Revista Matemática Iberoamericana

An analysis of quantum Fokker-Planck models: A Wigner function approach

Anton Arnold, José L. López, Peter A. Markowich, and Juan Soler

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The analysis of dissipative transport equations within the framework of open quantum systems with Fokker-Planck-type scattering is carried out from the perspective of a Wigner function approach. In particular, the well-posedness of the self-consistent whole-space 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 Fokker-Planck 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.

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Rev. Mat. Iberoamericana, Volume 20, Number 3 (2004), 771-814.

First available in Project Euclid: 27 October 2004

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Primary: 35Q40: PDEs in connection with quantum mechanics 35S10: Initial value problems for pseudodifferential operators 81Q99: None of the above, but in this section 81V99: None of the above, but in this section

Open quantum system Wigner equation large-time behavior self-similarity


Arnold, Anton; López, José L.; Markowich, Peter A.; Soler, Juan. An analysis of quantum Fokker-Planck models: A Wigner function approach. Rev. Mat. Iberoamericana 20 (2004), no. 3, 771--814.

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