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.
Publié le : 2004-10-14
Classification:
Open quantum system,
Wigner equation,
large-time behavior,
self-similarity,
35Q40,
35S10,
81Q99,
81V99
@article{1098885435,
author = {Arnold, Anton and L\'opez, Jos\'e L. and Markowich, Peter A. and Soler, Juan},
title = {An analysis of quantum Fokker-Planck models: A Wigner function approach},
journal = {Rev. Mat. Iberoamericana},
volume = {20},
number = {1},
year = {2004},
pages = { 771-814},
language = {en},
url = {http://dml.mathdoc.fr/item/1098885435}
}
Arnold, Anton; López, José L.; Markowich, Peter A.; Soler, Juan. An analysis of quantum Fokker-Planck models: A Wigner function approach. Rev. Mat. Iberoamericana, Tome 20 (2004) no. 1, pp. 771-814. http://gdmltest.u-ga.fr/item/1098885435/