Physics – Quantum Physics
Scientific paper
2002-04-15
J. Math. Phys. 43 (2002) 5446-5458
Physics
Quantum Physics
11 pages, latex, no figures, slight changes and a few references added, to appear in J. Math. Phys
Scientific paper
10.1063/1.1505126
Structures of quantum Fokker-Planck equations are characterized with respect to the properties of complete positivity, covariance under symmetry transformations and satisfaction of equipartition, referring to recent mathematical work on structures of unbounded generators of covariant quantum dynamical semigroups. In particular the quantum optical master-equation and the quantum Brownian motion master-equation are shown to be associated to $\mathrm{U(1)}$ and $\mathrm{R}$ symmetry respectively. Considering the motion of a Brownian particle, where the expression of the quantum Fokker-Planck equation is not completely fixed by the aforementioned requirements, a recently introduced microphysical kinetic model is briefly recalled, where a quantum generalization of the linear Boltzmann equation in the small energy and momentum transfer limit straightforwardly leads to quantum Brownian motion.
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