Variational Perturbation Theory for Fokker-Planck Equation with Nonlinear Drift

Details Variational Perturbation Theory for Fokker-Planck Equation with Nonlinear Drift Variational Perturbation Theory for Fokker-Planck Equation with Nonlinear Drift

2004-12-30

arxiv.org/abs/cond-mat/0412750v1

European Physical Journal B 45, 355-368 (2005)

Physics

Condensed Matter

Statistical Mechanics

Author Information under http://www.theo-phys.uni-essen.de/tp/ags/pelster_dir/

Scientific paper

10.1140/epjb/e2005-00195-2

We develop a recursive method for perturbative solutions of the Fokker-Planck equation with nonlinear drift. The series expansion of the time-dependent probability density in terms of powers of the coupling constant is obtained by solving a set of first-order linear ordinary differential equations. Resumming the series in the spirit of variational perturbation theory we are able to determine the probability density for all values of the coupling constant. Comparison with numerical results shows exponential convergence with increasing order.

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