Wigner series and (semi)classical limits with periodic potentials
Journées équations aux dérivées partielles (1993), article no. 16, 13 p.
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     title = {Wigner series and (semi)classical limits with periodic potentials},
     booktitle = {},
     series = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     eid = {16},
     pages = {1--13},
     publisher = {Ecole polytechnique},
     year = {1993},
     mrnumber = {94i:82021},
     zbl = {0807.35139},
     language = {en},
     url = {http://archive.numdam.org/item/JEDP_1993____A16_0/}
}
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Markowich, Peter A.; Mauser, Norbert J.; Poupaud, Frédéric. Wigner series and (semi)classical limits with periodic potentials. Journées équations aux dérivées partielles (1993), article  no. 16, 13 p. http://archive.numdam.org/item/JEDP_1993____A16_0/

[1] N.W. Ashcroft and N.D. Mermin. Solid State Physics. Holt, Rinehart, Winston, 1976.

[2] N.L. Balazs and B.K. Jennings. Wigner and Other Distribution Functions in Mock Phase Spaces. Phys. Rep., 104:347-391, 1984. | MR

[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] B. Helffer and T. Sjostrand. Microlocal Analysis ... Springer Lecture Notes in Physics 345, 1989.

[5] P. Kasperkovitz and M. Peev. Wigner-Weyl Formalisms for Toroidal Geometries. Technical report, TU Vienna, 1993.

[6] P.L. Lions and T. Paul. Sur les Mesures de Wigner. Revista Mat. Iberoamericana, to appear, 1993. | MR | Zbl

[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. | MR | Zbl

[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. | Zbl

[9] N.J. Mauser. The Wigner-Poisson Problem in the One-Band Approximation. in preparation, 1993.

[10] P. Gerard. Mesures Semi-Classiques et Ondes de Bloch. Sem. Ecole Polytechnique, XVI, 1991. | Numdam | MR | Zbl

[11] M. Reed and B. Simon. Methods of Modern Mathematical Physics IV. Academic Press, 4th edition, 1987.

[12] K. Takahashi. Distribution Functions in Classical and Quantum Mechanics. Prog. of Theor. Phys. Suppl., 98:109-156, 1989. | MR

[13] V.I. Tatarskii. The Wigner Representation of Quantum Mechanics. Sov. Phys. Usb., 26:311-327, 1983. | MR

[14] C.H. Wilcox. Theory of Bloch Waves. J. d'Analyse Mathematique, 33:146 - 167, 1978. | MR | Zbl