---
_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.'
acknowledgement: The authors are indebted to H. Spohn for discussions. F.C. and L.E.
were partially supported by the Erwin Schrödinger Institute in Vienna (Austria)
during their visit, and they thank this institution for its hospitality. This work
was supported by the TMR-Network ``Asymptotic Methods in Kinetic Theory'' number
ERB FMBX CT97 0157 (F.C., F.F., and P.A.M.) and by NSF Grant DMS-9970323 (L.E.).
article_processing_charge: No
article_type: original
author:
- first_name: François
full_name: Castella, François
last_name: Castella
- first_name: László
full_name: Erdös, László
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
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: 2023-05-03T09:02:11Z
day: '01'
doi: 10.1023/A:1018667323830
extern: '1'
intvolume: ' 100'
issue: 3-4
language:
- iso: eng
month: '01'
oa_version: None
page: 543 - 601
publication: Journal of Statistical Physics
publication_identifier:
issn:
- 0022-4715
publication_status: published
publisher: Springer
publist_id: '4160'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Fokker-Planck equations as scaling limits of reversible quantum systems
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 100
year: '2000'
...