@phdthesis{BJHTUP11_1991__0293__P0_0, author = {Kerdelhu\'e, Philippe}, title = {\'Equation de {Schr\"odinger} magn\'etique p\'eriodique avec sym\'etries triangulaires et hexagonales : structure hi\'erarchique du spectre}, series = {Th\`eses d'Orsay}, publisher = {Universit\'e de Paris-Sud Centre d'Orsay}, number = {293}, year = {1991}, language = {fr}, url = {http://archive.numdam.org/item/BJHTUP11_1991__0293__P0_0/} }
TY - BOOK AU - Kerdelhué, Philippe TI - Équation de Schrödinger magnétique périodique avec symétries triangulaires et hexagonales : structure hiérarchique du spectre T3 - Thèses d'Orsay PY - 1991 IS - 293 PB - Université de Paris-Sud Centre d'Orsay UR - http://archive.numdam.org/item/BJHTUP11_1991__0293__P0_0/ LA - fr ID - BJHTUP11_1991__0293__P0_0 ER -
%0 Book %A Kerdelhué, Philippe %T Équation de Schrödinger magnétique périodique avec symétries triangulaires et hexagonales : structure hiérarchique du spectre %S Thèses d'Orsay %D 1991 %N 293 %I Université de Paris-Sud Centre d'Orsay %U http://archive.numdam.org/item/BJHTUP11_1991__0293__P0_0/ %G fr %F BJHTUP11_1991__0293__P0_0
Kerdelhué, Philippe. Équation de Schrödinger magnétique périodique avec symétries triangulaires et hexagonales : structure hiérarchique du spectre. Thèses d'Orsay, no. 293 (1991), 116 p. http://numdam.org/item/BJHTUP11_1991__0293__P0_0/
[Av-Si] Stability of gaps for periodic potential under variations of a magnetic field. J. Phys. A : Math. Gen. 18 (1985) p 2199-2205. | MR | Zbl | DOI
- :[Beals] Characterization of P.D.O. and applications. Duke Math J44 (1977) p 45-57. | MR | Zbl | DOI
:[Be] Schrödinger operators with almost periodic potentials. Springer lecture notes in physics 153.
:[BKS] Analysis of the spectrum of a particle on a triangular lattice with two magnetic fluxes by algebraic and numerical methods. Preprint (Juin 1990). | MR | Zbl
, , et :[Be-Si] Cantor spectrum for the almost Mathieu equation. Journal of Functional Analysis, vol 48, N°3, Oct 1982. | Zbl
[Ca] An infinite number of wells in the semi-classical limit. Asymptotic Analysis 1990 vol 3 n°3 p 189-214. | MR | Zbl | DOI
:[Cl-Wa] Magnetic subband structure of electron in hexagonal lattices. Physical review B, volume 19, number 12 p 6068-6074. | DOI
et :[CFKS] Schrödinger operators with applications to quantum mechanics and global geometry, Text and Monographs in Physics, Springer Verlag. | MR | Zbl
, , et :[Gu-He-Tr] Walk inside Hofstadter's butterfly. Journal de Physique France 50 (1989) p2019-2058. | DOI
, et :[Ha]1 Double wells. Comm. Math. phys. 75 (1980) p239-261. | MR | Zbl | DOI
:[Ha]2 The band structure of a one dimension periodic system in the scaling limit. Ann. of Physics 119 (1974) p 351-369. | MR | Zbl | DOI
:[He-Ro]1 Calcul fonctionnel par la transformée de Mellin et applications. Journal of Functional Analysis, vol 53, N° 3, Oct 1983. | MR | Zbl | DOI
et :[He-Ro]2 Puits de potentiel généralisés et asymptotique semi-classique. Annales de l'IHP (section physique théorique) vol 41, N° 3, 1984, p 2291-331. | MR | Zbl | Numdam
et :[He-Ro]3 Asymptotique des niveaux d'énergie pour des hamiltoniens à un degré de liberté. Duke Math Journal (1982) vol 49, n° 4. | MR | Zbl | DOI
et :[Ho] Energy level and wave functions for Bloch electrons in rational and irrational magnetic fields. Physical Review B 14 (1976) p 2239-2249. | DOI
:[He-Sj]1 Multiple wells in the semi classical limit 1. Comm PDE, 9(4) (1984), p 334-408. | MR | Zbl | DOI
