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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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.

Article information

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

Dates
First available in Project Euclid: 27 October 2004

Permanent link to this document
https://projecteuclid.org/euclid.rmi/1098885435

Mathematical Reviews number (MathSciNet)
MR2124489

Zentralblatt MATH identifier
1062.35097

Subjects
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

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

Citation

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. https://projecteuclid.org/euclid.rmi/1098885435


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