论文标题
振荡器晶格同步时，由kardar-parisi-zhang波动驱动的非平衡临界性
Nonequilibrium criticality driven by Kardar-Parisi-Zhang fluctuations in the synchronization of oscillator lattices
论文作者
论文摘要
振荡器集合的同步在整个非线性科学中普遍存在，从经典或量子力学到生物学，再到人体组装。传统上，主要重点是识别过渡到同步的阈值参数值以及这种过渡的性质。在这里，我们表明，将振荡器晶格作为离散的生长界面提供了对动力学过程的独特见解，在该过程中，该晶格长期达到同步。努力研究了库拉莫托模型的概括，该模型允许奇数或非ODD耦合，我们阐明了振荡器晶格的同步，作为通用量表不变性的一个实例，因此系统将显示时空的关键性，在很大程度上不论参数值如何。系统的临界特性（如缩放指数值和满足满足的动态缩放尺度的ANSATZ）属于与柱状障碍的动力学上的粗糙界面的普遍性类别，即Edwards-Wilkinson的临界类别（同等的Edwards-Wilkinson（随机介质）中的Larkin模型，或Kardar-Parisi-parisi-parisi-Zhang（Kardar-Parisi-Zhang）（kardar-parisi-Zhang）（kardar-parisi-zhang）等方程（Kardar-parisi-Zhang）等方程（ （非ODD）耦合。从动力学粗糙化的角度来看，我们发现的关键特性非常创新，尤其是关于波动的统计数据，其特征是它们的概率分布函数（PDF）和协方差。尽管后者恰好是larkin模型的模型，而与耦合的对称性不论，但在通用的非ODD耦合情况下，PDF原来是与KPZ非线性相关的Tracy-Widom分布。这将振荡器晶格的同步分为具有强烈通用波动的强烈相关，低维（经典和量子）系统。
The synchronization of oscillator ensembles is pervasive throughout nonlinear science, from classical or quantum mechanics to biology, to human assemblies. Traditionally, the main focus has been the identification of threshold parameter values for the transition to synchronization as well as the nature of such transition. Here, we show that considering an oscillator lattice as a discrete growing interface provides unique insights into the dynamical process whereby the lattice reaches synchronization for long times. Working on a generalization of the Kuramoto model that allows for odd or non-odd couplings, we elucidate synchronization of oscillator lattices as an instance of generic scale invariance, whereby the system displays space-time criticality, largely irrespective of parameter values. The critical properties of the system (like scaling exponent values and the dynamic scaling Ansatz which is satisfied) fall into universality classes of kinetically rough interfaces with columnar disorder, namely, those of the Edwards-Wilkinson (equivalently, the Larkin model of an elastic interface in a random medium) or the Kardar-Parisi-Zhang (KPZ) equations, for Kuramoto (odd) coupling and generic (non-odd) couplings, respectively. From the point of view of kinetic roughening, the critical properties we find turn out to be quite innovative, especially concerning the statistics of the fluctuations as characterized by their probability distribution function (PDF) and covariance. While the latter happens to be that of the Larkin model irrespective of the symmetry of the coupling, in the generic non-odd coupling case the PDF turns out to be the Tracy-Widom distribution associated with the KPZ nonlinearity. This brings the synchronization of oscillator lattices into a remarkably large class of strongly-correlated, low-dimensional (classical and quantum) systems with strong universal fluctuations.
