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F. Fagnola, L. Neumann:
"Quantum Fokker-Planck models: Limiting case in the Lindblad condition";
in: "ASC Report 14/2009", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2009, ISBN: 978-3-902627-02-5.

In this article we study stationary states and the long time asymptotics for the
quantum Fokker-Planck equation. We continue the investigation of an earlier
work in which we derived convergence to a steady state if the Lindblad condition
DppDqq −D2
pq
2/4 is satisfied with strict inequality. Here we extend
our results to the limiting case that turns out to be more difficult because irreducibility
of the quantum Markov semigroup does not follow from triviality
of the generalized commutator with position and momentum operators.

Quantum Markov Semigroups, Quantum Fokker Planck, steady

http://www.asc.tuwien.ac.at/preprint/2009/asc14x2009.pdf