Linear systems with adiabatic fluctuations

Details Linear systems with adiabatic fluctuations Linear systems with adiabatic fluctuations

1998-07-02

arxiv.org/abs/cond-mat/9807031v1

J. Phys. A., vol. 31, 3937-3948 (1998)

Physics

Condensed Matter

Statistical Mechanics

Plain Latex, no figure, 21 pages

Scientific paper

10.1088/0305-4470/31/17/005

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 \alpha/|\mu|, where \alpha is the strength of fluctuations and 1/|\mu| 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.

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