TY - JOUR
AB - 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.
AU - Castella, François
AU - László Erdös
AU - Frommlet, Florian
AU - Markowich, Peter A
ID - 2732
IS - 3-4
JF - Journal of Statistical Physics
TI - Fokker-Planck equations as scaling limits of reversible quantum systems
VL - 100
ER -