Skip to main content
SpringerLink
Log in

Geometric Forces on Point Fluxes in Quantum Hall Fluids

  • Published:
Journal of Statistical Physics Aims and scope Submit manuscript

Abstract

The forces that act on a point flux carrying an integral number of flux units in quantum Hall fluids are related to the adiabatic curvature associated with families of Landau Hamiltonians. We calculate the forces due to external fields, Lorentz and Magnus forces, and the forces due to mutual interaction of point fluxes. The forces are different for the plane and the torus, but agree at the thermodynamic limit of large tori.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  1. M. V. Berry, Proc. Roy. Soc. A 392:45 (1984); The quantum phase: Five years after, in Geometric Phases in Physics, A. Shapere and F. Wilezek, eds. (World Scientific, 1989).

    Google Scholar 

  2. B. Simon, Phys. Rev. Lett. 51:2167 (1983).

    Google Scholar 

  3. M. Tinkham, Introduction to Superconductivity (McGraw-Hill, 1975); E. B. Sonin, Rev. Mod. Phys. 59:87 (1987), and cond-mat/9606099.

  4. N. B. Kopnin, G. E. Volovik, and Ü. Parts, Europhys. Lett. 32:651 (1995).

    Google Scholar 

  5. D. J. Thouless, P. Ao, and Q. Niu, Phys. Rev. Lett. 76:3758 (1996).

    Google Scholar 

  6. R. Laughlin, in The Quantum Hall Effect, R. E. Prange and S. M. Girvin, eds. (Springer, 1987).

  7. M. Stone, The Quantum Hall Effect (World Scientific, Singapore, 1992).

    Google Scholar 

  8. B. I. Halperin, P. A. Lee, and N. Read, Phys. Rev. B 47:7312 (1993); R. L. Willet, R. R. Ruel, K. W. West, and L. N. Pfieffer, Phys. Rev. Lett. 71:3846 (1993).

    Google Scholar 

  9. D. H. Lee and M. P. A. Fisher, Int. J. Mod. Phys. 5:2675 (1991).

    Google Scholar 

  10. F. Wilczek, Fractional Statistics and Anyon Superconductivity (World Scientific, 1990).

  11. D. J. Thouless, J. Math. Phys. 35:1 (1994).

    Google Scholar 

  12. D. J. Thouless, M. Kohmoto, P. Nightingale, and M. den Nijs, Phys. Rev. Lett. 49:40 (1982).

    Google Scholar 

  13. R. Seiler, in Recent Developments in Quantum Mechanics, A. Boutet de Monvel et al., eds. (Kluwer, Netherland, 1991).

    Google Scholar 

  14. J. Zak, Phys. Rev. A 134:1602, ibid. 1607 (1964).

    Google Scholar 

  15. J. E. Avron, R. Seiler, and B. Simon, Comm. Math. Phys. 159: 399 (1994).

    Google Scholar 

  16. J. Bellissard, A. van Elst, and H. Schultz-Baldes, J. Math. Phys. 35:5373 (1994).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, Technion, 32000, Haifa, Israel

    J. E. Avron

  2. Steklov Mathematical Institute, 191011, St.-Petersburg, Russia

    P. G. Zograf

Authors
  1. J. E. Avron
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. G. Zograf
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Avron, J.E., Zograf, P.G. Geometric Forces on Point Fluxes in Quantum Hall Fluids. Journal of Statistical Physics 92, 1193–1201 (1998). https://doi.org/10.1023/A:1023013231163

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1023013231163

Search

Navigation