Quantum hydrodynamic and diffusion models derived from the entropy principle

Pierre Degond, Samy Gallego, Florian Méhats, Christian Ringhofer

Research output: Chapter in Book/Report/Conference proceedingChapter

10 Scopus citations

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.

Original languageEnglish (US)
Title of host publicationQuantum Transport
Subtitle of host publicationModelling, Analysis and Asymptotics - Lectures given at the C.I.M.E. Summer School
PublisherSpringer Verlag
Pages111-168
Number of pages58
ISBN (Print)9783540795735
DOIs
StatePublished - Jan 1 2008

Publication series

NameLecture Notes in Mathematics
Volume1946
ISSN (Print)0075-8434

ASJC Scopus subject areas

  • Algebra and Number Theory

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    Degond, P., Gallego, S., Méhats, F., & Ringhofer, C. (2008). Quantum hydrodynamic and diffusion models derived from the entropy principle. In Quantum Transport: Modelling, Analysis and Asymptotics - Lectures given at the C.I.M.E. Summer School (pp. 111-168). (Lecture Notes in Mathematics; Vol. 1946). Springer Verlag. https://doi.org/10.1007/978-3-540-79574-2_3