Time Correlations and Diffusion of a Conservative Forced Pendulum

概要

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The time correlations and diffusion of chaotic orbits in a periodically forced pendulum without friction are studied. The pendulum exhibits a Poincare section with period T at times t = jT (j = 0, 1, 2, ・・・). The imerelation function C(t) ≡ (p(t}p(0)} of the angular velocity p(t) oscillates with period T, even as t → ∞, since the average quantities of the system have a periodicity with period T, due to the periodic external force. Studying the approach to asymptotic oscillation, we find that the time-correlation function C(t) exhibits an inverse power decay t^<-(β-1) (1 <β < 2), where there exist islands of accelerator-mode tori. Then, it is also shown that the power spectrum I_p(ω) of p(t) obeys an inverse power law ω^<-(2-β) for small frequency ω 2π<</T. We also calculate the mean square displacement σ^2(n) of the angular variable q_n ≡ q(nT] on the Poincare section, and show thatσ^2(n) ∞ n^ζ(ζ= 3 - 3) for n → ∞, leading to anomolous diffusion with 1< ζ< 2.
理論物理学刊行会の論文
2003-02-25