Communications in Mathematical Sciences

Volume 5 (2007)

Number 4

On quantum hydrodynamic and quantum energy transport models

Pages: 887 – 908



Pierre Degond

Samy Gallego

Florian Mehats


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.


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

2010 Mathematics Subject Classification

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

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