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Prog. Theor. Phys. Vol. 55 No. 2 (1976) pp. 411-429

[ Full Text PDF : FREE ACCESS (1237K) ]

Statistical-Mechanical Theory of Random Frequency Modulations and Generalized Brownian Motions

Michio Tokuyama and Hazime Mori

Department of Physics, Kyushu University, Fukuoka

(Received June 27, 1975)

Abstract:

It is shown that the Heisenberg equation of motion can be transformed exactly into the reduced form dA(t)/dt = [ iΩ-\intt0ψ(s)ds] ·A(t)+g(t), where A(t) is an arbitrary column vector of dynamical variables, Ω is a frequency matrix determining collective oscillations, and g(t) is a fluctuating force. ψ(t) differs from the memory function and is related to the time-correlation function of g(t) by ψ(t) = (g(t), g*(0))·(A(t), A*(0))-1. This equation of motion is shown to give a statistical-mechanical theory of random frequency modulations, including Kubo's theory of the stochastic Liouville equation, and to lead to a new theory of generalized Brownian motions which complements a memory-function theory given by Mori.


URL : http://ptp.ipap.jp/link?PTP/55/411/
DOI : 10.1143/PTP.55.411

[ Full Text PDF : FREE ACCESS (1237K) ] Citation:

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