et :[He-Sj]2 Multiple wells in the semi classical limit 2. Annales de l'IHP (section physique théorique), 49, n° 2 (1985) p 127-212. | MR | Zbl | Numdam
et :[He-Sj]3 Effet tunnel pour l'équation de Schrödinger avec champ magnétique. Annales Sc Norm Sup di Pisa Ser IV 14 (4) (1987) p 625-657. | MR | Zbl | Numdam
et :[He-Sj]4 Analyse semi classique pour l'équation de Harper. Mémoire de la SMF n° 34 (1988). | Zbl | Numdam
et :[He-Sj]5 Analyse semi classique pour l'équation de Harper 2 : comportement semi-classique près d'un rationnel. Mémoire de la SMF n° 40 (1989). | MR | Zbl | Numdam
et :[He-Sj]6 Semi classical analysis for Harper equation 3. Cantor structure of the spectrum. Mémoire de la SMF n° 39. Tome 117, fascicule 4 (1989). | MR | Zbl | Numdam
et :[He-Sj]7 Résonances en limite semi-classique. Bulletin de la SMF (1986), tome 114, fasc. 3, mémoire n° 24-25. | MR | Zbl | Numdam
et :[He-Sj]8 On diamagnetism and de Haas-van Halphen effect. Ann Inst. Henri poincaré. (section phys. th.) Vol 52 n°4 (1990) p 303-375. | MR | Zbl | Numdam
et[Ho] Energy levels and wave functions of Bloch electrons in rational and irrational magnetic fields. Phys. Rev. B 14 (1976), p 2239-2249. | DOI
:[La-Li] Mécanique quantique.
:[Me-Sj] Fourier Integral Opérators with complex valued phase functions. Springer Lecture Notes in Mathematics n° 459, p 121-223. | MR | Zbl
and :[Ou] Analyse semi classique pour des opérateurs de Schrödinger avec potentiel périodique. Journal of functional analysis Vol 72, N°1, May 1987. | MR | Zbl | DOI
:[Re-Si] Methods of modem mathematical physics. Academic Press. | Zbl
et :[Ro] Autour de l'approximation semi-classique. Progress in Mathematics, vol n°28, Birkhauser. | MR | Zbl
:[SI]1 Almost periodic Schrödinger operators : a review. Advances in Applied Mathematics 3, (1982) p 463-490. | MR | Zbl
:[SI]2 Semi-classical analysis of low lying eigenvalues I et II. Ann. IHP t38, 1983 p 295-307. Ann. of Math n°120, p 89-118. | MR | Zbl
:[SI]3 Semi-classical analysis of low lying eigenvalues III. Width of the ground state band in strongly coupled solids. Ann. of Physics 158 (1984) p415-420. | MR | Zbl
:[Sj]1 Singularités analytiques microlocales. Astérisque n° 95 (1982). | MR | Zbl | Numdam
:[Sj]2 Analytic singularities of solutions of boundary value problem. Proceedings of the Nato Advanced Study Institute (1980). Reidel Publishing Company. | MR | Zbl
:[So] Unusual band structure, wave functions and electrical conductance in crystals with incommensurate periodic potentials. Physics Reports (review section of physics letters) 126, n° 4 (1985) p 189-244.
:[VM] The coexistence problem for the discret Mathieu operator. Comm. in Math. Phys. Vol 122 n° 1 (1989) p23-34. | MR | Zbl | DOI
.[Wi]1 critical properties of electron eigenstates in incommensurable systems. Proc. R. Soc. London A 391 (1984), p 305-350. | MR
:[Wi]2 Von Neumann lattices of Wannier functions for Bloch electrons in a magnetic field. Proc. R. Soc. London A 403 (1986), p 135-166. | MR
:[Wi]3 An exact effective Hamiltonian for a perturbed Landau level. Journal of Phys.A, 20, n° 7, 11 mai 1987, p 1761-. | MR | Zbl | DOI
:[Wi]4 An exact renormalisation group for Bloch electrons in a magnetic field. Journal of Physics A Gen 20 (1987) 4337-4354. | MR | DOI
:[Wi-Au] Semi-classical analysis of phase space lattices with threefold symetry. Preprint (1989).
et :