Coherent flows of self-propelled particles are characterized by vortices and jets that sustain chaotic flows, referred to as active turbulence. Here, we reveal a transition between defect-free active turbulence and active turbulence laden with defects. Interestingly, we show that concurrent to the transition from defect-free active turbulence to defect-laden turbulence is the restoration of the previously broken $U(1)$-symmetry and fast decay of the two-point correlations which suggests a symmetry-breaking transition. By stability analyses of the topological charge density field, we provide an analytical prediction of the activity threshold for the transition to the defect-laden active turbulent state. Moreover, despite the distinct symmetry features between the defect-free and defect-laden active turbulence, we demonstrate universal behaviors for the self-similarity of the flow fluctuations at large scales, and exponential decay of polarity power spectrum, at small length scales compared to the active energy injection length. It is further shown that increasing the self-propulsion of the active particles results in exponential rarefaction of topological defects and a transition from active defect-laden turbulence to a flocking state. These findings reveal new dynamical transitions between distinct spatiotemporal organization patterns in polar active mater.

中文翻译：

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极性活性物质中无缺陷和有缺陷湍流之间的对称破缺转变

自推进粒子的相干流的特征在于维持混沌流的涡流和射流，称为主动湍流。在这里，我们揭示了无缺陷主动湍流和充满缺陷的主动湍流之间的过渡。有趣的是，我们表明，与从无缺陷活动湍流到含有缺陷的湍流的转变同时存在的是先前破坏的 $U(1)$-对称性的恢复和两点相关性的快速衰减，这表明对称性破坏过渡。通过拓扑电荷密度场的稳定性分析，我们提供了向充满缺陷的活性湍流状态转变的活性阈值的分析预测。此外，尽管无缺陷和有缺陷的主动湍流之间存在明显的对称特征，我们展示了与有功能量注入长度相比，在小长度尺度上流动波动的自相似性和极性功率谱的指数衰减的普遍行为。进一步表明，增加活性粒子的自推进力会导致拓扑缺陷的指数稀疏和从充满活性缺陷的湍流过渡到植绒状态。这些发现揭示了极地活性物质中不同时空组织模式之间的新动态转变。进一步表明，增加活性粒子的自推进力会导致拓扑缺陷的指数稀疏和从充满活性缺陷的湍流过渡到植绒状态。这些发现揭示了极地活性物质中不同时空组织模式之间的新动态转变。进一步表明，增加活性粒子的自推进力会导致拓扑缺陷的指数稀疏和从充满活性缺陷的湍流过渡到植绒状态。这些发现揭示了极地活性物质中不同时空组织模式之间的新动态转变。