MODIFICATION OF LINEAR-RESPONSE THEORY FOR MEAN-FIELD APPROXIMATIONS

In the framework of statistical descriptions of many particle systems, the influence of mean-field approximations on the linear response the ory is studied. A procedure, analogous to one where no mean-field appr oximation is involved, is used in order to determine the first order r esponse of the distribution function to the perturbation. Subsequently , the effect of the mean-field approximations is examined when formula ting Green-Kubo relations for transport coefficients on the determinis tic Liouvillean level and the stochastic Fokker-Planck level. On the d eterministic level, the Vlasov equation is employed to prove the Green -Kubo formula for the electric conductivity tensor in its well known f orm. One finds that the interpretation of the Green-Kubo formula is ch anged when applying Vlasov's mean-field approximation. On the stochast ic level, the Gaussian approximation of the bead-spring model fur dilu te polymer solutions, including hydrodynamic interaction, is considere d in homogeneous shear flow. The commonly known Green-Kubo formula fur the viscosity is found to be invalid in the Gaussian approximation, a nd the appropriate modification to the formula is given.