@article{2732,
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.},
author = {Castella, François and László Erdös and Frommlet, Florian and Markowich, Peter A},
journal = {Journal of Statistical Physics},
number = {3-4},
pages = {543 -- 601},
publisher = {Springer},
title = {{Fokker-Planck equations as scaling limits of reversible quantum systems}},
doi = {10.1023/A:1018667323830},
volume = {100},
year = {2000},
}