An Analysis of Quantum Fokker-Planck Models: A Wigner Function Approach

@article{Arnold2004AnAO,
  title={An Analysis of Quantum Fokker-Planck Models: A Wigner Function Approach},
  author={Anton Arnold and Jos{\'e} Luis L{\'o}pez and Peter A. Markowich and Juan Soler},
  journal={Revista Matematica Iberoamericana},
  year={2004},
  volume={20},
  pages={771-814}
}
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… 
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