Linear systems with adiabatic fluctuations

Abstract

We consider a dynamical system subjected to weak but adiabatically slow fluctuations of an external origin. Based on the 'adiabatic following' approximation we carry out an expansion in α|μ|^−L, where α is the strength of fluctuations and |μ|^−L refers to the time scale of evolution of the unperturbed system to obtain a linear differential equation for the average solution. The theory is applied to the problems of a damped harmonic oscillator and diffusion in a turbulent fluid. The result is the realization of a 'renormalized' diffusion constant or damping constant for the respective problems. The applicability of the method has been analysed critically.