--- _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' ...