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

9 Citations (Scopus)

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 publicationLecture Notes in Mathematics
Pages111-168
Number of pages58
Volume1946
DOIs
StatePublished - 2008

Publication series

NameLecture Notes in Mathematics
Volume1946
ISSN (Print)00758434

Fingerprint

Quantum Hydrodynamics
Hydrodynamic Model
Diffusion Model
Entropy
Wigner Equation
Quantum Entropy
Moment
Quantum Transport
Minimizer
System of equations
Numerical Simulation
Model
Review
Framework

ASJC Scopus subject areas

  • Mathematics (miscellaneous)

Cite this

Degond, P., Gallego, S., Méhats, F., & Ringhofer, C. (2008). Quantum hydrodynamic and diffusion models derived from the entropy principle. In Lecture Notes in Mathematics (Vol. 1946, pp. 111-168). (Lecture Notes in Mathematics; Vol. 1946). https://doi.org/10.1007/978-3-540-79574-2_3

Quantum hydrodynamic and diffusion models derived from the entropy principle. / Degond, Pierre; Gallego, Samy; Méhats, Florian; Ringhofer, Christian.

Lecture Notes in Mathematics. Vol. 1946 2008. p. 111-168 (Lecture Notes in Mathematics; Vol. 1946).

Research output: Chapter in Book/Report/Conference proceedingChapter

Degond, P, Gallego, S, Méhats, F & Ringhofer, C 2008, Quantum hydrodynamic and diffusion models derived from the entropy principle. in Lecture Notes in Mathematics. vol. 1946, Lecture Notes in Mathematics, vol. 1946, pp. 111-168. https://doi.org/10.1007/978-3-540-79574-2_3
Degond P, Gallego S, Méhats F, Ringhofer C. Quantum hydrodynamic and diffusion models derived from the entropy principle. In Lecture Notes in Mathematics. Vol. 1946. 2008. p. 111-168. (Lecture Notes in Mathematics). https://doi.org/10.1007/978-3-540-79574-2_3
Degond, Pierre ; Gallego, Samy ; Méhats, Florian ; Ringhofer, Christian. / Quantum hydrodynamic and diffusion models derived from the entropy principle. Lecture Notes in Mathematics. Vol. 1946 2008. pp. 111-168 (Lecture Notes in Mathematics).
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