Le papillon de Hofstadter
Séminaire Bourbaki : volume 1991/92, exposés 745-759, Astérisque, no. 206 (1992), Talk no. 745, 33 p.
     author = {Bellissard, Jean},
     title = {Le papillon de {Hofstadter}},
     booktitle = {S\'eminaire Bourbaki : volume 1991/92, expos\'es 745-759},
     author = {Collectif},
     series = {Ast\'erisque},
     note = {talk:745},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {206},
     year = {1992},
     zbl = {0791.46057},
     mrnumber = {1206063},
     language = {fr},
     url = {http://www.numdam.org/item/SB_1991-1992__34__7_0/}
AU  - Bellissard, Jean
TI  - Le papillon de Hofstadter
BT  - Séminaire Bourbaki : volume 1991/92, exposés 745-759
AU  - Collectif
T3  - Astérisque
N1  - talk:745
PY  - 1992
IS  - 206
PB  - Société mathématique de France
UR  - http://www.numdam.org/item/SB_1991-1992__34__7_0/
LA  - fr
ID  - SB_1991-1992__34__7_0
ER  - 
%0 Book Section
%A Bellissard, Jean
%T Le papillon de Hofstadter
%B Séminaire Bourbaki : volume 1991/92, exposés 745-759
%A Collectif
%S Astérisque
%Z talk:745
%D 1992
%N 206
%I Société mathématique de France
%U http://www.numdam.org/item/SB_1991-1992__34__7_0/
%G fr
%F SB_1991-1992__34__7_0
Bellissard, Jean. Le papillon de Hofstadter, in Séminaire Bourbaki : volume 1991/92, exposés 745-759, Astérisque, no. 206 (1992), Talk no. 745, 33 p. http://www.numdam.org/item/SB_1991-1992__34__7_0/

[AL] S. Alexander -Superconductivity of networks. A percolation approach to the effect of disorder, Phys. Rev., B27, (1983), 1541-1557. | MR

[AA] S. Aubry, G. Andre -Analyticity breaking and the Anderson localization in incommensurate lattices, Ann. Israeli Phys. Soc., 3, (1980), 133. | MR | Zbl

[AU] S. Aubry -The new concept of transition by breaking of analyticity in cristallographic models, Solid State Sci., 8, (1978), 264. | MR

[AMS] J. Avron, P. H. M. Van Mouche, B. Simon - On the measure of the spectrum for the almost Mathieu operator, Preprint CALTECH, 1990, Commun. Math. Phys.. | MR

[AZ] Ya. Azbel -Energy spectrum of a conduction electron in a magnetic field, Sov. Phys. JETP, 19(3), (1964), 634.

[BEI] J. Bellissard - C * -Algebras in solid state physics : $2D$ electrons in a uniform magnetic field, in Operator Algebras and Application, Vol.2, D. E. Evans & M.Takesaki Eds., Cambridge University Press, (1988). | MR | Zbl

[BE2] J. Bellissard -Almost Periodicity in Solid State Physics and C*- Algebras, in The Harald Bohr Centenary, C.Berg & B.Fuglede Eds., The Danish Royal Acad. Sci., 42:3, (1989), 35-75. | MR | Zbl

[BE3] J. Bellissard - The Rotation Algebra, Lecture donnée à l'école d'été de Nantes, Juin 1991, en préparation.

[BKS] J. Bellissard, C. Kreft, R. Seiler -Analysis of the spectrum of a particle on a triangular lattice with two magnetic fluxes by algebraic and numerical methods, J. Phys., A24, (1991), 2329-2353. | MR | Zbl

[BES] J. Bellissard, B. Simon - Cantor Spectrum for the Almost Mathieu Equation, J. Funct. Anal., 48, (1982), 408-419. | MR | Zbl

[BV] J. Bellissard, M. Vittot -Heisenberg's picture and non commutative geometry in the semi-classical limit in qauntum Mechanics, Ann. Inst. Henri Poincaré, 52, (1990), 175-235. | Numdam | MR | Zbl

[CH] W. G. Chambers - Phys Rev., A140, (1965), 135-143.

[CEY] M. D. Choi, G. Elliott, K. Yui -Gauss polynomials and the rotation Algebra, Inventiones Math., (1991). | Zbl

[GE] P. G. De Gennes -Diamagnétisme de grains supraconducteurs près d'un seuil de percolation, C.R. Acad. Sci., B292, (1981), 9-12; Champ critique d'une boucle supraconductrice ramifiée, C.R. Acad. Sci., B292, (1981), 279-282.

