Nishikawa Isao, Tanaka Gouhei, Aihara Kazuyuki
Institute of Industrial Science, The University of Tokyo, Tokyo 153-8505, Japan.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Aug;88(2):024102. doi: 10.1103/PhysRevE.88.024102. Epub 2013 Aug 30.
Universal scaling laws form one of the central issues in physics. A nonstandard scaling law or a breakdown of a standard scaling law, on the other hand, can often lead to the finding of a new universality class in physical systems. Recently, we found that a statistical quantity related to fluctuations follows a nonstandard scaling law with respect to the system size in a synchronized state of globally coupled nonidentical phase oscillators [I. Nishikawa et al., Chaos 22, 013133 (2012)]. However, it is still unclear how widely this nonstandard scaling law is observed. In the present paper, we discuss the conditions required for the unusual scaling law in globally coupled oscillator systems and validate the conditions by numerical simulations of several different models.
普适标度律是物理学的核心问题之一。另一方面，非标准标度律或标准标度律的失效，往往能促使人们在物理系统中发现新的普适类。最近，我们发现，在全局耦合的非相同相位振子的同步状态下，一个与涨落相关的统计量相对于系统大小遵循非标准标度律[I. 西川等人，《混沌》22, 013133 (2012)]。然而，目前尚不清楚这种非标准标度律的观测范围有多广。在本文中，我们讨论了全局耦合振子系统中这种异常标度律所需的条件，并通过对几种不同模型的数值模拟来验证这些条件。
