Le papillon de Hofstadter revisité
Mémoire de la Société mathématique de France, no. 43 (1990) , 96 p. 
@book{MSMF_1990_2_43__1_0,
     author = {Helffer, B. and Kerdelhue, P. and Sj\"ostrand, J.},
     title = {Le papillon de {Hofstadter} revisit\'e},
     series = {M\'emoire de la Soci\'et\'e math\'ematique de France},
     year = {1990},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {43},
     doi = {10.24033/msmf.349},
     zbl = {0732.44004},
     language = {fr},
     url = {https://www.numdam.org/item/MSMF_1990_2_43__1_0/}
}
TY  - BOOK
AU  - Helffer, B.
AU  - Kerdelhue, P.
AU  - Sjöstrand, J.
TI  - Le papillon de Hofstadter revisité
T3  - Mémoire de la Société mathématique de France
PY  - 1990
IS  - 43
PB  - Société mathématique de France
UR  - https://www.numdam.org/item/MSMF_1990_2_43__1_0/
DO  - 10.24033/msmf.349
LA  - fr
ID  - MSMF_1990_2_43__1_0
ER  - 
%0 Book
%A Helffer, B.
%A Kerdelhue, P.
%A Sjöstrand, J.
%T Le papillon de Hofstadter revisité
%S Mémoire de la Société mathématique de France
%D 1990
%N 43
%I Société mathématique de France
%U https://www.numdam.org/item/MSMF_1990_2_43__1_0/
%R 10.24033/msmf.349
%G fr
%F MSMF_1990_2_43__1_0
Helffer, B.; Kerdelhue, P.; Sjöstrand, J. Le papillon de Hofstadter revisité. Mémoire de la Société mathématique de France, Nouvelle série, no. 43 (1990), 96 p. doi: 10.24033/msmf.349

[Au] S. Aubry : The new concept of transition by breaking of analyticity Solid State Sci.8 (1978), 264 | MR

[Av - Se] J. Avron - R. Seiler : Quantization of the Hall conductance for general multiparticle Schrödinger Hamiltonians. Phys. Rev. Letters Vol. 54, n° 4, Janvier 1985, p. 259-262 | MR

[Av - Si] J. Avron - B. Simon :

J. Avron - B. Simon [1] Almost periodic Schrödinger operators, I. Limit Periodic potentials Comm. in Math. Physics. 82 p. 101-120 (1981) | Zbl

J. Avron - B. Simon [2] Almost periodic Schrödinger operators, II The density of states Duke Math. Journal 50 (1983), 369-391 | Zbl | MR

J. Avron - B. Simon [3] Stability of gaps for periodic potentials under variation of a magnetic field J. Phys. A ; Math. Gen. 18 (1985) p 2199-2205 | Zbl | MR

[Az] Ya Azbel : Energy spectrum of a conduction electron in a magnetic field Soviet Physics JETP vol. 19, n° 3 Sept. 1964

[Be] J. Bellissard :

J. Bellissard [1] Almost periodicity in solid state Physics and C*-algebras "The Harald Bohr Centennary" Proceedings of the symposium held in Copenhaguen conference on almost periodic functions April : 24-25 1987 ; C. Berg, B. Fuglede Ed. The Royal Academy of Sciences, Editions, Copenhaguen 1989

J. Bellissard [2] C*-Algebras in solid State Physics-2D Electrons in a uniform magnetic field ; "operator algebras and applications" D.E. Evans and M. Takesaki Eds Cambridge University Press, Vol. 2 (1988) pp 49-76 | Zbl | MR

[Be - Li - Te] J. Bellissard - R. Lima - D. Testard : A metal-insulator transition for the almost Mathieu model Comm. in Math. Phys. 88, 207-234 (1983) | Zbl | MR

[Be - Si] J. Bellissard - B. Simon : Cantor Spectrum for the Almost Mathieu Equation Journal of functional Analysis, vol. 48, N° 3, Oct 1982 | Zbl | MR

[Ben - Pas] Benderskii - L. Pasteur : On the spectrum of the one-dimensional Schrödinger equation with a random potential. Math. USSR Sb. 11, 245 (1970) | Zbl

[Ch] R.G. Chambers : The wave function of a Bloch electron in a Magnetic field Proc. Phys. Soc. 89 (1966), 695-710

[C - E - Y] Man Duen Choi, Georges A. Elliott, Noriko Yui : Gauss polynomials and the rotation algebra Preprint Septembre 1988, et Inventiones matematicae Vol 99 Fasc. 2 1990 | Zbl | EuDML

[Cl - Wa] F. H. Claro, W. H. Wannier : Magnetic subband structure of electrons in hexagonal lattices Phys. Rev. B19 (1979), 6068-74

