Mécanique quantique sur le tore et dégénérescences dans le spectre
Séminaire de théorie spectrale et géométrie, Tome 11 (1992-1993), pp. 19-63. 
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     author = {Fr\'ed\'eric Faure},
     title = {M\'ecanique quantique sur le tore et d\'eg\'en\'erescences dans le spectre},
     journal = {S\'eminaire de th\'eorie spectrale et g\'eom\'etrie},
     pages = {19--63},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {11},
     year = {1992-1993},
     doi = {10.5802/tsg.130},
     zbl = {0979.81508},
     mrnumber = {1715942},
     language = {fr},
     url = {https://proceedings.centre-mersenne.org/articles/10.5802/tsg.130/}
}
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Frédéric Faure. Mécanique quantique sur le tore et dégénérescences dans le spectre. Séminaire de théorie spectrale et géométrie, Tome 11 (1992-1993), pp. 19-63. doi : 10.5802/tsg.130. https://proceedings.centre-mersenne.org/articles/10.5802/tsg.130/

[1] K.V. Klitzing. G. Dorda. M. Pepper. Phys. Rev. Lett. 45, 494 (1980). "New method for high-Accuracy Determination of the fine structure constant based on quantized Hall resistance".

[2] D.R. Hofstadter, "Energy levels and wave functions of Bloch electrons in rational and irrational magnetic fields" Phys. Rev. B 14, 6 , 2239 ( 1976).

[3] "L'avènement de la nano-électronique" La recherche 237, Nov. 1991, 1298.

[4] D. J. Thouless. M. Khomoto. M. P. Nightingale, and M. Den Nijs, Phys. Rev. Lett. 49, 405 ( 1982). "Quantized Hall conductance in a two-dimensional periodic potential".

[5] Y.S. Wu "Topological aspects of the quantum Hall effect" Proceedings at NATO Advanced Summer institute "Physics. Geometry and topology" at Banff. Alberta. Canada, August 14-25, 1989. | MR

[6] P. Lebœuf, J. Kurchan. M. Feingold and D. P. Arovas. Phys. Rev. Lett. 65, 3076 ( 1990): Chaos 2 125 ( 1992). "Phase-space localization: topological aspects of quantum chaos". | MR | Zbl

[7] D. P. Arovas, P. X. Bhatt. F. D. M. Haldane, P. B. Littlewood and R. Rammal, Phys. Rev. Lett. 60. 619 ( 1988). "Localization, Wave function topology, and the integer quantized Hall effect".

[8] M.V. Berry "Quantal phase factors accompanying adiabatic changes" Proc. Roy. Soc. Lond. 392, 45 ( 1984). | MR | Zbl

[9] A. M. Perelomov, "Generalized coherent states and their applications" (Springer. Berlin) 1986. | MR | Zbl

[10] M. Wilkinson. "Critical properties of electron eigenstates in incommensurate Systems" Proc. R. Soc. Lond. A 391, 305 ( 1984). | MR

[11] These de Armelle Barelli "Approche algébrique de la limite semi-classique. Electrons bidimensionels en champs magnétique et localisation dynamique". Université Paul Sabatier de Toulouse n° 1250.

[12]. W. M. Zhang. D. H. Feng and R. Gilmore, "Coherent states: theory and some applications" Rev. of Modem Phys. 62, 867 ( 1990). | MR

[13] J.R. Klauder and B.S. Skagerstam Coherent states. Applications in physics and mathematical physics, World Scientific ( 1984). | MR | Zbl

[14] P. Lebœuf and A. Voros "Chaos-revealing multiplicative representation of quantum eigenstates" J. Phys. A: Math. Gen. 23, 1765 ( 1990). | MR

[15] P. Leboeuf. A. Voros. "Quantum nodal points as fingerprints of classical chaos" Preprint. | MR

[16] A. Voros. P. Leboeuf. "Multiplicative formulation of quantum mechanics" Preprint Saclay Spht /91-179.

[17] A. Voros "Wentzel-Kramers-Brillovin method in the Bargmann representation" Phys. Rev. A 40. 6814 ( 1989). | MR

[18] J. Kurchan. P. Leboeuf. M. Saraceno "Semiclassical approximation in the coherent state representation" Phys. Rev. A 40, 6800 ( 1989). | MR

[19] T. Paul, A. Uribe " A construction of quasi-modes using coherent states" to appear in Ann. Inst. H. Poincaré, Phys. théor. | Numdam | MR | Zbl

[20] M. Nakahara, "Geometry. topologyand physics", graduate students series in physics, Adam Hilger, Bristol and N.Y. | MR | Zbl

[21] J. W. Milnor "Characteristic classes" Princeton university press 1974. | MR | Zbl

[22] Exposé de Yves Colin de Verdière "Fibrés en droites et valeurs propes multiples" à l'institut Fourier de Grenoble.le 17 déc. 1993.

[23] "Geometrie phases in physics" A. Shapere and F. Wilczek Advanced Series in Math. Physics Vol. 5.

[24] B. Simon, "Holonomy, the quantum adiabatic theorem and Berry's phase" Phys. Rev. Lett. 51, 2167 ( 1983). | MR

[25] M. V. Berry, X. L. Balazs, M. Tabor, A. Voros. "Quantum maps" Ann. of Phys. (N.Y.) 122 . 26, ( 1979). | MR

[26] P. Lebœuf "Phase space approach to quantum dynamics" J. Phys. A: Math. Gen. 24. 4575 ( 1991). | MR

[27] E. Bogomohiy, O. Bohigas, P. Leboeuf, "Distribution of roots of random polynomials" Phys. Rev. Lett. 68, 2726 ( 1992). | MR | Zbl

[28] "Chaos and Quantum Physics", edited by M.J. Giannoni, A. Voros, and J. Zinn-Justin, Les Houches Session LU, 1989 (Elsevier, Amsterdam, 1991). | MR

[29] Yves Colin De Verdiere, Comm. Math. Phys., 102, 497 ( 1985). | MR | Zbl

[30] R. Aurich and F. Steiner "Quantum eigenstates of a strongly chaotic System and the scar phenomenom" Preprint desy 93-057 ( 1993). | MR | Zbl

[31] B. Parisse and Y. Colin De Verdiere. Preprint.

[32] F. Bensch. H. J. Korsch, B. Mirbach, V. Ben-Tal "E.B.K. quantization of quasi-energies" J. Phys. A: Math. Gen. 25, 6761, ( 1992). | Zbl

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