The systematic adiabatic elimination of fast variables from a many-dimensional Fokker-Planck equation

W. Theiss and U.M. Titulaer

Physica A: Statistical Mechanics and its Applications, 1985, vol. 130, issue 1, 123-142

Abstract: The Chapman-Enskog method for the adiabatic elimination of fast variables is applied to a general Fokker-Planck equation linear in the fast variables. This equation is the counterpart of the generalized Haken-Zwanzig model, a system of coupled Langevin equations often encountered in quantum optics and in the theory of non-equilibrium phase transitions. After a few equilibration times for the fast variables the time dependence of smooth solutions of this Fokker-Planck equation is completely governed by the reduced distribution function of the slow variables, which obeys a closed evolution equation. We obtain an explicit perturbation series for the generator of this reduced evolution. The system considered here is the most general system for which the Chapman-Enskog hierarchy can be solved explicitly by exploiting an analogy between the unperturbed operator and the Hamiltonian for coupled harmonic oscillators.

Date: 1985
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:130:y:1985:i:1:p:123-142

DOI: 10.1016/0378-4371(85)90100-1

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