Fokker-Planck and Langevin Equations from Forward--Backward Path Integral
Quantum Physics
2009-11-06 v1
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.
Keywords
Cite
@article{arxiv.quant-ph/0008109,
title = {Fokker-Planck and Langevin Equations from Forward--Backward Path Integral},
author = {Hagen Kleinert},
journal= {arXiv preprint arXiv:quant-ph/0008109},
year = {2009}
}
Comments
Author Information under http://www.physik.fu-berlin.de/~kleinert/institution.html . Latest update of paper (including all PS fonts) at http://www.physik.fu-berlin.de/~kleinert/315