Dynamical localization for discrete and continuous random Schrödinger operators

Communications in Mathematical Physics

Volumn 194, Issue 2, 1998, Pages 323-341

  Germinet, F ^a   De Bievre S ^b  

^a UNIVERSITÉ PIERRE ET MARIE CURIE   (France)

^b UNIV LILLE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040163789     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200050360     Document Type: Article

References (27)

1. Aizenman, M.: Localization at weak disorder: Some elementary bounds. Rev. Math. Phys. 6, 1163-1182 (1994)
2. Barbaroux, J.M.: Dynamique quantique des milieux désordonnés. Thèse de doctorat, Toulon (1996)
3. Barbaroux, J.M., Combes, J.M., Hislop, P.D.: Landau Hamiltonian with unbounded random potentials. Preprint (1997)
4. Carmona, R., Klein, A., Martinelli, F.: Anderson localization for Bernoulli and other singular potentials. Commun. Math. Phys. 108, 41-66 (1987)
5. Carmona, R., Lacroix, J.: Spectral theory of random Schrödinger operator. Basel-Boston: Birkhaüser, 1990
6. Combes, J.M., Hislop, P.D.: Localization for some continuous, random Hamiltonian in d-dimension. J. Funct. Anal. 124, 149-180 (1994)
7. Combes, J.M., Hislop, P.D.: Landau Hamiltonians with random potentials: Localization and the density of states. Commun. Math. Phys. 177, 603-629 (1996)
8. Combes, J.M., Hislop, P.D., Mourre, E.: Spectral Averaging, Perturbation of Singular Spectra, and Localization. Trans. Amer. Math. Soc. 348, 4883-4894 (1996)
9. Cycon, H.L., Froese, R.G., Kirsch, W., Simon, B.: Schrödinger Operators. Berlin-Heidelberg-New York: Springer-Verlag, 1987
10. De Bièvre, S., Germinet, F.: Dynamical Localization for the random dimer model. Preprint (1998)
11. Del Rio, R., Jitomirskaya, S., Last, Y., Simon, B.: Operators with singular continuous spectrum IV: Hausdorff dimensions, rank one pertubations and localization. J. d'Analyse Math. 69, 153-200 (1996)
12. Delyon, F., Levy, Y., Souillard, Y.: Anderson localization for multi-dimensional systems at large disorder or large energy. Commun. Math. Phys. 100, 463-470 (1985)
13. Dorlas, T.C., Macris, N., Pulé, J.V: The Nature of the Spectrum for the Landau Hamiltonian with δ impurities. To appear in J. Stat. Phys.
14. von Dreifus, A., Klein, A.: A new proof of localization in the Anderson tight binding model. Commun. Math. Phys. 124, 285-299 (1989)
15. von Dreifus, H., Klein, A.: Localization for random Schrödinger operators with correlated potentials. Commun. Math. Phys. 140, 133-147 (1991)
16. Dunlap, D.H., Phillips, P.: Absence of localization in a random Dimer model. Phys. Rew. Lett. 61, 88 (1990)
17. Fröhlich, J., Spencer, T.: Absence of diffusion with Anderson tight binding model for large disorder or low energy. Commun. Math. Phys. 88, 151-184 (1983)
18. Fröhlich, J., Martinelli, F., Scoppola, E., Spencer, T.: Constructive proof of localization in the Anderson tight binding model. Commun. Math. Phys. 101, 21-46 (1985)
19. Germinet, F.: Dynamical Localization II with an Application to the Almost Mathieu Operator. Preprint (1997)
20. Jona-Lasinio, G., Martinelli, F., Scoppola, E.: Mutiple tunnelings in d-dimensions: a quantum particle in a hierarchical potential. Ann. Inst. Henri Poincaré, vol. 42, 73-108 (1985)
21. Klopp, F.: Localization for continuous Random Schrödinger Operators. Commun. Math. Phys. 167, 553-569 (1995)
22. Kunz, H.: Quantum Hall effect for electrons in random potential. Commun. Math. Phys. 112, 121-145 (1987)
23. Martinelli, F., Holden, H.: On absence of diffusion near the bottom of the spectrum for a random Schrödinger operator. Commun. Math. Phys. 93, 197-217 (1984)
24. Pastur, L., Figotin, A.: Spectra of Random and Almost-Periodic Operators. Berlin: Springer-Verlag, 1992
25. Reed, M., Simon, B.: Methods of modern mathematical physics Vol. I-IV, London: Academic Press, 1975
26. Simon, B., Wolff, T.: Singular continuous perturbation under rank one perturbation and localization for random Hamiltonians. Commun. Pure Appl. Math. 39, 75-90 (1986)
27. Wang, W.M.: Microlocalization, percolation and Anderson localization for the Schrödinger operator with a random potential. J. Funct. Anal. 146, 1-26 (1997)