Positivity of Lyapunov exponents for anderson-type models on two coupled strings

Electronic Journal of Differential Equations

Volumn 2007, Issue , 2007, Pages 1-18

  Boumaza, Hakim ^a   Stolz, Günter ^b  

^a INSTITUT DE MATHÉMATIQUES DE JUSSIEU   (France)

^b UNIVERSITY OF ALABAMA AT BIRMINGHAM   (United States)

Author keywords

Anderson model; Lyapunov exponents; Random operators

Indexed keywords

EID: 33947521537     PISSN: None     EISSN: 10726691     Source Type: Journal    
DOI: None     Document Type: Article

References (22)

1. S.ALBEVERIO, F.GESZTESY, R.HOEGH-K ROHN and H.HOLDEN, Solvable Models in Quantum Mechanics, Texts and Monographs in Physics) Springer, Berlin, 1988.
2. Y. BENOIST, Sous-groupes discrets des groupes de Lie, European Summer School in Group Theory, 1997.
3. P.BOUGEROL and J.LACROIX, Products of Random Matrices with Applications to Schrödinger Operators, Progr. Probab. Statist. 8, Birkhäuser, Boston, 1985.
4. R.CARMONA, A.KLEIN and F.MARTINELLI, Anderson localization for Bernoulli and other singular potentials, Commun. Math. Phys. 108 (1987), 41-66
5. R.CARMONA and J.LACROIX, Spectral Theory of Random Schrödinger Operators, Probability and Its Applications, Birkhäuser, Boston, 1990.
6. D.DAMANIK, Lyapunov exponents and spectral analysis of ergodic Schrödinger operators: A survey of Kotani theory and its applications, Preprint 2006, arXiv:math-ph/0605054
7. D.DAMANIK, D.LENZ and G.STOLZ, Lower Transport Bounds for One-dimensional Continuum Schrödinger Operators, Math. Ann. 336 (2006), 361-389.
8. D.DAMANIK, R.SIMS and G.STOLZ, Lyapunov exponents in continuum Bernoulli-Anderson models, Operator Theory : Advances and Applications 132, 121-130, Birkhaüser 2002.
9. D.DAMANIK, R. SIMS and G. STOLZ, Localization for one-dimensional, continuum, Bernoulli-Anderson models, Duke Mathematical Journal 114 (2002), 59-99.
10. C.GLAFFIG, Smoothness of the integrated density of states on strips, J. Funct. Anal. 92 (1990), 509-534.
11. I. YA. GOL'DSHEID and G.A. MARGULIS, Lyapunov indices of a product of random matrices, Russian Math. Survey 44:5 (1989), 11-71.
12. Y.GUIVARC'H and A.RAUGI, Frontière de Furstenberg, propriétés de contraction et théorèmes de convergence, Z. Wahrsch. Verw. Gebiete 69 (1985), no. 2, p.187-242.
13. Y.GUIVARC'H and A.RAUGI, Propriétés de contraction d'un semi-groupe de matrices inversibles. Coefficients de Liapunoff d'un produit de matrices aléatoires indépendantes, Israel J. Math. 65 (1989), no. 2, 165-196.
14. S.JITOMIRSKAYA, H.SCHULZ-BALDES and G.STOLZ, Delocalization in random polymer models, Commun. Math. Phys. 233 (2003), 27-48
15. W.KIRSCH, On a class of Random Schrödinger Operators, Advances in Applied Mathematics 6 (1985), p.177-187
16. W.KIRSCH, S.MOLCHANOV and L.PASTUR, One dimensional Schrödinger operator with unbounded potential: pure point spectrum, I., Funct. Anal. Appl., 3 (1990), 24-28
17. W.KIRSCH, S.MOLCHANOV, L.PASTUR and B.VAINBERG, Quasi ID localization: Deterministic and random potentials, Markov Processes Relat. Fields, 9 (2003), 687-708
18. A.KLEIN, J.LACROIX and A.SPEIS, Localization for the Anderson model on a Strip with Singular Potentials, J. Func. Anal. 94 (1990), 135-155.
19. S.KOTANI and B.SIMON, Stochastic Schrödinger operators and Jacobi Matrices on the Strip, Commun. Math. Phys. 119 (1988), no. 3, 403-429.
20. B.SIMON and T.SPENCER, Trace class perturbation and the absence of absolutely continuous spectrum, Commun. Math. Phys. 125 (1989), 113-125
21. P.STOLLMANN, Caught by Disorder -Bound States in Random Media, Progress in Mathematical Physics, Vol.20, Birkhäuser, 2001
22. G. STOLZ, Strategies in localization proofs for one-dimensional random Schrödinger operators, Proc. Indian Acad. Sci, 112 (2002), 229-243.