Skip to main content
SpringerLink
Log in

Generalized Spin Coherent States: Construction and Some Physical Properties

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

Abstract

A generalized deformation of the su(2) algebra and a scheme for constructing associated spin coherent states is developed. The problem of resolving the unity operator in terms of these states is addressed and solved for some particular cases. The construction is carried using a deformation of Holstein-Primakoff realization of the su(2) algebra. The physical properties of these states is studied through the calculation of Mandel’s parameter.

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. Schrödinger, E.: The constant crossover of micro-to macro mechanics. Naturwissenschaften 14, 664 (1926)

    Article  ADS  Google Scholar 

  2. Glauber, R.: The quantum theory of optical coherence. Phys. Rev. 130, 2529 (1963)

    Article  MathSciNet  ADS  Google Scholar 

  3. Glauber, R.: Coherent and incoherent states of radiation field. Phys. Rev. 131, 2766 (1963)

    Article  MathSciNet  ADS  Google Scholar 

  4. Klauder, J.R.: Continuous representation theory. I. Postulates of continuous representation theory. J. Math. Phys. 4, 1055 (1963)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  5. Klauder, J.R.: Generalized relation between quantum and classical dynamics. J. Math. Phys. 4, 1058 (1963)

    Article  MathSciNet  ADS  Google Scholar 

  6. Klauder, J.R., Skagertan, B.-S.: Coherent States. World Scientific, Singapore (1985)

    MATH  Google Scholar 

  7. Perelomov, A.M.: Generalized Coherent States and Their Applications. Springer, Berlin (1986)

    MATH  Google Scholar 

  8. Ali, S.T., Antoine, J.-P., Gazeau, J.-P.: Coherent States, Wavelets and Their Generalizations. Springer, New York (2000)

    Book  MATH  Google Scholar 

  9. Sklyanin, E.K.: Funct. Anal. Appl. 16, 262 (1982)

    MathSciNet  Google Scholar 

  10. de Boer, J., Harmsze, F., Tjin, T.: Non-linear finite W-symmetries and applications in elementary systems. Phys. Rep. 272, 139 (1996)

    Article  MathSciNet  ADS  Google Scholar 

  11. Kulish, P.P., Reshetikhin, N.Y.: J. Sov. Math. 23, 2435 (1983)

    Article  Google Scholar 

  12. Drinfeld, V.G.: In: Gleason, A.M. (ed.) Proceedings of ICM, Berkeley, 1986, p. 798. Am. Math. Soc., Berkeley (1987)

    Google Scholar 

  13. Bonatsos, D., Kolokotronis, P., Daskaloyannis, C.: Generalized deformed su(2) algebras, deformed parafermionic oscillators and finite W-algebras. Mod. Phys. Lett. A 10, 2197 (1995)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  14. Perelomov, A.M.: Coherent states for arbitrary Lie group. Commun. Math. Phys. 26, 222 (1972)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  15. Gilmore, R.: Geometry of symmetrized states. Ann. Phys. (N.Y.) 74, 391 (1972)

    Article  MathSciNet  ADS  Google Scholar 

  16. Drinfeld, V.G.: Quantum groups. In: Proc. of the 1986 Int. Congress of Math., p. 798. AMS, Berkeley (1987)

    Google Scholar 

  17. Jimbo, M.: A q-difference analogue of U(g) and the Yang-Baxter equation. Lett. Math. Phys. 10, 63 (1985)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  18. El Baz, M., Hassouni, Y., Madouri, F.: New construction of coherent states for generalized harmonic oscillators. Rep. Math. Phys. 50, 263 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  19. Jurčo, B.: On coherent states for the simplest quantum groups. Lett. Math. Phys. 21, 51 (1991)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  20. Ellinas, D.: Path integrals for quantum algebras and the classical limit. J. Phys. A 26, L543 (1993)

    Article  MathSciNet  ADS  Google Scholar 

  21. Macfarlane, A.J.: On q-Analogues of the quantum harmonic oscillator and the quantum group SU q (2). J. Phys. A 22, 4581 (1989)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  22. Arik, M., Coon, D.D.: Hilbert spaces of analytic functions and generalized coherent states. J. Math. Phys. 17, 524 (1976)

    Article  MathSciNet  ADS  Google Scholar 

  23. Katriel, J., Solomon, A.I.: Nonideal lasers, nonclassical light, and deformed photon states. Phys. Rev. A 49, 5149 (1994)

    Article  ADS  Google Scholar 

  24. Aizawa, N., Chakrabarti, R.: Coherent state on SU q (2) homogeneous space. J. Phys. A 42, 295208 (2009)

    Article  MathSciNet  Google Scholar 

  25. Berrada, K., El Baz, M., Saif, F., Hassouni, Y., Mnia, S.: Entanglement generation from deformed spin coherent states using a beam splitter. J. Phys. A, Math. Theor. 42, 285306 (2009)

