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An Analysis of Quantum FokkerPlanck Models: A Wigner Function Approach

Summary: An Analysis of Quantum Fokker­Planck Models:
A Wigner Function Approach
Anton Arnold,
Jos´e L. L´opez,
Peter A. Markowich,
and Juan Soler §
November 16, 2007
The analysis of dissipative transport equations within the framework
of open quantum systems with Fokker­Planck­type scattering is carried
out from the perspective of a Wigner function approach. In particular,
the well­posedness of the self­consistent whole­space problem in 3D is
analyzed: existence of solutions, uniqueness and asymptotic behavior in
time, where we adopt the viewpoint of mild solutions in this paper. Also,
the admissibility of a density matrix formulation in Lindblad form with
Fokker­Planck dissipation mechanisms is discussed. We remark that our
solution concept allows to carry out the analysis directly on the level of
the kinetic equation instead of on the level of the density operator.
AMS 1991 Subject classification: 35Q40, 35S10, 81Q99, 81V99
Key words: Open quantum system, Wigner equation, large­time behavior, self­


Source: Arnold, Anton - Institut für Analysis und Scientific Computing, Technische Universität Wien


Collections: Mathematics