A Note on quantum moment hydrodynamics and the entropy principle

Pierre Degond; Christian Ringhofer

doi:10.1016/S1631-073X(02)02595-5

A Note on quantum moment hydrodynamics and the entropy principle
[Une Note sur l'hydrodynamique des moments quantiques et le principe d'entropie]

Pierre Degond ¹ ; Christian Ringhofer ²

¹ MIP (UMR CNRS 5640), Université Paul Sabatier, 118, route de Narbonne, 31062 Toulouse cedex 4, France
² Department of Mathematics, Arizona State University, Tempe, AZ 85287-1804, USA

Comptes Rendus. Mathématique, Volume 335 (2002) no. 11, pp. 967-972.

Résumé
Abstract

Dans cette Note, nous montrons comment une version non-commutative du principe d'extremalisation de l'entropie permet de construire de nouveaux modèles hydrodynamiques quantiques.

In this Note, we show how a non-commutative version of the entropy extremalization principle allows one to construct new quantum hydrodynamic models.

Reçu le : 2002-06-03
Accepté le : 2002-10-16
Publié le : 2002-11-14

DOI : 10.1016/S1631-073X(02)02595-5

Affiliations des auteurs :

Pierre Degond ¹ ; Christian Ringhofer ²

¹ MIP (UMR CNRS 5640), Université Paul Sabatier, 118, route de Narbonne, 31062 Toulouse cedex 4, France
² Department of Mathematics, Arizona State University, Tempe, AZ 85287-1804, USA

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     title = {A {Note} on quantum moment hydrodynamics and the entropy principle},
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     doi = {10.1016/S1631-073X(02)02595-5},
     language = {en},
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Pierre Degond; Christian Ringhofer. A Note on quantum moment hydrodynamics and the entropy principle. Comptes Rendus. Mathématique, Volume 335 (2002) no. 11, pp. 967-972. doi : 10.1016/S1631-073X(02)02595-5. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02595-5/

Bibliographie
Cité par

[1] P. Degond, C. Ringhofer, Quantum moment hydrodynamics and the entropy principle, Manuscript

[2] D. Ferry; H. Grubin Modelling of quantum transport in semiconductor devices, Solid State Phys, Volume 49 (1995), pp. 283-448

[3] C. Gardner The quantum hydrodynamic model for semiconductor devices, SIAM J. Appl. Math, Volume 54 (1994), pp. 409-427

[4] C. Gardner; C. Ringhofer The smooth quantum potential for the hydrodynamic model, Phys. Rev. E, Volume 53 (1996), pp. 157-167

[5] C. Gardner; C. Ringhofer The Chapman–Enskog expansion and the quantum hydrodynamic model for semiconductor devices, VLSI Design, Volume 10 (2000), pp. 415-435

[6] I. Gasser; P. Markowich; C. Ringhofer Closure conditions for classical and quantum moment hierarchies in the small temperature limit, Transport Theory Statist. Phys, Volume 25 (1996), pp. 409-423

[7] H. Grubin; J. Krekovski Quantum moment balance equations and resonant tunneling structures, Solid State Electron, Volume 32 (1989), pp. 1071-1075

[8] C.D. Levermore Moment closure hierarchies for kinetic theories, J. Statist. Phys, Volume 83 (1996), pp. 1021-1065

[9] R. Luzzi (arXiv: v2 11 Sep 1999) | arXiv

[10] V.G. Morozov; G. Röpke Zubarev's method of a nonequilibrium statistical operator and some challenges in the theory of irreversible processes, Condensed Matter Phys, Volume 1 (1998), pp. 673-686

[11] I. Muller; T. Ruggeri Rational Extended Thermodynamics, Springer Tracts Nat. Philos, 37, Springer, 1998

[12] M.A. Shubin Pseudodifferential Operators and Spectral Theory, Springer, 1980

[13] D.N. Zubarev; V.G. Morozov; G. Röpke Statistical Mechanics of Nonequilibrium Processes, Vol. 1, Basic Concepts, Kinetic Theory, Akademie-Verlag, Berlin, 1996

Nicola Zamponi Some fluid-dynamic models for quantum electron transport in graphene via entropy minimization, Kinetic Related Models, Volume 5 (2012) no. 1, p. 203 | DOI:10.3934/krm.2012.5.203
Ansgar Jüngel Quantum Drift-Diffusion Equations, Transport Equations for Semiconductors, Volume 773 (2009), p. 1 | DOI:10.1007/978-3-540-89526-8_12
Cory D. Hauck; C. David Levermore; Andre L. Tits, 2008 47th IEEE Conference on Decision and Control (2008), p. 5092 | DOI:10.1109/cdc.2008.4739510
Pierre Degond; Samy Gallego; Florian Méhats; Christian Ringhofer Quantum Hydrodynamic and Diffusion Models Derived from the Entropy Principle, Quantum Transport, Volume 1946 (2008), p. 111 | DOI:10.1007/978-3-540-79574-2_3
Philippe Bechouche; Frédéric Poupaud; Juan Soler Quantum transport and Boltzmann operators, Journal of Statistical Physics, Volume 122 (2006) no. 3, pp. 417-436 | DOI:10.1007/s10955-005-8082-y | Zbl:1149.82338
Pierre Degond; Florian M�hats; Christian Ringhofer Quantum Energy-Transport and Drift-Diffusion Models, Journal of Statistical Physics, Volume 118 (2005) no. 3-4, p. 625 | DOI:10.1007/s10955-004-8823-3
Pierre Degond; Christian Ringhofer Binary quantum collision operators conserving mass momentum and energy., Comptes Rendus. Mathématique. Académie des Sciences, Paris, Volume 336 (2003) no. 9, pp. 785-790 | DOI:10.1016/s1631-073x(03)00185-7 | Zbl:1037.82030

Cité par 7 documents. Sources : Crossref, zbMATH

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