Iatsenko D, McClintock P V E, Stefanovska A
Department of Physics, Lancaster University, Lancaster LA1 4YB, UK.
Nat Commun. 2014 Jun 20;5:4118. doi: 10.1038/ncomms5118.
Large networks of coupled oscillators appear in many branches of science, so that the kinds of phenomena they exhibit are not only of intrinsic interest but also of very wide importance. In 1975, Kuramoto proposed an analytically tractable model to describe these systems, which has since been successfully applied in many contexts and remains a subject of intensive research. Some related problems, however, remain unclarified for decades, such as the existence and properties of the oscillator glass state. Here we present a detailed analysis of a very general form of the Kuramoto model. In particular, we find the conditions when it can exhibit glassy behaviour, which represents a kind of synchronous disorder in the present case. Furthermore, we discover a new and intriguing phenomenon that we refer to as super-relaxation where the oscillators feel no interaction at all while relaxing to incoherence. Our findings offer the possibility of creating glassy states and observing super-relaxation in real systems.
耦合振子的大型网络出现在许多科学分支中，因此它们所展现出的各类现象不仅具有内在的研究价值，而且具有极为广泛的重要性。1975年，仓本提出了一个易于进行分析处理的模型来描述这些系统，自那时起该模型已在许多情况下得到成功应用，并且仍然是深入研究的主题。然而，一些相关问题几十年来一直未得到澄清，比如振子玻璃态的存在及其性质。在此，我们对仓本模型的一种非常一般的形式进行了详细分析。特别地，我们找到了它能够呈现玻璃态行为的条件，在当前情况下，玻璃态行为表现为一种同步无序状态。此外，我们发现了一种新的、有趣的现象，我们将其称为超弛豫，即振子在弛豫到非相干状态时完全感受不到相互作用。我们的研究结果为在实际系统中创造玻璃态并观察超弛豫提供了可能性。
