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

Arnold, Anton, et al. "An analysis of quantum Fokker-Planck models: a Wigner function approach.." Revista Matemática Iberoamericana 20.3 (2004): 771-814. <http://eudml.org/doc/39732>.

@article{Arnold2004,
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.},
author = {Arnold, Anton, López, José L., Markowich, Peter A., Soler, Juan},
journal = {Revista Matemática Iberoamericana},
keywords = {Ecuación de Fokker-Planck; Transformada de Wigner; Wigner-Poisson-Fokker-Planck system; local-in-time solutions; uniqueness; stability; large-time behavior},
language = {eng},
number = {3},
pages = {771-814},
title = {An analysis of quantum Fokker-Planck models: a Wigner function approach.},
url = {http://eudml.org/doc/39732},
volume = {20},
year = {2004},
}

TY - JOUR
AU - Arnold, Anton
AU - López, José L.
AU - Markowich, Peter A.
AU - Soler, Juan
TI - An analysis of quantum Fokker-Planck models: a Wigner function approach.
JO - Revista Matemática Iberoamericana
PY - 2004
VL - 20
IS - 3
SP - 771
EP - 814
AB - 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.
LA - eng
KW - Ecuación de Fokker-Planck; Transformada de Wigner; Wigner-Poisson-Fokker-Planck system; local-in-time solutions; uniqueness; stability; large-time behavior
UR - http://eudml.org/doc/39732
ER -