标题： 极端同步转换 显示英文标题

标题： Extreme Synchronization Transitions

摘要： 在自然和人造系统中，转变点标志着突然的秩序变化，因此对于理解整体系统特征至关重要。受最近实验观察的启发，我们在此揭示了耦合振子中一类有趣的变化——极端同步转变，从异步无序状态转变为几乎完全有序相的同步状态。尽管这种转变看起来像是一种不连续或爆炸性的相变，但它表现出显著不同的特征。首先，这种转变已经在$N$单位的有限系统中发生，因此构成了多维系统的有趣分歧，而不是仅在热力学极限$N\rightarrow \infty$中出现的真实相变。其次，同步阶参数从大约$N^{-1/2}$数量级的中等值跳变为几乎立即接近理论最大值$1$的值，一旦跨越临界耦合强度。我们分析性地解释了复化Kuramoto振子中这种极端转变背后的机制。极端转变也可能发生在其他耦合振子系统以及某些渗透过程中。在应用方面，它们的发生影响着我们确保或防止强形式的有序性的能力，例如在生物系统和工程系统中。 显示英文摘要

摘要： Across natural and human-made systems, transition points mark sudden changes of order and are thus key to understanding overarching system features. Motivated by recent experimental observations, we here uncover an intriguing class of transitions in coupled oscillators, extreme synchronization transitions, from asynchronous disordered states to synchronous states with almost completely ordered phases. Whereas such a transition appears like discontinuous or explosive phase transitions, it exhibits markedly distinct features. First, the transition occurs already in finite systems of $N$ units and so constitutes an intriguing bifurcation of multi-dimensional systems rather than a genuine phase transition that emerges in the thermodynamic limit $N\rightarrow \infty$ only. Second, the synchronization order parameter jumps from moderate values of the order of $N^{-1/2}$ to values extremely close to $1$, its theoretical maximum, immediately upon crossing a critical coupling strength. We analytically explain the mechanisms underlying such extreme transitions in coupled complexified Kuramoto oscillators. Extreme transitions may similarly occur across other systems of coupled oscillators as well as in certain percolation processes. In applications, their occurrence impacts our ability of ensuring or preventing strong forms of ordering, for instance in biological and engineered systems.