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Table des matières de ce fascicule Helffer, B.; Kerdelhue, P.; Sjöstrand, J. Le papillon de Hofstadter revisité. Mémoires de la Société Mathématique de France, Sér. 2, 43 (1990), p. 1-87 Texte intégral djvu | pdf | Analyses Zbl 0732.44004 | 1 citation dans Numdam URL stable: http://www.numdam.org/item?id=MSMF_1990_2_43__1_0 Bibliographie [Av - Se] J. Avron - R. Seiler : Quantization of the Hall conductance for general multiparticle Schrödinger Hamiltonians. Phys. Rev. Letters Vol. 54, n° 4, Janvier [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 ( Article | Zbl 0484.35069 J. Avron - B. Simon [2] Almost periodic Schrödinger operators, II The density of states Duke Math. Journal 50 ( Article | MR 85i:34009a | Zbl 0544.35030 J. Avron - B. Simon [3] Stability of gaps for periodic potentials under variation of a magnetic field J. Phys. A ; Math. Gen. 18 ( [Az] Ya Azbel : Energy spectrum of a conduction electron in a magnetic field Soviet Physics JETP vol. 19, n° 3 Sept. [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 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 ( [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 ( Article | MR 85i:82055 | Zbl 0542.35059 [Be - Si] J. Bellissard - B. Simon : Cantor Spectrum for the Almost Mathieu Equation Journal of functional Analysis, vol. 48, N° 3, Oct [Ben - Pas] Benderskii - L. Pasteur : On the spectrum of the one-dimensional Schrödinger equation with a random potential. Math. USSR Sb. 11, 245 ( [Ch] R.G. Chambers : The wave function of a Bloch electron in a Magnetic field Proc. Phys. Soc. 89 ( [C - E - Y] Man Duen Choi, Georges A. Elliott, Noriko Yui : Gauss polynomials and the rotation algebra Preprint Septembre [Cl - Wa] F. H. Claro, W. H. Wannier : Magnetic subband structure of electrons in hexagonal lattices Phys. Rev. B19 ( [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 0619.47005 [El] G.A. Elliott : Gaps in the spectrum of an almost periodic Schrödinger operator C.R. Math. Rep. Acad. Sci. Canada 4 ( [Gu - He - Tr] J.P. Guillement - B. Helffer - P. Treton : Walk inside Hofstadter's butterfly Journal de Physique France 50 ( [He - Ro] B. Helffer - D. Robert : Calcul fonctionnel par la transformée de Mellin et opérateurs admissibles Journal of Functional Analysis 53 ( [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 Numdam | Zbl 0714.34130 B. Helffer, J. Sjostrand [2] Analyse semi-classique pour l'équation de Harper II preprint nov. Numdam | Zbl 0714.34131 B. Helffer, J. Sjostrand [3] Semi-classical analysis for Harper's equation III preprint Orsay (avril Numdam | Zbl 0725.34099 B. Helffer, J. Sjostrand [4] Equation de Schrödinger avec champ magnétique et équation de Harper ; Preprint Dec. B. Helffer, J. Sjostrand [5] On Diamagnetism and de Haas-Van Alphen effect Preprint Paris-sud, mai Numdam | Zbl 0715.35070 [Ho] D. Hofstadter : Energy Levels and Wave functions of Bloch electrons in rational and irrational magnetic fields Phys. Rev. B 14 ( [J - M] R. Johnson - J. Moser : The rotation number for almost periodic potentials Comm. in Math. Phys. 84, ( Article | MR 83h:34018 | Zbl 0497.35026 [Kh] A. Ya Khinchin : Continued fractions Phoenix Science Series ( [Mo] P. (Van) Mouche : P. (Van) Mouche [1] Clustering and Nesting of Energy spectra Proceedings ICIAM 87, Paris la Villette, June 29-July 3 P. (Van) Mouche [2] The coexistence problem for the discrete Mathieu operator Preprint Février 88 et Comm. in Math. Physics Vol 122 n° 1, Article | MR 90e:47027 | Zbl 0669.34016 [Pi-Vo] M. Pimsner, D. Voiculescu : Imbedding the irrational rotation C*-algebra into an AF-algebra Journal Operator theory 4, [Sh] M.A. Shubin : The spectral theory and the index of elliptic operators with almost periodic coefficients Russian Math. Surveys, 34, ( [Si] B. Simon : Almost periodic Schrödinger operators. A review Advances in applied Mathematics 3 p. 463-490 ( [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, ( [Wa] G.H. Wannier : Phys. Status Solidi B 88, 757 ( [Wilk] M. Wilkinson : M. Wilkinson [1] Critical properties of electron eigenstates in incommensurate systems Proc. Royal Society of London A391 p 305-350 ( 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 ( M. Wilkinson [3] An exact effective hamiltonian for a perturbed Landau Level Journal of Physics A, Vol. 20, n° 7, 11 May M. Wilkinson [4] An exact renormalization group for Bloch electrons in a magnetic fields. Journal of Physics A, Vol. 20, p. 4337-4354 MR 88j:81087 |
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