Quantum Hall effect on the hyperbolic plane in the presence of disorder

Letters in Mathematical Physics

Volumn 47, Issue 3, 1999, Pages 215-236

  Carey, A ^a   Hannabus, K ^b   Mathai, V ^a  

^a UNIVERSITY OF ADELAIDE   (Australia)

^b NONE

Author keywords

C* algebras; Cyclic cohomology; Ergodic action; Fuchsian groups; Gaps in extended states; Harper operator; Hyperbolic space; K theory; Quantum Hall effect; Random potentials

Indexed keywords

EID: 0000246962     PISSN: 03779017     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1007589817182     Document Type: Article

References (24)

1. Bellissard, J., van Elst, A. and Schulz-Baldes, H.: The non-commutative geometry of the quantum Hall effect, J. Math. Phys. 35 (1994), 5373-5451.
2. Brüning, J. and Sunada, T.: On the spectrum of gauge-periodic elliptic operators. Méthodes semi-classiques, Vol. 2 (Nantes, 1991), Astérisque 210 (1992), 65-74.
3. Brüning, J. and Sunada, T.: On the spectrum of gauge-periodic elliptic operators. Méthodes semi-classiques, Vol. 2 (Nantes, 1991), Astérisque 210 (1992), 65-74.
4. Carey, A., Hannabuss, K., Mathai, V. and McCann, P.: Quantum Hall effect on the hyperbolic plane, Comm. Math. Phys, 190(3) (1998), 629-673.
5. Choi, M., Elliott, G. and Yui, N.: Gauss polynomials and the rotation algebra, Invent. Math. 99(2) (1990), 225-246.
6. Comtet, A.: On the Landau levels on the hyperbolic plane, Ann. Phys. 173 (1987), 185-209.
7. Comtet, A. and Houston, P.: Effective action on the hyperbolic plane in a constant external field, J. Math. Phys. 26 (1985), 185-191.
8. Connes, A.: Noncommutative differential geometry. Publ. Math. IHES 62 (1986), 257-360.
9. Connes, A.: Noncommutative Geometry, Academic Press, San Diego, 1994.
10. Gromov, M.: Volume and bounded cohomology, Publ. Math. IHES 56 (1982), 5-99.
11. Ji, R. and Schweitzer, L.: Spectral invariance of smooth crossed products, and rapid decay locally compact groups, K-Theory 10(3) (1996) 283-305.
12. Mathai, V.: in preparation.
13. McCann, P. J.: Geometry and the integer quantum Hall effect, in: A. L. Carey and M. K. Murray (eds), Geometric Analysis and Lie Theory in Mathematics and Physics, Cambridge Univ. Press, Cambridge, 1998, pp. 132-208.
14. Marcolli, M. and Mathai, V.: Twisted index theorem for good orbifolds and fractional quantum numbers, Preprint, 1998.
15. Mostow, G.: Strong Rigidity of Symmetric Spaces, Ann. of Math. Stud. 78, Princeton University Press, 1973.
16. Muhly, P., Renault, J. and Williams, P.: Equivalence and isomorphism for groupoid C*-algebras, J. Operator Theory 17 (1987), 3-22.
17. Nakamura, S. and Bellissard, J.: Low energy bands do not contribute to the quantum Hall effect, Comm. Math. Phys. 131 (1990), 283-305.
18. Renault, J.: A Groupoid Approach to C*-algebras, Lecture Notes in Math. 793, Springer, Berlin, 1980.
19. Renault, J.: Représentations des produits croisés d'algèbres de groupoïdes, J. Operator Theory 18 (1987), 67-97.
20. Renault, J.: The ideal structure of groupoid crossed product C*-algebras, J. Operator Theory 25 (1991), 3-36.
21. Rieffel, M.: C*-algebras associated with irrational rotations. Pacific J. Math. 93 (1981), 415-429.
22. Sunada, T.: A discrete analogue of periodic magnetic Schrödinger operators, Contemp. Math. 173 (1994), 283-299.
23. Xia, J.: Geometric invariants of the quantum hall effect, Comm. Math. Phys. 119 (1988), 29-50.
24. Zimmer, R.: Ergodic Theory and Semisimple Groups, Monogr. Math. 81, Birkhauser, Basel, 1984.