using Doob’s transform as a tool, we provide a mechanism to build classical time-crystal generators from the rare event statistics of some driven diffusive systems. An analysis of the Doob’s smart field in terms of the order parameter of the transition then leads to the time-crystal lattice gas (tcLG), a model of driven fluid subject to an external which presents a clear-cut steady-state phase transition to a time-crystalline phase characterized by a matter density wave which breaks continuous time-translation symmetry and displays rigidity and long-range spatio-temporal order, as required for a time crystal. A hydrodynamic analysis of the tcLG transition uncovers striking similarities, but also key differences, with the Kuramoto synchronization transition. Possible experimental realizations of the tcLG in colloidal fluids are also discussed.

中文翻译：

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从罕见事件中建立连续的时间晶体

在非平衡系统的波动中，对称对称的动态相变（DPT）大量存在。在这里，我们表明一类特殊DPT的光谱特征展示了最近发现的物质时晶相的指纹。使用Doob变换作为工具，我们提供了一种机制，可以从某些驱动扩散系统的稀有事件统计信息中构建经典的时间晶体生成器。然后，根据跃迁的阶跃参数对Doob的智能场进行分析，得出了时晶格气体（tcLG），这是一种受外部驱动的流体模型，呈现出清晰的稳态相变。以物质密度波为特征的时晶相，它打破了连续的时间平移对称性并显示出刚度和长期的时空顺序，根据时间晶体的要求。对tcLG过渡的流体动力学分析揭示了与仓本同步过渡的惊人相似之处，但也有关键区别。还讨论了tcLG在胶体液中可能的实验实现。