The Memory Function and Chaos-Induced Friction in the Chaotic Henon-Heiles System(Condensed Matter and Statistical Physics)

概要

論文の詳細を見る
A non-Markovian linear stochastic equation for the momentum Py(t) is derived for the purpose of clarifying transport processes in the chaotic Henon-Heiles system with the aid of the Mori projection operator formalism. For the time correlation function C_y(t)≡<y(t)y(O)> of the coordinate y(t), this leads to an integrable linear evolution equation. Then, the memory function γ(t) enables us to define a frequency-dependent chaos-induced friction coefficient of the system, γ(iω). We show that this friction coefficient is related to the time correlation function φ(t) of a nonlinear force f(t), which can be computed numerically. Thus, in the case that the total energy is E=1/6, it turns out that the structure of the frequency-dependent friction coefficient γr(ω) consists of three sharp peaks at frequencies ω=0, 0.859 and 1.891. This leads to a three-term approximation of the memory function, γ(t), with a correlation time T_γ〜5T (with T=2π). It is also shown that the structure of the power spectrum I_y(ω) of y(t) consists of four sharp peaks at frequencies ω=0, 0.500, 0.797 and 1.000. This leads to a four-term approximation of the time correlation function C_y(t) with a correlation time T_M〜6T. The frequencies and line widths of the sharp peaks of I_y(ω) are given by the friction coefficient γ(iω).
理論物理学刊行会の論文
2006-12-25