    Article  Google Scholar 

  26. Bonatsos, D., Daskaloyannis, C., Kolokotronis, P.: Generalized deformed SU(2) algebra. J. Phys. A, Math. Gen. 26, L871 (1993)

    Article  MathSciNet  ADS  Google Scholar 

  27. El Baz, M., Hassouni, Y.: Special deformed exponential functions leading to more consistent Klauder’s coherent states. Phys. Lett. A 300, 361 (2002)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  28. Curado, E.M.F., Rego-Monteiro, M.A.: Multi-parametric deformed Heisenberg algebras: a route to complexity. J. Phys. A 34, 3253 (2001)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  29. Biedenharn, L.C.: The quantum group SU q (2) and a q-analogue of the boson operators. J. Phys. A 22, L873 (1989)

    Article  MathSciNet  ADS  Google Scholar 

  30. Perelomov, A.M.: On the completeness of some subsystems of q-deformed coherent states. Helv. Phys. Acta 68, 554 (1996)

    MathSciNet  Google Scholar 

  31. Barbier, R., Meyer, J., A Kibler, M.: Uqp(u2) model for rotational bands of nuclei. J. Phys. G, Nucl. Part. Phys. 20, L13–L19 (1994)

    Article  ADS  Google Scholar 

  32. Zhangb, S.: The specific heat and equation of state for the q-analogue of the harmonic lattice. Phys. Lett. A 202, 18 (1995)

    Article  MathSciNet  ADS  Google Scholar 

  33. Arik, M., Atakishiyev, N.M., Wolf, K. Bernardo: Quantum algebraic structures compatible with the harmonic oscillator Newton equation. J. Phys. A, Math. Gen. 32, L371–L376 (1999)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  34. Schwinger, J.: In: Biedenharn, L.C., Van Dam, H. (eds.) On the Quantum Theory of Angular Momentum. Academic Press, New York (1965)

    Google Scholar 

  35. Jordan, P.: Der Zusammenhang der symmetrischen une linearen Gruppen und das Mehrkörperpoblem. Z. Phys. 94, 531 (1935)

    Article  MATH  ADS  Google Scholar 

  36. Holstein, T., Primakoff, H.: Field dependence of the intrinsic domain magnetization of a ferromagnet. Phys. Rev. 58, 1098 (1940)

    Article  MATH  ADS  Google Scholar 

  37. Gazeau, J.P., Champagne, B.: The Fibonacci-deformed harmonic oscillator. In: Algebraic Methods in Physics. CRM Series in Theoretical and Mathematical Physics, vol. 3. Springer, Berlin (2001)

    Google Scholar 

  38. Jurčo, B., Stovicek, P.: Coherent states for quantum compact groups. Commun. Math. Phys. 182, 221 (1996)

    Article  MATH  ADS  Google Scholar 

  39. Skoda, Z.: Coherent states for Hopf algebras. Lett. Math. Phys. 81, 1 (2007)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  40. Gasper, G., Rahman, M.: Basic Hypergeometric Series. Encyclopedia of Mathematics and Its Applications, vol. 35. Cambridge University Press, Cambridge (1990)

    MATH  Google Scholar 

  41. Klauder, J.R., Penson, K.A., Sixdeniers, J.-M.: Constructing coherent states through solutions of Stieltjes and Hausdorff moment problems. Phys. Rev. A 64, 013817 (2001)

    Article  ADS  Google Scholar 

  42. Chakrabarti, R., Vassan, S.S.: J. Phys. A, Math. Gen. 37, 10561 (2004)

    Article  MATH  ADS  Google Scholar 

  43. Paris, R.B., Kaminski, D.: Asymptotic and Mellin-Barnes integrals. Cambridge University Press, Cambridge (2001)

    Book  Google Scholar 

  44. Mandel, L., Wolf, E.: Optical Coherence and Quantum Optics. Cambridge University Press, Cambridge (1995)

    Google Scholar 

  45. Quesne, C.: New q-deformed coherent states with an explicitly known resolution of unity. J. Phys. A, Math. Gen. 35, 9213 (2002)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  46. Chakrabarti, R., Jagannathan, R.: A (p,q)-oscillator realization of two-parameter quantum algebras. J. Phys. A 24, L711 (1991)

    Article  MathSciNet  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratoire de Physique Théorique, Faculté des Sciences, Université Mohammed V-Agdal, Av. Ibn Battouta, B.P. 1014, Agdal Rabat, Morocco

    K. Berrada, M. El Baz & Y. Hassouni

  2. The Abdus Salam International Centre for Theoretical Physics, Trieste, Italy

    K. Berrada

Authors
  1. K. Berrada
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. El Baz
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Y. Hassouni
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to K. Berrada.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Berrada, K., Baz, M.E. & Hassouni, Y. Generalized Spin Coherent States: Construction and Some Physical Properties. J Stat Phys 142, 510–523 (2011). https://doi.org/10.1007/s10955-011-0124-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10955-011-0124-z

Keywords

Search

Navigation