About this Journal Submit a Manuscript Table of Contents
Advances in Mathematical Physics
Volume 2011 (2011), Article ID 393417, 17 pages
http://dx.doi.org/10.1155/2011/393417
Research Article

Generalized Binomial Probability Distributions Attached to Landau Levels on the Riemann Sphere

1Department of Mathematics, Faculty of Sciences, Mohammed V University, P.O. BOX 1014, Agdal, Rabat 10000, Morocco
2Department of Mathematics, Faculty of Technical Sciences, Sultan Moulay Slimane University, P.O. Box 523, Béni Mellal 23000, Morocco

Received 8 March 2011; Accepted 29 March 2011

Academic Editor: Ali Mostafazadeh

Copyright © 2011 A. Ghanmi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. D. Stoler, B. E. A. Saleh, and M. C. Teich, “Binomial states of the quantized radiation field,” Optica Acta, vol. 32, no. 3, pp. 345–355, 1985.
  2. R. Lo Franco, G. Compagno, A. Messina, and A. Napoli, “Bell's inequality violation for entangled generalized Bernoulli states in two spatially separate cavities,” Physical Review A, vol. 72, no. 5, pp. 1–9, 2005. View at Publisher · View at Google Scholar
  3. W. Feller, An Introduction to Probability Theory and Its Applications, vol. 1, John Wiley & Sons, New York, NY, USA, 2nd edition, 1957.
  4. E. V. Ferapontov and A. P. Veselov, “Integrable Schrödinger operators with magnetic fields: factorization method on curved surfaces,” Journal of Mathematical Physics, vol. 42, no. 2, pp. 590–607, 2001. View at Publisher · View at Google Scholar · View at MathSciNet
  5. J. Peetre and G. K. Zhang, “Harmonic analysis on the quantized Riemann sphere,” International Journal of Mathematics and Mathematical Sciences, vol. 16, no. 2, pp. 225–243, 1993. View at Publisher · View at Google Scholar
  6. G. Iwata, “Non-hermitian operators and eigenfunction expansions,” Progress of Theoretical Physics, vol. 6, pp. 216–226, 1951. View at Zentralblatt MATH
  7. R. Lo Franco, G. Compagno, A. Messina, and A. Napoli, “Correspondence between generalized binomial field states and coherent atomic states,” European Physical Journal, vol. 160, no. 1, pp. 247–257, 2008. View at Publisher · View at Google Scholar
  8. R. L. Franco, G. Compagno, A. Messina, and A. Napoli, “Generation of entangled two-photon binomial states in two spatially separate cavities,” Open Systems and Information Dynamics, vol. 13, no. 4, pp. 463–470, 2006. View at Publisher · View at Google Scholar
  9. R. Lo Franco, G. Compagno, A. Messina, and A. Napoli, “Generating and revealing a quantum superposition of electromagnetic-field binomial states in a cavity,” Physical Review A, vol. 76, no. 1, article 011804, 2007. View at Publisher · View at Google Scholar
  10. Hong-Chen Fu and Ryu Sasaki, “Generalized binomial states: ladder operator approach,” Journal of Physics A, vol. 29, no. 17, pp. 5637–5644, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. W. Magnus, F. Oberhettinger, and R. P. Soni, Formulas and Theorems for the Special Functions of Mathematical Physics, Springer, New York, NY, USA, 3rd edition, 1966.
  12. A. Hafoud, “Analyse spaectrale concrète d'une famille de déformation du Laplacien de Fubini-Study sur l'espace projectif complexe 2().,” , Ph.D. thesis, Department of Mathematics, Faculty of Sciences, Rabat, Morocco, 2002.
  13. J.-P. Gazeau, Coherent states in quantum physics, Wiley-VCH Verlag GmbH & Co. KGaA Weinheim, New York, NY, USA, 1st edition, 2009.
  14. N. J. Vilenkin and A. U. Klimyk, Representation of Lie Groups and Special Functions, vol. 1, 1991.
  15. Z. Mouayn, “Coherent states attached to the spectrum of the Bochner Laplacian for the Hopf fibration,” Journal of Geometry and Physics, vol. 59, no. 2, pp. 256–261, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  16. A. M. Perelomov, “Coherent states for arbitrary Lie group,” Communications in Mathematical Physics, vol. 26, pp. 222–236, 1972. View at Publisher · View at Google Scholar
  17. L. Mandel, “Sub-poissonian photon statistics in resonance fluorescence,” Optics Letters, vol. 4, pp. 205–207, 1979.