@book{MSMF_1989_2_39__1_0, author = {Helffer, B. and Sj\"ostrand, J.}, title = {Semi-classical analysis for {Harper's} equation. {III} : {Cantor} structure of the spectrum}, series = {M\'emoires de la Soci\'et\'e Math\'ematique de France}, publisher = {Soci\'et\'e math\'ematique de France}, number = {39}, year = {1989}, doi = {10.24033/msmf.346}, zbl = {0725.34099}, language = {en}, url = {http://archive.numdam.org/item/MSMF_1989_2_39__1_0/} }
TY - BOOK AU - Helffer, B. AU - Sjöstrand, J. TI - Semi-classical analysis for Harper's equation. III : Cantor structure of the spectrum T3 - Mémoires de la Société Mathématique de France PY - 1989 IS - 39 PB - Société mathématique de France UR - http://archive.numdam.org/item/MSMF_1989_2_39__1_0/ DO - 10.24033/msmf.346 LA - en ID - MSMF_1989_2_39__1_0 ER -
%0 Book %A Helffer, B. %A Sjöstrand, J. %T Semi-classical analysis for Harper's equation. III : Cantor structure of the spectrum %S Mémoires de la Société Mathématique de France %D 1989 %N 39 %I Société mathématique de France %U http://archive.numdam.org/item/MSMF_1989_2_39__1_0/ %R 10.24033/msmf.346 %G en %F MSMF_1989_2_39__1_0
Helffer, B.; Sjöstrand, J. Semi-classical analysis for Harper's equation. III : Cantor structure of the spectrum. Mémoires de la Société Mathématique de France, Serie 2, no. 39 (1989), 132 p. doi : 10.24033/msmf.346. http://numdam.org/item/MSMF_1989_2_39__1_0/
[AM] Foundations of Mechanics, Benjamin/Cumming publ. Co. (1978), | Zbl | MR
, ,[AuAn] Proc. Israel Phys. Soc. Ed.C.G.Kuper 3 (Adam Hilger, Bristol) (1979), 133-, | Zbl
, ,[AvSi] Stability of gaps for periodic potentials under a variation of a magnetic field, J. Phys. A, 18 (1985), 2199-2205, | Zbl | MR
, ,[Az] Energy spectrum of a conduction electron in a magnetic field, Soviet Physics JETP, 19, n°3, Sept 1964.
,[Be] Schrödinger operators with almost periodic potentials, Springer Lecture Notes in Physics, 153,
,[BeSi] Cantor spectrum for the almost Mathieu equation, J. Funct. An., 48, n°3, Oct. 1982, | Zbl | MR
, ,[GeS] Semi-classical resonances generated by a closed trajectory of hyperbolic type, Comm. Math. Phys., 108 (1987), 391-421. | Zbl
, ,[GrS] Front d'onde analytique et sommes de carrés de champs de vecteurs, Duke Math. J., 52, n° 1 (1985), 35-51, | Zbl | MR
, ,[HR1] Calcul fonctionnel par la transformée de Mellin et applications, J. Funct. An., 53, n°3, oct. 1983. | MR
, ,[HR2] Puits de potentiel généralisés et asymptotique semiclassique, Ann. I.H.P. (section Phys. théorique), 41, n°3, (1984), 291-331, | Zbl | MR | Numdam
, ,[HS1] Analyse semi-classique pour l'équation de Harper, Preprint (1987)
, ,[HS2] Analyse semi-classique pour l'équation de Harper II Comportement semi-classique près d'un rationnel, Preprint.
, ,[HS3] Structure Cantorienne du spectre de l'opérateur de Harper, Sém. des Equations aux Dérivées partielles, Ecole polytechnique, March 1988, | Zbl | Numdam
, ,[HS4] Multiple wells in the semiclassical limit I, Comm. PDE, 9(4) (1984), 337-408, | Zbl | MR
, ,[HS5] Multiple wells in the semiclassical limit II, Ann. I.H.P. (section Phys. théorique), 42, n°2, (1985), 127-212, | Zbl | Numdam
, ,[HS6] Effet tunnel pour l'équation de Schrödinger avec champ magnétique, Ann. Sc. Norm. Sup., to appear, | Zbl | Numdam
, ,[HS7] Résonances en limite semi-classique, Bull. de la SMF, 114, fasc. 3, (mémoire n°24-25). | Zbl | Numdam
, ,[Ho] Energy levels and wave functions for Bloch electrons in rational and irrational magnetic fields, Phys. Rev. B 14 (1976), 2239-2249,
,[L] Lagrangian analysis and quantum mechanics, MIT Press (1981). | Zbl | MR
,[Mo] The coexistence problem for the discrete Mathieu operator, Preprint (1988),
,[No] Two dimensional operators in periodic fields, J. Sov. Math., 28, n°1, January 1985,
,[O] Asymptotics and special functions, Academic Press, New York, London, 1974. | Zbl | MR
,[Si] Almost periodic Schrödinger operators: a review, Advances in applied math. 3, (1982), 463-490, | Zbl | MR
,[S1] Singularités analytiques microlocales, Astérisque 95 (1982), | Zbl | MR | Numdam
,[S2] Resonances generated by non-degenerate critical points, Springer Lecture Notes in Mathematics, n°1256, 402-429, | 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), 189-244,
,[W1] Critical properties of electron eigenstates in incommensurate systems, Proc. R. Soc. London A391 (1984), 305-350, | MR
,[W2] Von Neumann lattices of Wannier functions for Bloch electrons in a magnetic field, Proc. R. Soc. London A403 (1986), 135-166, | MR
,[W3] An exact effective Hamiltonian for a perturbed Landau level, Journal of Phys. A, 20, n°7, 11-May 1987, 1761-, | Zbl | MR
,[W4] An exact renormalisation group for Bloch electrons in a magnetic field, Journal of Physics A, to appear.
,Cited by Sources: