English

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

R2 v1 2026-07-22T19:28:42.167Z