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Quantum Hydrodynamic and Diffusion Models Derived from the Entropy Principle

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Quantum Transport

Part of the book series: Lecture Notes in Mathematics ((LNMCIME,volume 1946))

Abstract

In these notes, we review the recent theory of quantum hydrodynamic and diffusion models derived from the entropy minimization principle. These models are obtained by taking the moments of a collisional Wigner equation and closing the resulting system of equations by a quantum equilibrium. Such an equilibrium is defined as a minimizer of the quantum entropy subject to local constraints of given moments. We provide a framework to develop this minimization approach and successively apply it to quantum hydrodynamic models and quantum diffusion models. The results of numerical simulations show that these models capture well the various features of quantum transport.

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Author information

Authors and Affiliations

  1. Institut de Mathématiques, Université de Toulouse, 118 route de Narbonne, 31062, Toulouse Cedex 9, France

    Pierre Degond & Samy Gallego

  2. IRMAR (UMR CNRS 6625), Université de Rennes, Campus de Beaulieu, 35042, Rennes Cedex, France

    Florian Méhats

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

    Christian Ringhofer

Authors
  1. Pierre Degond
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  2. Samy Gallego
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  3. Florian Méhats
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  4. Christian Ringhofer
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Editors and Affiliations

  1. Institut de Mathématiques, Université de Toulouse, 118 route de Narbonne, 31062, Toulouse Cedex 9, France

    Naoufel Ben Abdallah

  2. Dipartimento di Matematica Applicata, Università di Firenze, Via S.Marta 3, 50139, Firenze, Italy

    Giovanni Frosali

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Degond, P., Gallego, S., Méhats, F., Ringhofer, C. (2008). Quantum Hydrodynamic and Diffusion Models Derived from the Entropy Principle. In: Abdallah, N.B., Frosali, G. (eds) Quantum Transport. Lecture Notes in Mathematics, vol 1946. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79574-2_3

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