Fokker-Planck equations as scaling limits of reversible quantum systems
Castella, François
László Erdös
Frommlet, Florian
Markowich, Peter A
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.
Springer
2000
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http://purl.org/coar/resource_type/c_6501
https://research-explorer.app.ist.ac.at/record/2732
Castella F, Erdös L, Frommlet F, Markowich P. Fokker-Planck equations as scaling limits of reversible quantum systems. <i>Journal of Statistical Physics</i>. 2000;100(3-4):543-601. doi:<a href="https://doi.org/10.1023/A:1018667323830">10.1023/A:1018667323830</a>
info:eu-repo/semantics/altIdentifier/doi/10.1023/A:1018667323830
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