On quantum hydrodynamic and quantum energy transport models
Abstract
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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