On quantum hydrodynamic and quantum energy transport models

Pierre Degond (1) , Samy Gallego (1) , Florian Méhats (2)

1 MIP - Mathématiques pour l'Industrie et la Physique
2 IRMAR - Institut de Recherche Mathématique de Rennes

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

Keywords: density operator; quantum Liouville equation; quantum entropy; quantum local equilibrium; quantum hydrodynamics; quantum energy transport; commutators; gauge invariance

Domains: Numerical Analysis [math.NA]

Pierre Degond, Samy Gallego, Florian Méhats. On quantum hydrodynamic and quantum energy transport models. Communications in Mathematical Sciences, 2007, 5 (4), pp.887-908. ⟨hal-00368759⟩