Memory Function Approach to Chaos and Turbulence and the Continued Fraction Expansion (Condensed Matter and Statistical Physics)

概要

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The chaotic orbits of dynamical systems are deterministic and predictable on short timescales T_r, but they become stochastic and random on long timescales TM (≫ T_r) due to the orbital instability of chaos. This randomization of chaotic orbits has been formulated recently by deriving a non-Markovian stochastic equation for macrovariables in terms of a fluctuating force and a memory function. In order to develop this memory function approach to chaos and turbulence, we explore the following problems by studying the Duffing oscillator and the Navier-Stokes equation for an incompressible fluid : 1) the physical meaning of the projection of macrovariables A (t) onto A (0) ; 2) the method of calculating the short-lived motion with short timescale T_r, which determines the memory functions and the macroscopic transport coefficients due to chaos and turbulence ; 3) the continued fraction expansion of the memory function, and the order estimation of short timescales T_r and long timescales TM ; 4) the relation between the memory function and the time correlation function of a nonlinear force, which gives computable theoretical expressions for the macroscopic transport coefficients.
理論物理学刊行会の論文
2004-05-25