LINEAR-SYSTEMS WITH ADIABATIC FLUCTUATIONS

We consider a dynamical system subjected to weak but adiabatically slo w fluctuations of an external origin. Based on the 'adiabatic followin g' approximation we carry out an expansion in alpha\mu\(-1), where alp ha is the strength of fluctuations and \mu\-1 refers to the time scale of evolution of the unperturbed system to obtain a linear differentia l equation for the average solution. The theory is applied to the prob lems of a damped harmonic oscillator and diffusion in a turbulent flui d. The result is the realization of a 'renormalized' diffusion constan t or damping constant for the respective problems. The applicability o f the method has been analysed critically.