Lyapunov exponents for unitary Anderson models

Journal of Mathematical Physics

Volumn 48, Issue 4, 2007, Pages

  Hamza, Eman ^a   Stolz, Günter ^a  

^a UNIVERSITY OF ALABAMA AT BIRMINGHAM   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34247594524     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2713996     Document Type: Article

References (20)

1. Bellissard, J., Trends and Developments in the Eighties (World Scientific, Singapore, 1985), pp. 1-106.
2. Bougerol, P. and Lacroix, J., Products of Random Matrices with Applications to Schr ödinger Operators, Progress in Probability and Statistics Vol. 8 (Birkhäuser, Boston, MA, 1985).
3. Blatter, G. and Browne, D., " Zener tunneling and localization in small conducting rings., " Phys. Rev. B 37, 3856-3880 (1988).
4. Bourget, O., Howland, J. S., and Joye, A., " Spectral analysis of unitary band matrices., " Commun. Math. Phys. 234, 191-227 (2003).
5. Carmona, R. and Lacroix, J. Spectral Theory of Random Schrödinger Operators, Probability and its Applications (Birkhäuser, Boston, MA, 1990).
6. Cantero, M. J., Moral, L., and Velázquez, L., " Five-diagonal matrices and zeros of orthogonal polynomials on the unit circle., " Linear Algebr. Appl. 362, 29-56 (2003).
7. Chernov, N. and Dolgopyat, D., " Brownian Brownian motion-I., " Mem. Am. Math. Soc. (to be published).
8. Carmona, R., Klein, A., and Martinelli, F., " Anderson localization for Bernoulli and other singular potentials., " Commun. Math. Phys. 108, 41-66 (1987).
9. Combescure, M., Recurrent Versus Diffusive Quantum Behavior for Time Dependent Hamiltonians, Operator Theory, Advances and Applications Vol. 57 (Birkhäuser, Basel, 1992).
10. Damanik, D., Sims, R., and Stolz, G., " Localization for one-dimensional, continuum, Bernoulli-Anderson models., " Duke Math. J. 114, 59-100 (2002).
11. De Bìvre, S. and Germinet, F., " Dynamical localization for the random dimer Schrödinger operator., " J. Stat. Phys. 98, 1135-1148 (2000).
12. Dunlap, D. H., Phillips, P. W., and Wu, H.-L., " Absence of localization in a random-dimer model., " Phys. Rev. Lett. 65, 88-91 (1990).
13. Hamza, E., Joye, A., and Stolz, G., " Localization for random unitary operators., " Lett. Math. Phys. 75, 255-272 (2006).
14. Howland, J. S., Schrödinger Operators, Lecture Notes in Physics Vol. 403 (Springer, Berlin, 1992), pp. 100-122.
15. Jitomirskya, S., Schulz-Baldes, H., and Stolz, G., " Delocalization in random polymer models., " Commun. Math. Phys. 233, 27-48 (2003).
16. Joye, A., " Density of states and Thouless formula for random unitary band matrices., " Ann. Henri Poincare 5, 347-379 (2004).
17. Lenz, D. (unpublished).
18. Joye, A., " Fractional moment estimates for random unitary band matrices., " Lett. Math. Phys. 72, 51-64 (2005).
19. Simon, B., Orthogonal Polynomials on the Unit Circle, AMS Colloquium Publications Vols. 54.1 and 54.2 (American Mathematical Society, Providence, RI, 2005).
20. Walters, P., An Introduction to Ergodic Theory, Graduate Texts in Mathematics Vol. 79 (Springer-Verlag, New York, 1982).