A quantum-transport model for semiconductors : the Wigner-Poisson problem on a bounded Brillouin zone

Pierre Degond; Peter A. Markowich

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1990)

  • Volume: 24, Issue: 6, page 697-709
  • ISSN: 0764-583X

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Degond, Pierre, and Markowich, Peter A.. "A quantum-transport model for semiconductors : the Wigner-Poisson problem on a bounded Brillouin zone." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 24.6 (1990): 697-709. <http://eudml.org/doc/193612>.

@article{Degond1990,
author = {Degond, Pierre, Markowich, Peter A.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {quantum Liouville equation; transport of electrons in semiconductors; semiconductor crystal lattice; self-consistent potential; Poisson equation; global existence; uniqueness},
language = {eng},
number = {6},
pages = {697-709},
publisher = {Dunod},
title = {A quantum-transport model for semiconductors : the Wigner-Poisson problem on a bounded Brillouin zone},
url = {http://eudml.org/doc/193612},
volume = {24},
year = {1990},
}

TY - JOUR
AU - Degond, Pierre
AU - Markowich, Peter A.
TI - A quantum-transport model for semiconductors : the Wigner-Poisson problem on a bounded Brillouin zone
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1990
PB - Dunod
VL - 24
IS - 6
SP - 697
EP - 709
LA - eng
KW - quantum Liouville equation; transport of electrons in semiconductors; semiconductor crystal lattice; self-consistent potential; Poisson equation; global existence; uniqueness
UR - http://eudml.org/doc/193612
ER -

References

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  2. [2] R. DAUTRAY and J. L. LIONS, Analyse Mathématique et Calcul Numérique pour les Sciences et les Techniques. Tome 3, Masson, Paris, 1985. Zbl0642.35001MR902802
  3. [3] F. GOLSE, P. L. LIONS, B. PERTHAME and R. SENTIS, Regularity of the Moments of the Solution of a Transport Equation. J. Funct. Anal. 88, pp. 110-125, 1988. Zbl0652.47031MR923047
  4. [4] J. C. GUILLOT, J. RALSTON and E. TRUBOWITZ, Semi-Classical Asymptotics in Solid State Physics. Communications in Math. Phys., vol. 116, n°3, pp. 401-415, 1988. Zbl0672.35014MR937768
  5. [5] C. KITTEL, Introduction to Solid States Physics, J. Wiley and Sons, New York, 1968. Zbl0052.45506
  6. [6] P. A. MARKOWICH and C. RINGHOFER, An Analysis of the Quantum Liouville Equation. To appear in ZAMM, 1988. Zbl0682.46047MR990011
  7. [7] P. A. MARKOWICH, On the Equivalence of the Schrödinger and the Quantum Liouville Equations. To appear in Math. Meth. In the Appl. Sci., 1988. Zbl0696.47042MR1001097
  8. [8] A. PAZY, Semigroups of Linear Operators and Applications to Partial Differential Equations. Springer Verlag, New York-Berlin-Heidelberg-Tokyo, 1983. Zbl0516.47023MR710486
  9. [9] V. I. TATARSKII, The Wigner Representation of Quantum Mechanics. Sov. Phys. Usp., vol. 26, n°4, pp. 311-327, 1983. MR730012
  10. [10] A. ARNOLD, P. DEGOND, P. A. MARKOWICH and H. STEINRÜCK, The Wigner-Poisson Equation in a Crystal, to appear in : Applied Mathematics Letters, 1989. Zbl0822.58070MR1003856
  11. [11] P. DEGOND, P. A. MARKOWICH and H. STEINRÜCK, A Mathematical Derivation of the Wigner-Poisson Problem on a bounded Brillouin Zone from the Schrödinger Equation, manuscript. 

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