Reduced Equations of Motion for Generalized Fluxes and Forces in the Contiued-Fraction Expansion

概要

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With the aid of Mori's projection operator method, it is shown that the mechanical equations of motion for flux variables can be transformed rigorously into the reduced form da_j(t)/dt=iw_j・a_j(t)-∫^t_0ds[ψ_j(t-s)+φ_j(t-s)]・a_j(s)+g_j(t)+f_j(t), where a_j(t) is a column matrix of generalized fluxes standing for the j-th order time derivative of the column matrix of state variable a_0(t),ψ_0(t)≡0, g_0(t)≡0 ω_j is a frequency matrix. f_j(t) is Mori's j-th order random force and φ_j(t) is the corresponding memory matrix. A new fluctuating force g_j(t) and the corresponding memory matrix ψ_j(t) represent the effects of lower-order fluxes. The temporal behaviour of g_j(t) is quite different from that of f_j(t), and the Laplace transform of ψ_j(t) is represented by an inverted continued fraction of finite order whose poles are all purely imaginary. The Laplace transform of time-correlation matrices of a_j(t) and a_k(0) are given in terms of these memory-spectrum matrices ψ_j[z] and φ_j[z].
理論物理学刊行会の論文
1980-06-25