[{"publication_status":"published","author":[{"full_name":"Castella, François","first_name":"François","last_name":"Castella"},{"first_name":"László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"László Erdös","orcid":"0000-0001-5366-9603"},{"full_name":"Frommlet, Florian","last_name":"Frommlet","first_name":"Florian"},{"last_name":"Markowich","first_name":"Peter","full_name":"Markowich, Peter A"}],"year":"2000","quality_controlled":0,"issue":"3-4","publisher":"Springer","intvolume":" 100","date_published":"2000-01-01T00:00:00Z","doi":"10.1023/A:1018667323830","status":"public","publication":"Journal of Statistical Physics","publist_id":"4160","citation":{"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","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.","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","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.","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.","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."},"extern":1,"volume":100,"title":"Fokker-Planck equations as scaling limits of reversible quantum systems","date_created":"2018-12-11T11:59:18Z","page":"543 - 601","type":"journal_article","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."}],"date_updated":"2021-01-12T06:59:20Z","month":"01","_id":"2732","day":"01"}]