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Quantum Hydrodynamic and Diffusion Models Derived from the Entropy Principle

  • Pierre Degond
  • Samy Gallego
  • Florian Méhats
  • Christian Ringhofer
Part of the Lecture Notes in Mathematics book series (LNM, 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.

Keywords

Density Operator Collision Operator Entropy Minimization Pressure Tensor Weyl Quantization 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Pierre Degond
    • 1
  • Samy Gallego
    • 1
  • Florian Méhats
    • 2
  • Christian Ringhofer
    • 3
  1. 1.Institut de MathématiquesUniversité de ToulouseToulouse Cedex 9France
  2. 2.IRMAR (UMR CNRS 6625)Université de RennesRennes CedexFrance
  3. 3.Department of MathematicsArizona State UniversityTempeUSA

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