Linear systems with adiabatic fluctuations

Banik, Suman Kumar ; Ray, Deb Shankar (1998) Linear systems with adiabatic fluctuations Journal of Physics A: Mathematical and General, 31 (17). pp. 3937-3948. ISSN 0305-4470

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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.

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