Localization Properties of the Chalker-Coddington Model

Annales Henri Poincare

Volumn 11, Issue 7, 2010, Pages 1341-1373

  Asch, Joachim ^a   Bourget, Olivier ^b   Joye, Alain ^c  

^a Universite du Sud   (France)

^b PONTIFICIA UNIVERSIDAD CATÓLICA DE CHILE   (Chile)

^c INSTITUT FOURIER   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 78649639592     PISSN: 14240637     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00023-010-0056-1     Document Type: Article

References (27)

1. Arnold L.: Random dynamical systems. Springer Monographs in Mathematics. Springer, Berlin (1998).
2. Avron J. E., Seiler R., Simon B.: Charge deficiency, charge transport and comparison of dimensions. Comm. Math. Phys. 159, 399-422 (1994).
3. Bourget O.: Singular continuous Floquet operator for periodic quantum systems. J. Math. Anal. Appl. 301, 65-83 (2005).
4. Bourget O., Howland J. S., Joye A.: Spectral analysis of unitary band matrices. Commun. Math. Phys. 234, 191-227 (2003).
5. Bougerol, P., Lacroix, J.: Products of Random Matrices with Applications to Schrödinger Operators. Progress in Probability and Statistics, vol. 8. Birkhäuser, Boston (1985).
6. Boumaza H.: Hölder continuity of the IDS for matrix-valued Anderson models. Rev. Math. Phys. 20, 873-900 (2008).
7. Boumaza H., Stolz G.: Positivity of Lyapunov exponents for Anderson-type models on two coupled strings. Elecron. J. Differ. Equ. 47, 11-18 (2007).
8. Bellissard J., van Elst A., Schulz-Baldes H.: The noncommutative geometry of the quantum Hall effect. J. Math. Phys. 35, 5373-5451 (1994).
9. Combescure M.: Spectral properties of a periodically kicked quantum Hamiltonian. J. Stat. Phys. 59, 679-690 (1990).
10. Chalker J. T., Coddington P. D.: Percolation, quantum tunneling and the integer Hall effect. J. Phys. C 21, 2665-2679 (1988).
11. Colin de Verdière Y., Parisse B.: Équilibre instable en régime semi-classique. I. Concentration microlocale. Commun. Partial Differ. Equ. 19, 1535-1563 (1994).
12. Craig W., Simon B.: Subharmonicity of the Lyaponov index. Duke Math. J. 50, 551-560 (1983).
13. Craig W., Simon B.: Log Hölder continuity of the integrated density of states for stochastic Jacobi matrices. Commun. Math. Phys. 90(2), 207-218 (1983).
14. Fertig H. A., Halperin B. I.: Transmission coefficient of an electron through a saddle-point potential in a magnetic field. Phys. Rev. B 36, 7969-7976 (1987).
15. Graf, G. M.: Aspects of the integer quantum Hall effect. Spectral theory and mathematical physics: a Festschrift in honor of Barry Simon's 60th birthday. In: Proceedings of symposium of Pure Mathematics vol. 76, Part 1, pp. 429-442. American Mathematical Society, Providence, RI (2007).
16. Germinet F., Klein A., Schenker J.: Dynamical delocalization in random Landau Hamiltonians. Ann. Math. 166, 215-244 (2007).
17. Goldsheǐd I. Ya., Margulis G. A.: Lyapunov exponents of a product of random matrices. Uspekhi Mat. Nauk 44, 13-60 (1989).
18. Helffer B., Sjöstrand J.: Analyse semi-classique pour l'équation de Harper. Mémoires de la S. M. F. 34, 1-113 (1988).
19. Hamza E., Joye A., Stolz G.: Localization for random unitary operators. Lett. Math. Phys. 75, 255-272 (2006).
20. Joye A.: Density of states and Thouless formula for random unitary band matrices. Ann. Henri Poincaré 5, 347-379 (2004).
21. Kramer B., Ohtsuki T., Kettemann S.: Random network models and quantum phase transitions in two dimensions. Phys. Rep. 417, 211-342 (2005).
22. Kotani S., Simon B.: Localization in general one-dimensional random systems. Commun. Math. Phys. 112, 103-119 (1987).
23. Roemer, R., Schulz-Baldes, H.: Random phase property and the Lyapunov spectrum for disordered multi-channel systems (preprint, 2009). http://de. arxiv. org/abs/0910. 5808.
24. Simon B.: Trace ideals and their applications, 2nd edn. Mathematical Surveys and Monographs, 120. American Mathematical Society (2005).
25. Trugman S. A.: Localization, percolation, and the quantum Hall effect. Phys. Rev. B 27, 7539-7546 (1983).
26. Thouless D. J., Kohmoto M., Nightingale M. P., den Nijs N.: Quantized Hall conductance in a two-dimensional periodic potential. Phys. Rev. Lett. 49, 405-408 (1982).
27. Wang W. M.: Microlocalization, percolation, and Anderson localization for the magnetic Schrödinger operator with a random potential. J. Funct. Anal. 146, 1-26 (1997).