Fokker-Planck and Langevin Equations from Forward--Backward Path Integral
arXiv:quant-ph/0008109 · doi:10.1006/aphy.2001.6158
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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