Transitions d’Anderson pour des opérateurs de Schrödinger quasi-périodiques en dimension 1
Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (1998-1999), Exposé no. 4, 14 p.
Fedotov, Alexander 1 ; Klopp, Frédéric 2

1 Department of Mathematical Physics, St Petersburg State University, 1, Ulianovskaja, 198904 St Petersburg-Petrodvoretz, Russi
2 Département de Mathématique, Institut Galilée, U.R.A 7539 C.N.R.S, Université de Paris-Nord, Avenue J.-B. Clément, F-93430 Villetaneuse, France
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     title = {Transitions {d{\textquoteright}Anderson} pour des op\'erateurs de {Schr\"odinger} quasi-p\'eriodiques en dimension 1},
     journal = {S\'eminaire \'Equations aux d\'eriv\'ees partielles (Polytechnique) dit aussi "S\'eminaire Goulaouic-Schwartz"},
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     publisher = {Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
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Fedotov, Alexander; Klopp, Frédéric. Transitions d’Anderson pour des opérateurs de Schrödinger quasi-périodiques en dimension 1. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (1998-1999), Exposé no. 4, 14 p. http://www.numdam.org./item/SEDP_1998-1999____A4_0/

[1] S. Aubry and G. André. Analyticity breaking and Anderson localization in incommensurate lattices. Ann. Isr. Phys. Soc., 3, 133-164 1980. | MR | Zbl

[2] J. Avron and B. Simon. Almost periodic Schrödinger operators, II. the integrated density of states. Duke Mathematical Journal, 50:369–391, 1983. | MR | Zbl

[3] J. Bellissard, R. Lima, and D. Testard. Metal-insulator transition for the Almost Mathieu model. Communications in Mathematical Physics, 88:207–234, 1983. | MR | Zbl

[4] V. Buslaev and A. Fedotov. Monodromization and Harper equation. In Séminaires d’équations aux dérivées partielles, volume XXI, Palaiseau, 1994. Ecole Polytechnique. | Numdam | Zbl

[5] R. Carmona and J. Lacroix. Spectral Theory of Random Schrödinger Operators. Birkhäuser, Basel, 1990. | MR | Zbl

[6] H.L. Cycon, R.G. Froese, W. Kirsch, and B. Simon. Schrödinger Operators. Springer Verlag, Berlin, 1987. | MR | Zbl

[7] M. Eastham. The spectral theory of periodic differential operators. Scottish Academic Press, Edinburgh, 1973. | Zbl

[8] L. H. Eliasson. Discrete one-dimensional quasi-periodic Schrödinger operators with pure point spectrum. Acta Mathematica, 179:153–196, 1997. | MR | Zbl

[9] L. H. Eliasson. Reducibility and point spectrum for linear quasi-periodic skew products. In Proceedings of the ICM 1998,Berlin, volume II, pages 779–787, 1998. | MR | Zbl

[10] A. Fedotov and F. Klopp. Anderson transitions for quasi-periodic Schrödinger operators in dimension 1. in progress.

[11] A. Fedotov and F. Klopp. A complex WKB analysis for adiabatic problems. in progress.

[12] A. Fedotov and F. Klopp. The monodromy matrix for one-dimensional adiabatic quasi-periodic Schrödinger operators I. in progress.

[13] A. Fedotov and F. Klopp. The monodromy matrix for one-dimensional adiabatic quasi-periodic Schrödinger operators II. in progress.

[14] A. Fedotov and F. Klopp. The monodromy matrix for a family of almost periodic equations in the adiabatic case. Preprint, Fields Institute, Toronto, 1997.

[15] D. Gilbert and D. Pearson. On subordinacy and analysis of the spectrum of one-dimensional Schrödinger operators. Journal of Mathematical Analysis and its Applications, 128:30–56, 1987. | MR | Zbl

[16] B. Helffer and J. Sjöstrand. Analyse semi-classique pour l’équation de Harper. Mémoires de la Société Mathématique de France, 34, 1988. | Numdam | Zbl

[17] B. Helffer and J. Sjöstrand. Semi-classical analysis for Harper’s equation III. Cantor structure of the spectrum. Mémoires de la Société Mathématique de France, 39, 1989. | Numdam | Zbl

[18] H. Hiramoto and M. Kohmoto. Electronic spectral and wavefunction properties of one-dimensional quasi-periodic systems: a scaling approach. International Journal of Modern Physics B, 164(3–4):281–320, 1992. | MR

[19] T. Janssen. Aperiodic Schrödinger operators. In R. Moody, editor, The Mathematics of Long-Range Aperiodic Order, pages 269–306. Kluwer, 1997. | MR | Zbl

[20] S. Jitomirskaya. Almost everything about the almost Mathieu operator. II. In XIth International Congress of Mathematical Physics (Paris, 1994), pages 373–382, Cambridge, 1995. Internat. Press. | MR | Zbl

[21] P. Kargaev and E. Korotyaev. Effective masses and conformal mappings. Communications in Mathematical Physics, 169:597–625, 1995. | MR | Zbl

[22] Y. Last. Almost everything about the almost Mathieu operator. I. In XIth International Congress of Mathematical Physics (Paris, 1994), pages 366–372, Cambridge, 1995. Internat. Press. | MR | Zbl

[23] Y. Last and B. Simon. Eigenfunctions, transfer matrices, and absolutely continuous spectrum of one-dimensional Schrödinger operator. Technical report, Caltech, 1996.

[24] V. Marchenko and I. Ostrovskii. A characterization of the spectrum of Hill’s equation. Math. USSR Sbornik, 26:493–554, 1975. | Zbl

[25] H. McKean and P. van Moerbeke. The spectrum of Hill’s equation. Inventiones Mathematicae, 30:217–274, 1975. | Zbl

[26] L. Pastur and A. Figotin. Spectra of Random and Almost-Periodic Operators. Springer Verlag, Berlin, 1992. | MR | Zbl

[27] V. Sprindzhuk. Metric theory of Diophantine approximation. Wiley, New-York, 1979. | MR | Zbl

[28] E.C. Titschmarch. Eigenfunction expansions associated with second-order differential equations. Part II. Clarendon Press, Oxford, 1958. | Zbl