[GH] J. P. Guillement, B. Helffer, P. Treton- Walk inside Hofstadter's butterfly, J. Phys. France, 50, (1989), 2019-2058.

[HA] P. G. Harper -Single Band Motion of Conduction Electrons in a Uniform Magnetic Field, Proc.Phys. Soc. London, A68, (1955), 874. | Zbl

[HR] B. Helffer, D. Robert -Calcul fonctionnel de la transformée de Mellin et applications, J. Funct. Anal., 53, (1983). | MR | Zbl

[HS0] B. Helffer, J. Sjöstrand -Microlocal Analysis for the Periodic Magnetic Schrödinger Equation and related questions, C.I.M.E Lectures (1989), in Lecture Notes in Math.. | Zbl

[HS1] B. Helffer, J. Sjöstrand -Analyse semi-classique pour l'équation de Harper (application à l'étude de l'équation de Schrödinger avec champ magnétique), Mémoires de la S.M.F., (1989). | Numdam | Zbl

[HS2] B. Helffer, J. Sjöstrand -Analyse semi-classique pour l'équation de Harper II. Comportement semi-classique près d'un rationnel, Mémoires de la S.M.F n°40, 118, (1990), 1-139. | Numdam | MR | Zbl

[HS3] B. Helffer, J. Sjöstrand -Semi-classical analysis for Harper's equation III, Mémoires de la S.M.F., (1991). | Numdam | Zbl

[HO] D. R. Hofstadter -Energy levels and wave functions of Bloch electrons in a rational or irrational magnetic field, Phys. Rev., B14, (1976), 2239.

[KL] K. Von Klitzing, G. Dorda, M. Pepper -Realization of a resistance standard based on fundamental constants, Phys. Rev. Letters, 45, (1980), 494-497.

[LA] L. Landau -Diamagnetismus der Metalle, Z. für Phys., 64, (1930), 629-637. | JFM

[LU] J. M. Luttinger -The Effect of a Magnetic Field on Electrons in a Periodic Potential, Phys. Rev., 84, (1951), 814. | MR | Zbl

[MO] P. Van Mouche -The coexistence problem for the discrete Mathieu operator, Comm. Math. Phys., 122, (1989), 23-34. | MR | Zbl

[PCR] B. Pannetier, J. Chaussy, R. Rammal - Experimental Determination of the (H, T) Phase Diagram of a Superconducting Network, J. de Physique Lettres 44, (1983), L853-L858.

[PCRV] B. Pannetier, J. Chaussy, R. Rammal, J. C. Villegier - Experimental Fine Tuning of the Frustration: 2D Superconducting Networks in a Magnetic Field, Phys. Rev. Letters, 53, (1984), 1845-1848.

[PED] G. Pedersen -C*-Algebras and their automorphism groups, Academic Press, London, New-York, (1979). | MR | Zbl

[PE] R. Peierls -Zur Theorie des Diamagnetismus von Leitungelektronen, Z. für Phys., 80, (1933), 763-791. | Zbl

[RB1] R. Rammal, J. Bellissard -Ground State of the Fermi Gas in 2D Lattices with a Magnetic Field: New Exact Results, Europhys. Letters, 13, (1990), 205-210.

[RB2] R. Rammal, J. Bellissard -An algebraic semi-classical approach to Bloch electrons in a magnetic field, J. Phys. France, 51, (1990), 1803-1830. | MR

[SI] Ya. G. Sinai -Anderson localization for the one dimensional difference Schrödinger operator with quasiperiodic potentials, in Proc. Int. Congress Math. Phys. Marseille 1986, World Scientific Pub. Co., Singapore, (1987), pp. 870-903. | MR

[SO] J. B. Sokoloff -Unusual band structure, wave functions and electrical conductance in crystals with incommensurable periodic potentials, Phys. Reports, 126, (1985), 189-244.

[TH] D. Thouless -Bandwidths for a quasiperiodic tight-binding model, Phys. Rev., B28, (1983), 4272-4276.

[TKN2] D. Thouless, M. Kohmoto, M. Nightingale, M. Den Nijs -Quantized Hall Conductance in two dimensional periodic potential, Phys. Rev. Letters, 49, (1982), 405.

[WI] M. Wilkinson -Critical Properties of Electron Eigenstates in Incommensurate Systems, Proc. Roy. Soc. London, A391, (1984), 305-350. | MR

[ZA] J. Zak -Magnetic Translation Group, Phys. Rev., A134, (1964), 1602- 1607; Magnetic Translation Group II: Irreducible Representations, Phys. Rev., A134, (1964), 1607-1611. | MR | Zbl