Open Access
December 2007 On quantum hydrodynamic and quantum energy transport models
Pierre Degond, Samy Gallego, Florian Mehats
Commun. Math. Sci. 5(4): 887-908 (December 2007).


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.


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Pierre Degond. Samy Gallego. Florian Mehats. "On quantum hydrodynamic and quantum energy transport models." Commun. Math. Sci. 5 (4) 887 - 908, December 2007.


Published: December 2007
First available in Project Euclid: 3 January 2008

zbMATH: 1134.82016
MathSciNet: MR2375052

Primary: 81Q05 , 81S05 , 81S30 , 81V70 , 82C10 , 82C70 , 82D37

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

Rights: Copyright © 2007 International Press of Boston

Vol.5 • No. 4 • December 2007
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