Collective 1/f fluctuation by pseudo-Casimir-invariants
Collective 1/f fluctuation by pseudo-Casimir-invariants
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DOI：
10.1103/physreve.98.020201
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发表时间：
2018-08-27
影响因子：
2.4
通讯作者：
Kaneko, Kunihiko
中科院分区：
文献类型：
--
作者：
Yamaguchi, Yoshiyuki Y.;Kaneko, Kunihiko
在这项研究中，我们提出了一个通用的场景来解释多自由度哈密顿动力系统在远程相互作用下的1/f波动，包括粉红色噪声。在热力学极限下，这类系统的动力学可以用具有无限个卡西米尔不变量的弗拉索夫方程来描述。在有限系统中，它们变成伪不变量，产生准平稳状态。然后动力学在它们上面表现出缓慢的运动，直到伪卡西米尔不变量有效的时间尺度。直接数值模拟证实，这种长时间的相关性导致了集体变量的1/f波动。采用不同的哈密顿量，改变相互作用的范围和粒子的数目，证明了这种1/f涨落的普遍性。
In this study, we propose a universal scenario explaining the 1/f fluctuation, including pink noises, in Hamiltonian dynamical systems with many degrees of freedom under long-range interaction. In the thermodynamic limit, the dynamics of such systems can be described by the Vlasov equation, which has an infinite number of Casimir invariants. In a finite system, they become pseudoinvariants, which yield quasistationary states. The dynamics then exhibit slow motion over them, up to the timescale where the pseudo-Casimir-invariants are effective. Such long-time correlation leads to 1/f fluctuations of collective variables, as is confirmed by direct numerical simulations. The universality of this collective 1/f fluctuation is demonstrated by taking a variety of Hamiltonians and changing the range of interaction and number of particles.