Wigner series and (semi)classical limits with periodic potentials

Peter A. Markowich; Norbert J. Mauser; Frédéric Poupaud

Journées équations aux dérivées partielles (1993)

  • Volume: 1993, Issue: 16, page 1-13
  • ISSN: 0752-0360

How to cite

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Markowich, Peter A., Mauser, Norbert J., and Poupaud, Frédéric. "Wigner series and (semi)classical limits with periodic potentials." Journées équations aux dérivées partielles 1993.16 (1993): 1-13. <http://eudml.org/doc/93267>.

@article{Markowich1993,
author = {Markowich, Peter A., Mauser, Norbert J., Poupaud, Frédéric},
journal = {Journées équations aux dérivées partielles},
keywords = {Wigner-Weyl transform; Vlasov equation; semiconductor device modelling; semiclassical Liouville equation},
language = {eng},
number = {16},
pages = {1-13},
publisher = {Ecole polytechnique},
title = {Wigner series and (semi)classical limits with periodic potentials},
url = {http://eudml.org/doc/93267},
volume = {1993},
year = {1993},
}

TY - JOUR
AU - Markowich, Peter A.
AU - Mauser, Norbert J.
AU - Poupaud, Frédéric
TI - Wigner series and (semi)classical limits with periodic potentials
JO - Journées équations aux dérivées partielles
PY - 1993
PB - Ecole polytechnique
VL - 1993
IS - 16
SP - 1
EP - 13
LA - eng
KW - Wigner-Weyl transform; Vlasov equation; semiconductor device modelling; semiclassical Liouville equation
UR - http://eudml.org/doc/93267
ER -

References

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  1. [1] N.W. ASHCROFT and N.D. MERMIN. Solid State Physics. Holt, Rinehart, Winston, 1976. Zbl1107.82300
  2. [2] N.L. BALAZS and B.K. JENNINGS. Wigner and Other Distribution Functions in Mock Phase Spaces. Phys. Rep., 104:347-391, 1984. MR85k:81052
  3. [3] S. BIEVRE and J.A. GONZALEZ. Semiclassical Behaviour of the Weyl Correspondence on the Circle. Proc. XIX Int. Col. Group Theor. Meth. - Salamanca, Anales di Fisica, 1992. 
  4. [4] B. HELFFER and T. SJOSTRAND. Microlocal Analysis ... Springer Lecture Notes in Physics 345, 1989. 
  5. [5] P. KASPERKOVITZ and M. PEEV. Wigner-Weyl Formalisms for Toroidal Geometries. Technical report, TU Vienna, 1993. Zbl0794.46056
  6. [6] P.L. LIONS and T. PAUL. Sur les Mesures de Wigner. Revista Mat. Iberoamericana, to appear, 1993. Zbl0801.35117MR95a:58124
  7. [7] P.A. MARKOWICH and N.J. MAUSER. The Classical Limit of a Self-consistent Quantum-Vlasov Equation in 3-D. Math. Mod. and Meth. in Appl. Sciences, 3:109-124, 1993. Zbl0772.35061MR94e:82065
  8. [8] P.A. MARKOWICH, N.J. MAUSER, and F. POUPAUD. A Wigner Function Approach to (Semi) classical Limits : Electrons in a Periodic Potential. submitted to J. on Math. Phys. Zbl0805.35106
  9. [9] N.J. MAUSER. The Wigner-Poisson Problem in the One-Band Approximation. in preparation, 1993. 
  10. [10] P. GERARD. Mesures Semi-Classiques et Ondes de Bloch. Sem. Ecole Polytechnique, XVI, 1991. Zbl0739.35096MR92k:35068
  11. [11] M. REED and B. SIMON. Methods of Modern Mathematical Physics IV. Academic Press, 4th edition, 1987. Zbl0401.47001
  12. [12] K. TAKAHASHI. Distribution Functions in Classical and Quantum Mechanics. Prog. of Theor. Phys. Suppl., 98:109-156, 1989. MR91a:81051
  13. [13] V.I. TATARSKII. The Wigner Representation of Quantum Mechanics. Sov. Phys. Usb., 26:311-327, 1983. MR85k:81061
  14. [14] C.H. WILCOX. Theory of Bloch Waves. J. d'Analyse Mathematique, 33:146 - 167, 1978. Zbl0408.35067MR82b:82068

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