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Quantum Energy-Transport and Drift-Diffusion Models

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Abstract

We show that Quantum Energy-Transport and Quantum Drift-Diffusion models can be derived through diffusion limits of a collisional Wigner equation. The collision operator relaxes to an equilibrium defined through the entropy minimization principle. Both models are shown to be entropic and exhibit fluxes which are related with the state variables through spatially non-local relations. Thanks to an h expansion of these models, h2 perturbations of the Classical Energy-Transport and Drift-Diffusion models are found. In the Drift-Diffusion case, the quantum correction is the Bohm potential and the model is still entropic. In the Energy-Transport case however, the quantum correction is a rather complex expression and the model cannot be proven entropic.

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Authors and Affiliations

  1. MIP, Laboratoire CNRS (UMR 5640), Université Paul Sabatier, 118, route de Narbonne, 31062, Toulouse Cedex 04, France

    Pierre Degond & Florian Méhats

  2. Department of Mathematics, Arizona State University, Tempe, Arizona, 85284-184, USA

    Christian Ringhofer

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  1. Pierre Degond
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  2. Florian Méhats
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  3. Christian Ringhofer
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Correspondence to Pierre Degond.

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Degond, P., Méhats, F. & Ringhofer, C. Quantum Energy-Transport and Drift-Diffusion Models. J Stat Phys 118, 625–667 (2005). https://doi.org/10.1007/s10955-004-8823-3

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