Short-time correlations of many-body systems described by nonlinear Fokker-Planck equations and Vlasov-Fokker-Planck equations

Analytical expressions for short-time correlation functions, diffusion coefficients, mean square displacement, and second order statistics of many-body systems are derived using a mean field approach in terms of nonlinear Fokker-Planck equations and Vlasov-Fokker-Planck equations. The results are illustrated for the Desai-Zwanzig model, the nonlinear diffusion equation related to the Tsallis statistics, and a Vlasov-Fokker-Planck equation describing bunch particles in particle accelerator storage rings.