Service de Physique de l'Etat Condensé, CEA-Saclay, 91191 Gif-sur-Yvette, France.
Phys Rev Lett. 2009 Oct 9;103(15):154103. doi: 10.1103/PhysRevLett.103.154103.
We show, using generic globally coupled systems, that the collective dynamics of large chaotic systems is encoded in their Lyapunov spectra: most modes are typically localized on a few degrees of freedom, but some are delocalized, acting collectively on the trajectory. For globally coupled maps, we show, moreover, a quantitative correspondence between the collective modes and some of the so-called Perron-Frobenius dynamics. Our results imply that the conventional definition of extensivity must be changed as soon as collective dynamics sets in.
我们使用通用的全局耦合系统表明，大型混沌系统的集体动力学被编码在它们的李雅普诺夫谱中：大多数模式通常局限于少数自由度，但有些模式是弥散的，集体作用于轨迹。此外，对于全局耦合映射，我们还展示了集体模式与所谓的佩龙-弗罗贝尼乌斯动力学之间的定量对应关系。我们的结果意味着，一旦集体动力学出现，就必须改变传统的扩展性定义。
