@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\'emoires de la Soci\'et\'e Math\'ematique de France}, publisher = {Soci\'et\'e math\'ematique de France}, number = {43}, year = {1990}, doi = {10.24033/msmf.349}, zbl = {0732.44004}, language = {fr}, url = {http://archive.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 - Mémoires de la Société Mathématique de France PY - 1990 IS - 43 PB - Société mathématique de France UR - http://archive.numdam.org/item/MSMF_1990_2_43__1_0/ DO - 10.24033/msmf.349 LA - fr ID - MSMF_1990_2_43__1_0 ER -
Helffer, B.; Kerdelhue, P.; Sjöstrand, J. Le papillon de Hofstadter revisité. Mémoires de la Société Mathématique de France, Série 2, no. 43 (1990), 96 p. doi : 10.24033/msmf.349. http://numdam.org/item/MSMF_1990_2_43__1_0/
[Au] The new concept of transition by breaking of analyticity Solid State Sci.8 (1978), 264 | MR
:[Av - Se] 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]
- :Almost periodic Schrödinger operators, I. Limit Periodic potentials Comm. in Math. Physics. 82 p. 101-120 (1981) | Zbl
[1]Almost periodic Schrödinger operators, II The density of states Duke Math. Journal 50 (1983), 369-391 | Zbl | MR
- [2]Stability of gaps for periodic potentials under variation of a magnetic field J. Phys. A ; Math. Gen. 18 (1985) p 2199-2205 | Zbl | MR
- [3][Az] Energy spectrum of a conduction electron in a magnetic field Soviet Physics JETP vol. 19, n° 3 Sept. 1964
:[Be]
: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
[1]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
[2][Be - Li - Te] A metal-insulator transition for the almost Mathieu model Comm. in Math. Phys. 88, 207-234 (1983) | Zbl | MR
- - :[Be - Si] Cantor Spectrum for the Almost Mathieu Equation Journal of functional Analysis, vol. 48, N° 3, Oct 1982 | Zbl | MR
- :[Ben - Pas] On the spectrum of the one-dimensional Schrödinger equation with a random potential. Math. USSR Sb. 11, 245 (1970) | Zbl
- :[Ch] The wave function of a Bloch electron in a Magnetic field Proc. Phys. Soc. 89 (1966), 695-710
:[C - E - Y] Gauss polynomials and the rotation algebra Preprint Septembre 1988, et Inventiones matematicae Vol 99 Fasc. 2 1990 | Zbl | EuDML
, , :[Cl - Wa] Magnetic subband structure of electrons in hexagonal lattices Phys. Rev. B19 (1979), 6068-74
, :[C - F - K - S] Schrödinger operators with applications to quantum mechanics and global geometry Texts and monographs in Physics, Springer Verlag | Zbl
- - - :[El] 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] Walk inside Hofstadter's butterfly Journal de Physique France 50 (1989) 2019-2058
- - :[He - Ro] Calcul fonctionnel par la transformée de Mellin et opérateurs admissibles Journal of Functional Analysis 53 (1983) p. 246-268 | Zbl | MR
- :[He - Sj]
, :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
, [1]Analyse semi-classique pour l'équation de Harper II preprint nov. 1988 ; à paraître aux mémoires de la SMF 1989 | Zbl | Numdam
, [2]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
, [3]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
, [4]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
, [5][Ho] Energy Levels and Wave functions of Bloch electrons in rational and irrational magnetic fields Phys. Rev. B 14 (1976), 2239-2249
:[J - M] The rotation number for almost periodic potentials Comm. in Math. Phys. 84, (1982), 403-438 ; 90, (1983), 317-318 | Zbl | MR
- :[Kh] Continued fractions Phoenix Science Series (1964)
:[Mo]
:Clustering and Nesting of Energy spectra Proceedings ICIAM 87, Paris la Villette, June 29-July 3 1987 | MR
[1]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
[2][Pi-Vo] Imbedding the irrational rotation C*-algebra into an AF-algebra Journal Operator theory 4, 1980 p. 211-218 | Zbl | MR
, :[Sh] The spectral theory and the index of elliptic operators with almost periodic coefficients Russian Math. Surveys, 34, (1979), 109-157 | Zbl | MR
:[Si] Almost periodic Schrödinger operators. A review Advances in applied Mathematics 3 p. 463-490 (1982) | Zbl | MR
:[T - K - N - N] Quantized Hall conductance in two dimensional periodic potential. Phys. Rev. Letters, 49, (1982), p. 405-408
, , , :[Wa] Phys. Status Solidi B 88, 757 (1978)
:[Wilk]
:Critical properties of electron eigenstates in incommensurate systems Proc. Royal Society of London A391 p 305-350 (1984) | MR
[1]Von Neumann lattices of Wannier functions for Bloch electrons in a magnetic field Proc. R. Soc. Lond. A 403, p 135-166 (1986) | MR
[2]An exact effective hamiltonian for a perturbed Landau Level Journal of Physics A, Vol. 20, n° 7, 11 May 1987, p. 1761 | Zbl | MR
[3]An exact renormalization group for Bloch electrons in a magnetic fields. Journal of Physics A, Vol. 20, p. 4337-4354 | MR
[4]Cité par Sources :