AI 中文总结
研究负最近邻耦合的库拉索夫振荡器非平衡排序动力学，通过连续近似等解释一维中缺陷密度等的反常指数，二维中几何挫折影响排序，表明确定性动力学和几何挫折可致慢弛豫等，无需无序或噪声。
AI 中文摘要
我们研究了具有负最近邻耦合的耦合库拉索夫振荡器的非平衡排序动力学，该耦合诱导了锯齿形反铁磁排序。在一维中，缺陷密度表现出异常缓慢的粗化，在与系统大小相关的时间（\(t_c(N)\sim N^z\)，\(z = 2\)）饱和之前，以\((D(t)\sim t^{-1/4})\)衰减。局部持续概率遵循拉伸指数形式\((P(t)\sim \exp(-c t^\alpha))\)，\((\alpha = 1/4)\)。这些指数与耦合强度无关，仅重新缩放特征时间尺度。\((\alpha=\delta=1/4)\)与\(z = 2\)的等式与一个独特的普适类一致。这些结果表明，确定性非线性动力学和几何挫折足以产生缓慢弛豫和反常标度，无需淬火无序或随机噪声。连续近似和相应的粗粒化偏微分方程为观察到的反常指数提供了理论解释，而线性稳定性分析解释了锯齿形有序状态的出现。在二维中，几何挫折抑制了完全排序，并产生了长寿命的亚稳态畴壁结构。在交叉和饱和之前观察到初始瞬态缺陷衰减。这些结果表明了挫折和连续相变量如何从根本上改变粗化动力学，并在确定性多体系统中产生异常缓慢的弛豫。
英文摘要
We investigate the nonequilibrium ordering dynamics of coupled Kuramoto oscillators with negative nearest-neighbor coupling, which induces a zigzag antiferromagnetic ordering. In one dimension, the defect density exhibits anomalously slow coarsening, decaying as $(D(t)\sim t^{-1/4})$ before saturating at a system-size-dependent time $(t_c(N)\sim N^z)$ with (z=2). The local persistence probability follows a stretched-exponential form, $(P(t)\sim \exp(-c t^α))$, with $(α=1/4)$. These exponents are observed are independent of the magnitude of the coupling, which merely rescales the characteristic time scale. The equality $(α=δ=1/4)$ together with (z=2) is consistent with a distinct universality class. These results demonstrate that deterministic nonlinear dynamics and geometric frustration alone are sufficient to generate slow relaxation and anomalous scaling, without quenched disorder or stochastic noise. A continuum approximation and the corresponding coarse-grained partial differential equation provide a theoretical explanation for the observed anomalous exponents, while linear stability analysis accounts for the emergence of the zigzag ordered state. In two dimensions, geometric frustration inhibits complete ordering and gives rise to long-lived metastable domain-wall structures. An initial transient defect decay is observed before crossover and saturation. These results demonstrate how frustration and continuous phase variables can fundamentally modify coarsening dynamics and generate anomalously slow relaxation in deterministic many-body systems.
DOI：10.1016/j.cnsns.2026.110621
