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

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  • Theiss, W.
  • Titulaer, U.M.

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.

Suggested Citation

  • Theiss, W. & Titulaer, U.M., 1985. "The systematic adiabatic elimination of fast variables from a many-dimensional Fokker-Planck equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 130(1), pages 123-142.
    • Handle: RePEc:eee:phsmap:v:130:y:1985:i:1:p:123-142
    DOI: 10.1016/0378-4371(85)90100-1
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    References listed on IDEAS

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    1. Kneller, Gerald R. & Titulaer, U.M., 1984. "The covariant form of the Klein-Kramers equation and the associated moment equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 129(1), pages 81-94.
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