Centre de diffusion de revues académiques mathématiques

 
 
 
 

Séminaire Équations aux dérivées partielles (Polytechnique)

Table des matières de ce volume | Article précédent | Article suivant
Alexander Fedotov; Frédéric Klopp
Transitions d’Anderson pour des opérateurs de Schrödinger quasi-périodiques en dimension 1
Séminaire Équations aux dérivées partielles (Polytechnique) (1998-1999), Exp. No. 4, 14 p.
Article PDF | Analyses Zbl 1067.82507

Bibliographie

[1] S. Aubry and G. André. Analyticity breaking and Anderson localization in incommensurate lattices. Ann. Isr. Phys. Soc., 3, 133-164 1980.  MR 626837 |  Zbl 0943.82510
[2] J. Avron and B. Simon. Almost periodic Schrödinger operators, II. the integrated density of states. Duke Mathematical Journal, 50:369–391, 1983. Article |  MR 700145 |  Zbl 0544.35030
[3] J. Bellissard, R. Lima, and D. Testard. Metal-insulator transition for the Almost Mathieu model. Communications in Mathematical Physics, 88:207–234, 1983. Article |  MR 696805 |  Zbl 0542.35059
[4] V. Buslaev and A. Fedotov. Monodromization and Harper equation. In Séminaires d’équations aux dérivées partielles, volume XXI, Palaiseau, 1994. Ecole Polytechnique. Cedram |  Zbl 0880.34082
[5] R. Carmona and J. Lacroix. Spectral Theory of Random Schrödinger Operators. Birkhäuser, Basel, 1990.  MR 1102675 |  Zbl 0717.60074
[6] H.L. Cycon, R.G. Froese, W. Kirsch, and B. Simon. Schrödinger Operators. Springer Verlag, Berlin, 1987.  MR 883643 |  Zbl 0619.47005
[7] M. Eastham. The spectral theory of periodic differential operators. Scottish Academic Press, Edinburgh, 1973.  Zbl 0287.34016
[8] L. H. Eliasson. Discrete one-dimensional quasi-periodic Schrödinger operators with pure point spectrum. Acta Mathematica, 179:153–196, 1997.  MR 1607554 |  Zbl 0908.34072
[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 1648125 |  Zbl 0901.34043
[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 915965 |  Zbl 0666.34023
[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 0714.34130
[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 0725.34099
[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 1152689
[19] T. Janssen. Aperiodic Schrödinger operators. In R. Moody, editor, The Mathematics of Long-Range Aperiodic Order, pages 269–306. Kluwer, 1997.  MR 1460027 |  Zbl 0883.47087
[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 1370694 |  Zbl 1052.82539
[21] P. Kargaev and E. Korotyaev. Effective masses and conformal mappings. Communications in Mathematical Physics, 169:597–625, 1995. Article |  MR 1328738 |  Zbl 0828.34076
[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 1370693 |  Zbl 1052.82541
[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 0343.34016
[25] H. McKean and P. van Moerbeke. The spectrum of Hill’s equation. Inventiones Mathematicae, 30:217–274, 1975.  Zbl 0319.34024
[26] L. Pastur and A. Figotin. Spectra of Random and Almost-Periodic Operators. Springer Verlag, Berlin, 1992.  MR 1223779 |  Zbl 0752.47002
[27] V. Sprindzhuk. Metric theory of Diophantine approximation. Wiley, New-York, 1979.  MR 548467 |  Zbl 0482.10047
[28] E.C. Titschmarch. Eigenfunction expansions associated with second-order differential equations. Part II. Clarendon Press, Oxford, 1958.  Zbl 0097.27601
Copyright Cellule MathDoc 2019 | Crédit | Plan du site