| In the framework of statistical descriptions of many particle systems, the influence of mean field approximations on the linear response theory is studied. A procedure, analogous to one where no mean field approximation is involved, is used in order to determine the first order response of the distribution function to the perturbation. Subsequently, the effect of the mean field approximations is examined when formulating Green-Kubo relations for transport coefficients on the deterministic Liouvillean level and the stochastic Fokker-Planck level. On the deterministic level, the Vlasov equation is employed to prove the Green-Kubo formula for the electric conductivity tensor in its well known form. One finds that the interpretation of the Green-Kubo formula is changed when applying Vlasov's mean field approximation. On the stochastic level, the Gaussian approximation of the bead-spring model for dilute polymer solutions, including hydrodynamic interaction, is considered in homogenous shear flow. The commonly known Green-Kubo formula for the viscosity is found to be invalid in the Gaussian approximation and the appropriate modification to the formula is given.
for LaTeX users @article{MH\"utter1996-54,
author = {M. H\"utter and H. C. \"Ottinger},
title = {Modification of Linear Response Theory for Mean Field Approximations},
journal = {Phys. Rev. E},
volume = {54},
pages = {2526-2530},
year = {1996}
}
\bibitem{MH\"utter1996-54} M. H\"utter, H.C. \"Ottinger,
Modification of Linear Response Theory for Mean Field Approximations,
Phys. Rev. E {\bf 54} (1996) 2526-2530.MH\"utter1996-54
M. H\"utter, H.C. \"Ottinger
Modification of Linear Response Theory for Mean Field Approximations
Phys. Rev. E,54,1996,2526-2530 |
mk@mat.ethz.ch
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