Mécanique quantique sur le tore et dégénérescences dans le spectre

 Access to full text

 Full (PDF)

1. [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. [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. [3] "L'avènement de la nano-électronique" La recherche 237, Nov. 1991, 1298. 
4. [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. [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. MR1153686
6. [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". Zbl1050.81538MR1082114
7. [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. [8] M.V. Berry"Quantal phase factors accompanying adiabatic changes" Proc. Roy. Soc. Lond. 392, 45 ( 1984). Zbl1113.81306MR738926
9. [9] A. M. Perelomov, "Generalized coherent states and their applications" (Springer. Berlin) 1986. Zbl0605.22013MR858831
10. [10] M. Wilkinson. "Critical properties of electron eigenstates in incommensurate Systems" Proc. R. Soc. Lond. A 391, 305 ( 1984). MR739684
11. [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. [12]. W. M. Zhang. D. H. Feng and R. Gilmore, "Coherent states: theory and some applications" Rev. of Modem Phys. 62, 867 ( 1990). MR1102385
13. [13] J.R. Klauder and B.S. SkagerstamCoherent states. Applications in physics and mathematical physics, World Scientific ( 1984). Zbl1050.81558MR826247
14. [14] P. Lebœuf and A. Voros"Chaos-revealing multiplicative representation of quantum eigenstates" J. Phys. A: Math. Gen. 23, 1765 ( 1990). MR1063405
15. [15] P. Leboeuf. A. Voros. "Quantum nodal points as fingerprints of classical chaos" Preprint. Zbl0832.35120MR1341144
16. [16] A. Voros. P. Leboeuf. "Multiplicative formulation of quantum mechanics" Preprint Saclay Spht /91-179. Zbl0832.35120
17. [17] A. Voros"Wentzel-Kramers-Brillovin method in the Bargmann representation" Phys. Rev. A 40. 6814 ( 1989). MR1031937
18. [18] J. Kurchan. P. Leboeuf. M. Saraceno"Semiclassical approximation in the coherent state representation" Phys. Rev. A 40, 6800 ( 1989). MR1031936
19. [19] T. Paul, A. Uribe" A construction of quasi-modes using coherent states" to appear in Ann. Inst. H. Poincaré, Phys. théor. Zbl0808.35118MR1254977
20. [20] M. Nakahara, "Geometry. topologyand physics", graduate students series in physics, Adam Hilger, Bristol and N.Y. Zbl0764.53001MR1065614
21. [21] J. W. Milnor"Characteristic classes" Princeton university press 1974. Zbl0298.57008MR440554
22. [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. [23] "Geometrie phases in physics" A. Shapere and F. Wilczek Advanced Series in Math. Physics Vol. 5. 
24. [24] B. Simon, "Holonomy, the quantum adiabatic theorem and Berry's phase" Phys. Rev. Lett. 51, 2167 ( 1983). MR726866
25. [25] M. V. Berry, X. L. Balazs, M. Tabor, A. Voros. "Quantum maps" Ann. of Phys. (N.Y.) 122 . 26, ( 1979). MR550311
26. [26] P. Lebœuf"Phase space approach to quantum dynamics" J. Phys. A: Math. Gen. 24. 4575 ( 1991). MR1132334
27. [27] E. Bogomohiy, O. Bohigas, P. Leboeuf, "Distribution of roots of random polynomials" Phys. Rev. Lett. 68, 2726 ( 1992). Zbl0969.81540MR1160289
28. [28] "Chaos and Quantum Physics", edited by M.J. Giannoni, A. Voros, and J. Zinn-Justin, Les Houches Session LU, 1989 (Elsevier, Amsterdam, 1991). MR1188415
29. [29] Yves Colin de Verdiere, Comm. Math. Phys., 102, 497 ( 1985). Zbl0592.58050MR818831
30. [30] R. Aurich and F. Steiner"Quantum eigenstates of a strongly chaotic System and the scar phenomenom" Preprint desy 93-057 ( 1993). Zbl0817.58050MR1333686
31. [31] B. Parisse and Y. Colin de Verdiere. Preprint. 
32. [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). Zbl0771.58021

1. Yves Colin de Verdière, Champs magnétiques classiques et quantiques
2. Yves Colin de Verdière, La méthode de moyennisation en mécanique semi-classique