Linear systems with adiabatic fluctuations
arXiv:cond-mat/9807031 · doi:10.1088/0305-4470/31/17/005
Abstract
We consider a dynamical system subjected to weak but adiabatically slow fluctuations of external origin. Based on the ``adiabatic following'' approximation we carry out an expansion in α/|μ|, where αis the strength of fluctuations and 1/|μ| 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 `renormalized' diffusion constant or damping constant for the respective problems. The applicability of the method has been critically analyzed.
arXiv commentPlain Latex, no figure, 21 pages