--- res: bibo_abstract: - '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.@eng' bibo_authorlist: - foaf_Person: foaf_givenName: François foaf_name: Castella, François foaf_surname: Castella - foaf_Person: foaf_givenName: László foaf_name: Erdös, László foaf_surname: Erdös foaf_workInfoHomepage: http://www.librecat.org/personId=4DBD5372-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0001-5366-9603 - foaf_Person: foaf_givenName: Florian foaf_name: Frommlet, Florian foaf_surname: Frommlet - foaf_Person: foaf_givenName: Peter foaf_name: Markowich, Peter foaf_surname: Markowich bibo_doi: 10.1023/A:1018667323830 bibo_issue: 3-4 bibo_volume: 100 dct_date: 2000^xs_gYear dct_isPartOf: - http://id.crossref.org/issn/0022-4715 dct_language: eng dct_publisher: Springer@ dct_title: Fokker-Planck equations as scaling limits of reversible quantum systems@ ...