A New Expansion of Dynamical Correlations in Stochastic Processes and Chaotic Dynamics

A new expansion method to obtain time correlation functions and large deviation sta-tistical characteristic functions in Markovian stochastic processes and chaotic dynamics is proposed. Because for chaotic dynamics no smooth, steady-state probability density exists, it is not convenient for formulating the problem of solving the eigenvalue problem to the time evolution operator. Instead, we use the Mori projection operator method with an operator projected on a state space larger than that spanned by the dynamical variable under con-sideration. Choosing the number of additional dynamical variables, we can systematically control the degree of approximations. §1. Deriving dynamical correlations from governing equations of motion Time correlation functions are important quantities to describe dynamical sta-tistics of condensed matter systems.1),2) Also, in stochastic processes and chaotic dynamics, time correlation functions are fundamental quantities for studying fluctu-ation statistics.3)–8) Furthermore, large deviation statistical characteristic functions are important to describe both Gaussian and non-Gaussian statistics of temporal fluctuations.6),9)–12) To derive these quantities from the governing dynamical equa