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Journal of Statistical Physics

, Volume 14, Issue 1, pp 49–65 | Cite as

Generalized phase space method in spin systems-spin coherent state representation

  • Yoshinori Takahashi
  • Fumiaki Shibata
Articles

Abstract

A generalized phase space method for spin operators is developed. With the use of a spin coherent state representation, mapping rules from spin operators onto ac-number space are established; simple formulas to calculate the mappedc-number functions are also derived. A product theorem, which gives a way of mapping a product of operators, is obtained in an intuitive form. This can be advantageously used to transform a Liouville equation into ac-number equation. As an illustrative example, the method is applied to the Heisenberg model of a magnet.

Key words

Generalized phase space mapping rules product theorem quasi-probability function 

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References

  1. 1.
    E. Wigner,Phys. Rev. 40:749 (1932).Google Scholar
  2. 2.
    R. KuboJ. Phys. Soc. Japan 19:2127 (1964).Google Scholar
  3. 3.
    K. E. Cahill and R. J. GlauberPhys. Rev. 177:1857 (1969).Google Scholar
  4. 4.
    G. S. Agarwal and E. Wolf,Phys. Rev. D 2:2161 (1970).Google Scholar
  5. 5.
    R. J. Glauber,Phys. Rev. 131:2766 (1963).Google Scholar
  6. 6.
    H. Haken, inHandbuch der Physik, L. Genzel, ed., Springer Verlag, Berlin-Heidelberg (1970), XXV/2c. Light and Matter; M. Lax,Phys. Rev. 172:350 (1968); F. Shibata and Y. Saito,J. Phys. Soc. Japan 38:1580 (1975).Google Scholar
  7. 7.
    F. Haake,Springer Tracts in Modern Physics, No.66 (1973), p. 98.Google Scholar
  8. 8.
    Y. Takahashi and F. Shibata,J. Phys. Soc. Japan 38:656 (1975).Google Scholar
  9. 9.
    J. M. Radcliffe,J. Phys. A 4:313 (1971).Google Scholar
  10. 10.
    F. T. Arecchi, E. Courtens, R. Gilmore, and H. Thomas,Phys. Rev. A 6:2211 (1972).Google Scholar
  11. 11.
    J. Schwinger, inQuantum Theory of Angular Momentum, L. Biedenharn and H. van Dam, eds., Academic Press, New York (1965).Google Scholar
  12. 12.
    M. E. Rose,Elementary Theory of Angular Momentum, Wiley, New York (1957).Google Scholar
  13. 13.
    Y. Takahashi, Master's Thesis, Department of Physics, University of Tokyo (1975).Google Scholar

Copyright information

© Plenum Publishing Corporation 1976

Authors and Affiliations

  • Yoshinori Takahashi
    • 1
  • Fumiaki Shibata
    • 1
  1. 1.Department of PhysicsUniversity of TokyoTokyoJapan

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