Systematic elimination of fast variables in linear systems

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 p...

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Bibliographic Details
Published in:Physica A 1983-01, Vol.119 (1), p.41-52
Main Authors: Geigenmüller, U., Titulaer, U.M., Felderhof, B.U.
Format: Article
Language:English
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Summary: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.
ISSN:0378-4371
1873-2119
DOI:10.1016/0378-4371(83)90144-9