On quantum hydrodynamic and quantum energy transport models

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

2010 Mathematics Subject Classification

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

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Published 1 January 2007