Theory of Diffusion and Intermittency in Chaotic system. III : New Approach to Temporal Correlations

概要

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A new statistical-mechanical approach to the temporal correlation in one-dimensional time series {u;t=0,1,2,3,…} generated by a chaotic dynamics is developed. This is done by studying poles of the Fourier transform of the moment M_t(q)≡<exp(qtz_t)>, where z_t≡t^<-1>Σ^<t-1> _<j=0>u_j is the scale-dependent average and the parameter q is real. The temporal correlations turn out to be specified with sets of characteristic frequencies {w_q} and line widths {γ_q}. It is shown that the conventional double-time correlation function theory deals only with the limit q→0. furthermore we will find that {w_q} and { γ_q} generally depend on q. This implies that different characteristic dynamics embedded in {u_t}, including motions which can be never described by the double-time correlation function approach, are able to be singled out in a unified way by controlling the parameter q.
理論物理学刊行会の論文
1987-08-25