Berlin 2005 – scientific programme

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DY: Dynamik und Statistische Physik

DY 31: Nonlinear Stochastic Systems I

DY 31.1: Talk

Monday, March 7, 2005, 10:30–10:45, TU H2032

Fluctuation-dissipation theorems and second order statistics of many-body systems described by means of nonlinear Fokker-Planck equations and Vlasov-Fokker-Planck equations — •Till Daniel Frank — Institute for Theoretical Physics, University of Münster, Wilhelm-Klemm-Str. 9, 48149 Münster, Germany

In line with mean field theory, we study stochastic properties of many-body systems in terms of nonlinear Fokker-Planck equations, in general, and Vlasov-Fokker-Planck equations, in particular. We show that the first order statistics of these models can be embedded into second and higher order statistics defined by self-consistent Langevin equations. We exploit this approach to derive exact analytical expressions for two-time point joint probability densities for some benchmark models and to address the fluctuation-dissipation theorem. In addition, we derive analytical expressions for short-time correlation functions and show how to determine time correlation functions in general in terms of hierarchies of coupled differential equations.

M. Shiino: Phys. Rev. A 36 (1987) 2393; M. Hütter and H. C. Öttinger: Phys. Rev. E 54 (1996) 2526

T.D. Frank: Phys. Lett. A, 319 (2003) 173; Physica A, 331 (2004) 391; Eur. Phys. Journal B 37 (2004) 139; Phys. Lett. A, 329 (2004) 475-485