Dynamical Aspects of External Nonwhite Noise

Abstract

The behavior of nonequilibrium systems under the influence of an external noise is the subject of active research. The theoretical and experimental aspects of this problem have been reviewed in a recent monograph by HORSTHEMKE and LEFEVER [l] (see also the papers by other authors in this volume). Most of the studies made so far concern the properties of time-independent stationary quantities, as for example the changes of the stationary distribution of the relevant variable of the system as a function of noise parameters. A different and less studied aspect of the problem concerns the effect of external noise on dynamical properties like the steady state correlation function and its associated relaxation time. A complete description of a system with random control parameters requires the understanding of these dynamical aspects. In this paper we discuss a mathematical framework in which these dynamical problems can be analyzed for a nonwhite external noise. In the white noise limit there exist well-known techniques to calculate time-dependent properties [2]. For a nonwhite noise, the formalism presented here gives a general basis to study dynamical properties of a non-Markovian process. Our discussion is made under the assumption of negligible internal fluctuations. This is a standard assumption in the study of external noise problems. A joint description of internal and external fluctuations and their coupling effects has been discussed elsewhere [3].