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

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

2000-08-25

arxiv.org/abs/quant-ph/0008109v1

Ann. Phys. 291 (2001) 14

Physics

Quantum Physics

Author Information under http://www.physik.fu-berlin.de/~kleinert/institution.html . Latest update of paper (including all P

Scientific paper

10.1006/aphy.2001.6158

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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