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Fokker-Planck and Langevin Equations from Forward--Backward Path Integral

Hagen Kleinert

quant-pharXiv:quant-ph/0008109

Abstract

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.

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