On Nonlinear Dynamics of Fluctuations

Abstract

A projection-operator method is developed for renormalizing kinetic coefficients by the nonlinear interaction between macroscopic modes in a nonlinear Langevin equation which is often used in studying anomalous transport phenomena near critical points and anomalous transport coefficients in two dimension. It is shown that the renormalization term is given by the time correlation of a new fluctuating force. Other theories are derived from this expression by making approximations. A relation between the Langevin fluctuating force and the transport fluctuating force is derived to clarify the relation between the Fokker-Planck equation approach by Green and Zwanzig and the linear equation-of-motion approach by one of the authors.