Fokker–Planck and Langevin Equations from the Forward–BackwardPath Integral
نویسنده
چکیده
Starting from a forward-backward path integral of a point particle in a bath of harmonic oscillators, we derive the Fokker–Planck and Langevin equations with and without inertia. Special emphasis is placed upon the correct operator order in the time evolution operator. The crucial step is the evaluation of a Jacobian with a retarded time derivative by analytic regularization. C © 2001 Academic Press
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Stochastic Toolkit for Uncertainty Quantification in complex nonlinear systems
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