Journal of Statistical Physics

, Volume 82, Issue 5–6, pp 1659–1668 | Cite as

Haldane exclusion statistics and the Boltzmann equation

  • R. K. Bhaduri
  • R. S. Bhalerao
  • M. V. N. Murthy
Short Communications


We generalize the collision term in the one-dimensional Boltzmann-Nordheim transport equation for quasiparticles that obey the Haldane exclusion statistics. For the equilibrium situation, this leads to the “golden rule” factor for quantum transitions. As an application of this, we calculate the density response function of a one-dimensional electron gas in a periodic potential, assuming that the particle-hole excitations are quasiparticles obeying the new statistics. We also calculate the relaxation time of a nuclear spin in a metal using the modified golden rule.

Key Words

Haldane exclusion statistics Boltzmann equation Fermigolden rule density response function 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    F. D. M. Haldane,Phys. Rev. Lett. 67:937 (1991).Google Scholar
  2. 2.
    F. D. M. Haldane,Phys. Rev. Lett. 60:635 (1988); B. S. Shastry,Phys. Rev. Lett. 60:639 (1988).Google Scholar
  3. 3.
    M. V. N. Murthy and R. Shankar,Phys. Rev. Lett. 72:3629 (1994).Google Scholar
  4. 4.
    A. Dasnières de Veigy and S. Ouvry,Phys. Rev. Lett. 72:600 (1994).Google Scholar
  5. 5.
    Y.-S. Wu,Phys. Rev. Lett. 73:922 (1994).Google Scholar
  6. 6.
    F. Calogero,J. Math. Phys. 10:2197 (1969).Google Scholar
  7. 7.
    B. Sutherland,J. Math. Phys. 12:246, 251 (1971);Phys. Rev. A 4:2019 (1971).Google Scholar
  8. 8.
    R. K. Bhaduri, M. V. N. Murthy, and M. K. Srivastava, McMaster University preprint (July 1995) cond-mat/9510085.Google Scholar
  9. 9.
    F. D. M. Haldane,Phys. Rev. Lett. 66:1529 (1991).Google Scholar
  10. 10.
    R. A. Cowley, D. A. Tennant, S. E. Nagler, and T. Perring,J. Magnetism Magnetic Materials 140–144:1651 (1995).Google Scholar
  11. 11.
    G. Mueller, H. Thomas, H. Beck, and J. C. Bonner,Phys. Rev. B 24:1429 (1981).Google Scholar
  12. 12.
    F. D. M. Haldane and M. R. Zirnbauer,Phys. Rev. Lett. 71:4055 (1993).Google Scholar
  13. 13.
    L. W. Nordheim,Proc. R. Soc. Lond. A 199:689 (1928).Google Scholar
  14. 14.
    J. J. Sakurai,Advanced Quantum Mechanics (Berjamin, Menlo Park, California, 1984), p. 38.Google Scholar
  15. 15.
    S. R. de Groot, W. A. van Leeuwen, and Ch. G. van Weert,Relativistic Kinetic Theory (North-Holland, Amsterdam, 1980).Google Scholar
  16. 16.
    S. Kagoshima, H. Nagasawa, and T. Sambongi,One-Dimensional Conductors (Springer-Verlag, Berlin, 1988), Chapter 2.Google Scholar
  17. 17.
    A. Abragam,The Principles of Nuclear Magnetism (Oxford, London, 1962), p. 358.Google Scholar

Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • R. K. Bhaduri
    • 1
  • R. S. Bhalerao
    • 2
  • M. V. N. Murthy
    • 3
  1. 1.Department of Physics and AstronomyMcMaster UniversityHamiltonCanada
  2. 2.Theoretical Physics GroupTata Institute of Fundamental ResearchBombayIndia
  3. 3.Institute of Mathematical SciencesMadrasIndia

Personalised recommendations