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Title: Collective 1/f fluctuation by pseudo-Casimir-invariants
Authors: Yamaguchi, Yoshiyuki Y.
Kaneko, Kunihiko
Author's alias: 山口, 義幸
Issue Date: Aug-2018
Publisher: American Physical Society (APS)
Journal title: Physical Review E
Volume: 98
Issue: 2
Thesis number: 020201(R)
Abstract: 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.
Rights: ©2018 American Physical Society
DOI(Published Version): 10.1103/PhysRevE.98.020201
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