JournalsrmiVol. 20, No. 3pp. 771–814

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

  • Anton Arnold

    Technische Universität Wien, Austria
  • José L. López

    Universidad de Granada, Spain
  • Peter A. Markowich

    Universität Wien, Austria
  • Juan Soler

    Universidad de Granada, Spain
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Abstract

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.

Cite this article

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

DOI 10.4171/RMI/407