Comptes Rendus
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]
Comptes Rendus. Mathématique, Volume 336 (2003) no. 9, pp. 785-790.

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

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.

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
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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

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  • Ansgar Jüngel The Wigner Equation, Transport Equations for Semiconductors, Volume 773 (2009), p. 1 | DOI:10.1007/978-3-540-89526-8_11
  • Pierre Degond; Samy Gallego; Florian Méhats An entropic quantum drift-diffusion model for electron transport in resonant tunneling diodes, Journal of Computational Physics, Volume 221 (2007) no. 1, pp. 226-249 | DOI:10.1016/j.jcp.2006.06.027 | Zbl:1107.82401
  • J.-P. Bourgade; P. Degond; F. Méhats; C. Ringhofer On quantum extensions to classical spherical harmonics expansion/Fokker-Planck models, Journal of Mathematical Physics, Volume 47 (2006) no. 4, p. 043302 | DOI:10.1063/1.2192968 | Zbl:1111.82028
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  • Samy Gallego; Florian Méhats Entropic Discretization of a Quantum Drift-Diffusion Model, SIAM Journal on Numerical Analysis, Volume 43 (2005) no. 5, p. 1828 | DOI:10.1137/040610556
  • Samy Gallego; Florian Méhats Numerical approximation of a quantum drift-diffusion model, Comptes Rendus. Mathématique. Académie des Sciences, Paris, Volume 339 (2004) no. 7, pp. 519-524 | DOI:10.1016/j.crma.2004.07.022 | Zbl:1058.65089

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