Advertisement

International Journal of Theoretical Physics

, Volume 46, Issue 1, pp 116–129 | Cite as

Hamiltonians for the Quantum Hall Effect on Spaces with Non-Constant Metrics

  • Paul Francis Bracken
Article

Abstract

The problem of studying the quantum Hall effect on manifolds with non constant metric is addressed. The Hamiltonian on a space with hyperbolic metric is determined, and the spectrum and eigenfunctions are calculated in closed form. The hyperbolic disk is also considered and some other applications of this approach are discussed as well.

Keywords

quantum Hall effect hyperbolic metric Hamiltonian Laplace-Beltrami operator 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Andrews, G., Askey, R., Roy, R. (1999). Special Functions, Cambridge University Press, Cambridge.MATHGoogle Scholar
  2. Barut, A. O., Raczka, R. (1986). Theory of Group Representations, Applications, World Scientific, Singapore.Google Scholar
  3. Bracken, P. (2001). Canadian Journal of Physics 79, 1121.CrossRefADSGoogle Scholar
  4. Char, B. W., Geddes, K. O., Gonnet, G. H., Leong, B., Monagan, M., Watt, S. (1991). Maple Library Reference Manual, Waterloo Maple Publishing.Google Scholar
  5. Chandelier, F., Georgelin, Y., Masson, T., Wallet, J.-C. (2004). Annals of Physics 314, 476.MATHCrossRefADSMathSciNetGoogle Scholar
  6. Chen, J., Ping, J., Wang, F. (2002). Group Representation Theory for Physicists, World Scientific, Singapore.MATHGoogle Scholar
  7. Comtet, A. (1987). Annals of Physics 173, 185.CrossRefADSMathSciNetGoogle Scholar
  8. De Witt, B. S. (1957). Reviews of Modern Physics 29(3), 377.CrossRefADSMathSciNetGoogle Scholar
  9. Ezawa, Z. F. (2000). Quantum Hall Effects, World Scientific, Singapore.MATHGoogle Scholar
  10. Haldane, F. D. (1983). Physical Review Letters 51, 605.CrossRefADSMathSciNetGoogle Scholar
  11. Hu, J. P., Zhang, S. C. (2002). Physical Review B 66, 125301.CrossRefADSGoogle Scholar
  12. Iengo, R., Li, D. (1994). Nuclear Physics B 413, 735.MATHCrossRefADSMathSciNetGoogle Scholar
  13. Jellal, A. (2005). Nuclear Physics B 725, 554.MATHCrossRefADSMathSciNetGoogle Scholar
  14. Karabali, D., Nair, V. P. (2002). Nuclear Physics B 641, 533.MATHCrossRefADSMathSciNetGoogle Scholar
  15. Karabali, D., Nair, V. P. (2004). Nuclear Physics B 679, 427.MATHCrossRefADSMathSciNetGoogle Scholar
  16. Khare, A. (2005). Fractional Statistics, Quantum Theory, World Scientific, Singapore.Google Scholar
  17. Luke, Y. L. (1969). The Special Functions, their Approximation, Vol. 1, Academic Press, New York.Google Scholar
  18. Zhang, S. C., Hu, J. P., cond-mat/0110572.Google Scholar
  19. Zhang, S. C., Hu, J. P. (2001). Science 294, 823CrossRefADSGoogle Scholar

Copyright information

© Springer Science + Business Media, Inc. 2006

Authors and Affiliations

  • Paul Francis Bracken
    • 1
  1. 1.Department of MathematicsUniversity of TexasEdinburgUSA

Personalised recommendations