Regensburg 2002 – scientific programme

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DY: Dynamik und Statistische Physik

DY 21: Nichtlineare Stochastische Systeme

DY 21.2: Talk

Tuesday, March 12, 2002, 10:15–10:30, H3

Variational Perturbation Theory for Markov Processes — •Jens Dreger¹, Hagen Kleinert¹, Axel Pelster¹, Mihai Putz^1,2, and Bodo Hamprecht¹ — ¹Institut für Theoretische Physik, Freie Universität Berlin, Arnimallee 14, D-14195 Berlin — ²Departimento di Chimica, Universita della Calabria, Via Pietro Bucci, I-87036 Arcavacata di Rende (CS), Italy

We extend variational perturbation theory to Markov processes. To this end we approximate a given stochastic process by a trial Brownian motion with a linear drift coefficient and an optimized coordinate-depending damping constant. In this way divergent perturbation expansions are transformed into convergent ones where the convergence extends to infinitely strong coupling strengths. We illustrate the procedure by calculating the time dependence of the conditional probability density for a nonlinear stochastic model with a bistable potential. In order to determine the corresponding pertubation expansion, we use for the first-order approach path integral methods. For higher orders we solve the Fokker-Planck equation by performing a double expansion with respect to the coupling strength and the coordinate which yields a recursive set of linear ordinary differential equations. The variational results for the conditional probability density show already in the first order for all times and coupling strengths no significant deviations from numerical solutions of the Fokker-Planck equation, the accuracy being systematically increased by higher-order calculations.