---
_id: '2732'
abstract:
- lang: eng
text: 'We consider a quantum particle moving in a harmonic exterior potential and
linearly coupled to a heat bath of quantum oscillators. Caldeira and Leggett derived
the Fokker Planck equation with friction for the Wigner distribution of the particle
in the large-temperature limit: however, their (nonrigorous) derivation was not
free of criticism, especially since the limiting equation is not of Lindblad form.
In this paper we recover the correct form of their result in a rigorous way. We
also point out that the source of the diffusion is physically restrictive under
this scaling. We investigate the model at a fixed temperature and in the large-time
limit, where the origin of the diffusion is a cumulative effect of many resonant
collisions. We obtain a heat equation with a friction term for the radial process
in phase space and we prove the Einstein relation in this case.'
author:
- first_name: François
full_name: Castella, François
last_name: Castella
- first_name: László
full_name: László Erdös
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Florian
full_name: Frommlet, Florian
last_name: Frommlet
- first_name: Peter
full_name: Markowich, Peter A
last_name: Markowich
citation:
ama: Castella F, Erdös L, Frommlet F, Markowich P. Fokker-Planck equations as scaling
limits of reversible quantum systems. *Journal of Statistical Physics*. 2000;100(3-4):543-601.
doi:10.1023/A:1018667323830
apa: Castella, F., Erdös, L., Frommlet, F., & Markowich, P. (2000). Fokker-Planck
equations as scaling limits of reversible quantum systems. *Journal of Statistical
Physics*. Springer. https://doi.org/10.1023/A:1018667323830
chicago: Castella, François, László Erdös, Florian Frommlet, and Peter Markowich.
“Fokker-Planck Equations as Scaling Limits of Reversible Quantum Systems.” *Journal
of Statistical Physics*. Springer, 2000. https://doi.org/10.1023/A:1018667323830.
ieee: F. Castella, L. Erdös, F. Frommlet, and P. Markowich, “Fokker-Planck equations
as scaling limits of reversible quantum systems,” *Journal of Statistical Physics*,
vol. 100, no. 3–4. Springer, pp. 543–601, 2000.
ista: Castella F, Erdös L, Frommlet F, Markowich P. 2000. Fokker-Planck equations
as scaling limits of reversible quantum systems. Journal of Statistical Physics.
100(3–4), 543–601.
mla: Castella, François, et al. “Fokker-Planck Equations as Scaling Limits of Reversible
Quantum Systems.” *Journal of Statistical Physics*, vol. 100, no. 3–4, Springer,
2000, pp. 543–601, doi:10.1023/A:1018667323830.
short: F. Castella, L. Erdös, F. Frommlet, P. Markowich, Journal of Statistical
Physics 100 (2000) 543–601.
date_created: 2018-12-11T11:59:18Z
date_published: 2000-01-01T00:00:00Z
date_updated: 2021-01-12T06:59:20Z
day: '01'
doi: 10.1023/A:1018667323830
extern: 1
intvolume: ' 100'
issue: 3-4
month: '01'
page: 543 - 601
publication: Journal of Statistical Physics
publication_status: published
publisher: Springer
publist_id: '4160'
quality_controlled: 0
status: public
title: Fokker-Planck equations as scaling limits of reversible quantum systems
type: journal_article
volume: 100
year: '2000'
...