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Systematic elimination of fast variables in linear systems

Author

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  • Geigenmüller, U.
  • Titulaer, U.M.
  • Felderhof, B.U.

Abstract

We consider linear systems in which some of the variables evolve on a much faster time scale than the remaining ones. By means of a systematic perturbation theory in the time-scale ratio we extract a reduced dynamics in terms of the slow variables only, valid after an initial transient period. The procedure provides a systematic extension of the usual adiabatic elimination scheme and gives corrections to it. We also find an expression for the long-time behavior of the correlation functions of the slow variables. These asymptotic expressions do not extrapolate back towards the equal-time correlations for t going to zero; the reason for this “initial slip” is given and its magnitude calculated. Method and results are illustrated with a simple example of coupled oscillators.

Suggested Citation

  • Geigenmüller, U. & Titulaer, U.M. & Felderhof, B.U., 1983. "Systematic elimination of fast variables in linear systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 119(1), pages 41-52.
    • Handle: RePEc:eee:phsmap:v:119:y:1983:i:1:p:41-52
    DOI: 10.1016/0378-4371(83)90144-9
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