Comptes Rendus
no. 9
Mathematical Problems in Mechanics/Mathematical Physics
Binary quantum collision operators conserving mass momentum and energy
[Opérateurs de collisions quantiques conservant la masse, l'impulsion et l'énergie]

Présenté par : Philippe G. Ciarlet

Pierre Degond1 ; Christian Ringhofer2
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 336 (2003) no. 9, pp. 785-790.

Dans cette Note, nous généralisons l'opérateur de collision de Boltzmann modélisant les collisions binaires particule–particule au cadre quantique, en utilisant un principe non-local de minimisation d'entropie quantique.

In this Note, we generalize the Boltzmann collision operator modeling binary particle–particle collisions to a quantum framework using nonlocal quantum entropy principles.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(03)00185-7
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 
@article{CRMATH_2003__336_9_785_0,
     author = {Pierre Degond and Christian Ringhofer},
     title = {Binary quantum collision operators conserving mass momentum and energy},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {785--790},
     publisher = {Elsevier},
     volume = {336},
     number = {9},
     year = {2003},
     doi = {10.1016/S1631-073X(03)00185-7},
     language = {en},
}
TY  - JOUR
AU  - Pierre Degond
AU  - Christian Ringhofer
TI  - Binary quantum collision operators conserving mass momentum and energy
JO  - Comptes Rendus. Mathématique
PY  - 2003
SP  - 785
EP  - 790
VL  - 336
IS  - 9
PB  - Elsevier
DO  - 10.1016/S1631-073X(03)00185-7
LA  - en
ID  - CRMATH_2003__336_9_785_0
ER  - 
%0 Journal Article
%A Pierre Degond
%A Christian Ringhofer
%T Binary quantum collision operators conserving mass momentum and energy
%J Comptes Rendus. Mathématique
%D 2003
%P 785-790
%V 336
%N 9
%I Elsevier
%R 10.1016/S1631-073X(03)00185-7
%G en
%F CRMATH_2003__336_9_785_0
Pierre Degond; Christian Ringhofer. Binary quantum collision operators conserving mass momentum and energy. Comptes Rendus. Mathématique, Volume 336 (2003) no. 9, pp. 785-790. doi : 10.1016/S1631-073X(03)00185-7. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(03)00185-7/

[1] P. Argyres Quantum kinetic equations for electrons in high electric and phonon fields, Phys. Lett. A, Volume 171 (1992)

[2] A. Arnold, J. Lopez, P. Markowich, J. Soler, An analysis of quantum Fokker–Planck models: A Wigner function approach, Preprint, 2002

[3] J. Barker; D. Ferry Self-scattering path-variable formulation of high-field, time-dependent, quantum kinetic equations for semiconductor transport in the finite collision–duration regime, Phys. Rev. Lett., Volume 42 (1997)

[4] C. Cercignani The Boltzmann Equation and Its Applications, Appl. Math. Sci., 67, Springer-Verlag, 1988

[5] P. Degond, C. Ringhofer, Quantum moment hydrodynamics and the entropy principle, J. Stat. Phys. (2002), submitted. Preprint available at URL: http://math.la.asu.edu/.~chris

[6] P. Degond; C. Ringhofer A note on quantum moment hydrodynamics and the entropy principle, C. R. Acad. Sci. Paris, Ser. 1, Volume 335 (2002), pp. 967-972

[7] F. Fromlet; P. Markowich; C. Ringhofer A Wignerfunction approach to phonon scattering, VLSI Design, Volume 9 (1999), pp. 339-350

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

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

Cité par Sources :

Commentaires - Politique

Ces articles pourraient vous intéresser

A Note on quantum moment hydrodynamics and the entropy principle

Pierre Degond; Christian Ringhofer

C. R. Math (2002)

Numerical approximation of a quantum drift-diffusion model

Samy Gallego; Florian Méhats

C. R. Math (2004)

Sur l'existence des opérateurs d'onde pour l'équation de Wigner dans les espaces L2,p

Hassan Emamirad; Philippe Rogeon

C. R. Math (2002)