Statistical-Mechanical Theory of Random Frequency Modulations and Generalized Brownian Motions
Michio Tokuyama, Hazime Mori · Progress of Theoretical Physics · 1976
It is shown that the Heisenberg equation of motion can be transformed exactly into the reduced form dA(t)/dt = [ iΩ-∫t0ψ(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.