Lauter Roland, Mitra Aditi, Marquardt Florian
Institut für Theoretische Physik II, Friedrich-Alexander-Universität Erlangen-Nürnberg, Staudtstr. 7, 91058 Erlangen, Germany.
Max Planck Institute for the Science of Light, Staudtstr. 2, 91058 Erlangen, Germany.
Phys Rev E. 2017 Jul;96(1-1):012220. doi: 10.1103/PhysRevE.96.012220. Epub 2017 Jul 24.
Phase oscillator lattices subject to noise are one of the most fundamental systems in nonequilibrium physics. We have discovered a dynamical transition which has a significant impact on the synchronization dynamics in such lattices, as it leads to an explosive increase of the phase diffusion rate by orders of magnitude. Our analysis is based on the widely applicable Kuramoto-Sakaguchi model, with local couplings between oscillators. For one-dimensional lattices, we observe the universal evolution of the phase spread that is suggested by a connection to the theory of surface growth, as described by the Kardar-Parisi-Zhang (KPZ) model. Moreover, we are able to explain the dynamical transition both in one and two dimensions by connecting it to an apparent finite-time singularity in a related KPZ lattice model. Our findings have direct consequences for the frequency stability of coupled oscillator lattices.
受噪声影响的相位振子晶格是非平衡物理学中最基本的系统之一。我们发现了一种动力学转变，它对这种晶格中的同步动力学有重大影响，因为它会导致相位扩散率呈数量级的爆发式增长。我们的分析基于广泛适用的Kuramoto-Sakaguchi模型，振子之间存在局部耦合。对于一维晶格，我们观察到相位扩展的普遍演化，这是通过与表面生长理论的联系所暗示的，如Kardar-Parisi-Zhang（KPZ）模型所描述的那样。此外，我们能够通过将其与相关KPZ晶格模型中明显的有限时间奇点联系起来，来解释一维和二维中的动力学转变。我们的发现对耦合振子晶格的频率稳定性有直接影响。
