In this paper, we consider two recently derived models: the Quantum Hydrodynamic
model (QHD) and the Quantum Energy Transport model (QET). We propose different equivalent
formulations of these models and we use a commutator formula for stating new properties of the models.
A gauge invariance lemma permits to simplify the QHD model for irrotational flows. We finish by
considering the special case of a slowly varying temperature and we discuss possible approximations
which will be helpful for future numerical discretizations.
Publié le : 2007-12-15
Classification:
density operator,
quantum Liouville equation,
quantum entropy,
quantum local equilibrium,
quantum hydrodynamics,
quantum energy transport,
commutators,
gauge invariance,
82C10,
82C70,
82D37,
81Q05,
81S05,
81S30,
81V70
@article{1199377556,
author = {Degond, Pierre and Gallego, Samy and Mehats, Florian},
title = {On quantum hydrodynamic and quantum energy transport models},
journal = {Commun. Math. Sci.},
volume = {5},
number = {1},
year = {2007},
pages = { 887-908},
language = {en},
url = {http://dml.mathdoc.fr/item/1199377556}
}
Degond, Pierre; Gallego, Samy; Mehats, Florian. On quantum hydrodynamic and quantum energy transport models. Commun. Math. Sci., Tome 5 (2007) no. 1, pp. 887-908. http://gdmltest.u-ga.fr/item/1199377556/