[C - F - K - S] H. L. Cycon - R. G. Froese - W. Kirsch - B. Simon : Schrödinger operators with applications to quantum mechanics and global geometry Texts and monographs in Physics, Springer Verlag | Zbl

[El] G.A. Elliott : Gaps in the spectrum of an almost periodic Schrödinger operator C.R. Math. Rep. Acad. Sci. Canada 4 (1982) p. 255-259 | Zbl | MR

[Gu - He - Tr] J.P. Guillement - B. Helffer - P. Treton : Walk inside Hofstadter's butterfly Journal de Physique France 50 (1989) 2019-2058

[He - Ro] B. Helffer - D. Robert : Calcul fonctionnel par la transformée de Mellin et opérateurs admissibles Journal of Functional Analysis 53 (1983) p. 246-268 | Zbl | MR

[He - Sj] B. Helffer, J. Sjostrand :

B. Helffer, J. Sjostrand [1] Analyse semi-classique pour l'équation de Harper (avec application à l'étude de l'équation de Schrödinger avec champ magnétique) ; Mémoires de la SMF 1988 | Zbl | Numdam

B. Helffer, J. Sjostrand [2] Analyse semi-classique pour l'équation de Harper II preprint nov. 1988 ; à paraître aux mémoires de la SMF 1989 | Zbl | Numdam

B. Helffer, J. Sjostrand [3] Semi-classical analysis for Harper's equation III preprint Orsay (avril 1988), à paraître aux mémoires de la SMF 1989 et annoncé au Séminaire EDP de l'école Polytechnique 87-88 | Zbl | Numdam

B. Helffer, J. Sjostrand [4] Equation de Schrödinger avec champ magnétique et équation de Harper ; Preprint Dec. 1988 et paru dans "Schrödinger operators", Proceedings, Sønderborg, Denmark, 1988 ; Lecture Notes in Physics n° 345, Springer Verlag | Zbl

B. Helffer, J. Sjostrand [5] On Diamagnetism and de Haas-Van Alphen effect Preprint Paris-sud, mai 1989 ; à paraître aux annales de l'IHP (section Physique théorique) | Zbl | Numdam | EuDML

[Ho] D. Hofstadter : Energy Levels and Wave functions of Bloch electrons in rational and irrational magnetic fields Phys. Rev. B 14 (1976), 2239-2249

[J - M] R. Johnson - J. Moser : The rotation number for almost periodic potentials Comm. in Math. Phys. 84, (1982), 403-438 ; 90, (1983), 317-318 | Zbl | MR

[Kh] A. Ya Khinchin : Continued fractions Phoenix Science Series (1964)

[Mo] P. (Van) Mouche :

P. (Van) Mouche [1] Clustering and Nesting of Energy spectra Proceedings ICIAM 87, Paris la Villette, June 29-July 3 1987 | MR

P. (Van) Mouche [2] The coexistence problem for the discrete Mathieu operator Preprint Février 88 et Comm. in Math. Physics Vol 122 n° 1, 1989, p. 23-34 | Zbl | MR

[Pi-Vo] M. Pimsner, D. Voiculescu : Imbedding the irrational rotation C*-algebra into an AF-algebra Journal Operator theory 4, 1980 p. 211-218 | Zbl | MR

[Sh] M.A. Shubin : The spectral theory and the index of elliptic operators with almost periodic coefficients Russian Math. Surveys, 34, (1979), 109-157 | Zbl | MR

[Si] B. Simon : Almost periodic Schrödinger operators. A review Advances in applied Mathematics 3 p. 463-490 (1982) | Zbl | MR

[T - K - N - N] D. Thouless, M. Kohmoto, M. Nightingale, M. De Nijs : Quantized Hall conductance in two dimensional periodic potential. Phys. Rev. Letters, 49, (1982), p. 405-408

[Wa] G.H. Wannier : Phys. Status Solidi B 88, 757 (1978)

[Wilk] M. Wilkinson :

M. Wilkinson [1] Critical properties of electron eigenstates in incommensurate systems Proc. Royal Society of London A391 p 305-350 (1984) | MR

M. Wilkinson [2] Von Neumann lattices of Wannier functions for Bloch electrons in a magnetic field Proc. R. Soc. Lond. A 403, p 135-166 (1986) | MR

M. Wilkinson [3] An exact effective hamiltonian for a perturbed Landau Level Journal of Physics A, Vol. 20, n° 7, 11 May 1987, p. 1761 | Zbl | MR

M. Wilkinson [4] An exact renormalization group for Bloch electrons in a magnetic fields. Journal of Physics A, Vol. 20, p. 4337-4354 | MR

Cité par Sources :