论文标题
嘈杂的库拉莫托模型中拓扑缺陷的动力学在二维
Dynamics of Topological Defects in the noisy Kuramoto Model in two dimensions
论文作者
论文摘要
我们考虑使用短距离耦合和内在频率的高斯分布的二维（2D）嘈杂的库拉莫托同步模型，并在淬灭后研究其订购动力学。我们认为既失水（惯性）和过度抑制的动力学，并表明该本质上平衡系统的长期特性不取决于单个振荡器的惯性。由于其相关长度保持有限，该模型没有表现出任何相变，作为内在频率分布的标准偏差的倒数。淬灭动力学通过域的生长进行，其特征长度最初遵循2D XY模型的生长定律，尽管并非由缺陷之间的平均分离给出。拓扑缺陷通常是免费的，破坏了2D XY模型的Berezinskii-Kosterlitz-无尽的场景。涡旋进行随机步行，让人联想到自避免自我的随机步行，这是由同步域之间的边界的动态网络所介绍的；具有长期超级扩散，带有异常指数$α= 3/2 $。
We consider the two-dimensional (2D) noisy Kuramoto model of synchronization with short-range coupling and a Gaussian distribution of intrinsic frequencies, and investigate its ordering dynamics following a quench. We consider both underdamped (inertial) and over-damped dynamics, and show that the long-term properties of this intrinsically out-of-equilibrium system do not depend on the inertia of individual oscillators. The model does not exhibit any phase transition as its correlation length remains finite, scaling as the inverse of the standard deviation of the distribution of intrinsic frequencies. The quench dynamics proceeds via domain growth, with a characteristic length that initially follows the growth law of the 2D XY model, although is not given by the mean separation between defects. Topological defects are generically free, breaking the Berezinskii-Kosterlitz-Thouless scenario of the 2D XY model. Vortices perform a random walk reminiscent of the self-avoiding random walk, advected by the dynamic network of boundaries between synchronised domains; featuring long-time super-diffusion, with the anomalous exponent $α=3/2$.
