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

Degond, Pierre1 ; Ringhofer, Christian2
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, Tome 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
Degond, Pierre 1 ; Ringhofer, Christian 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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Degond, Pierre; Ringhofer, Christian. Binary quantum collision operators conserving mass momentum and energy. Comptes Rendus. Mathématique, Tome 336 (2003) no. 9, pp. 785-790. doi : 10.1016/S1631-073X(03)00185-7. https://www.numdam.org/articles/10.1016/S1631-073X(03)00185-7/

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

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

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

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

  • Guo, Zhao Existence and uniqueness of time periodic solutions for quantum versions of three-dimensional Schrödinger equations, Analysis and Mathematical Physics, Volume 12 (2022) no. 4 | DOI:10.1007/s13324-022-00710-9
  • Jüngel, Ansgar The Wigner Equation, Transport Equations for Semiconductors, Volume 773 (2009), p. 1 | DOI:10.1007/978-3-540-89526-8_11
  • Degond, Pierre; Gallego, Samy; Méhats, Florian An entropic quantum drift-diffusion model for electron transport in resonant tunneling diodes, Journal of Computational Physics, Volume 221 (2007) no. 1, p. 226 | DOI:10.1016/j.jcp.2006.06.027
  • Bourgade, J.-P.; Degond, P.; Méhats, F.; Ringhofer, C. On quantum extensions to classical spherical harmonics expansion/Fokker-Planck models, Journal of Mathematical Physics, Volume 47 (2006) no. 4 | DOI:10.1063/1.2192968
  • Bechouche, Philippe; Poupaud, Frédéric; Soler, Juan Quantum Transport and Boltzmann Operators, Journal of Statistical Physics, Volume 122 (2006) no. 3, p. 417 | DOI:10.1007/s10955-005-8082-y
  • Degond, Pierre; M�hats, Florian; Ringhofer, Christian 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
  • Gallego, Samy; Méhats, Florian Entropic Discretization of a Quantum Drift-Diffusion Model, SIAM Journal on Numerical Analysis, Volume 43 (2005) no. 5, p. 1828 | DOI:10.1137/040610556

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