User menu

(p,q) deformations and (p,q)-vector coherent states of the Jaynes-Cummings model in the rotating wave approximation

Bibliographic reference Ben Geloun, Joseph ; Govaerts, Jan ; Hounkonnou, M. Norbert. (p,q) deformations and (p,q)-vector coherent states of the Jaynes-Cummings model in the rotating wave approximation. In: Journal of Mathematical Physics, Vol. 48, no.3, p. 032107 (2007)
Permanent URL http://hdl.handle.net/2078.1/184886
  1. Drinfeld V. G., On some unsolved problems in quantum group theory, Lecture Notes in Mathematics (1992) ISBN:9783540553052 p.1-8, 10.1007/bfb0101175
  2. Lorek A., Wess J., Dynamical symmetries inq-deformed quantum mechanics, 10.1007/bf01553994
  3. Arik M., Hilbert spaces of analytic functions and generalized coherent states, 10.1063/1.522937
  4. Biedenharn L C, The quantum group SUq(2) and a q-analogue of the boson operators, 10.1088/0305-4470/22/18/004
  5. Chakrabarti R, Jagannathan R, A (p, q)-oscillator realization of two-parameter quantum algebras, 10.1088/0305-4470/24/13/002
  6. Jackson F., Mess. Math., 38, 57 (1909)
  7. Ramanujan S., Mess. Math., 44, 10 (1915)
  8. Exton H., -Hypergeometric Functions and Application (1983)
  9. Floreanini R, LeTourneux J, Vinet L, More on the q-oscillator algebra and q-orthogonal polynomials, 10.1088/0305-4470/28/10/002
  10. Floreanini R, Lapointe L, Vinet L, A note on (p, q)-oscillators and bibasic hypergeometric functions, 10.1088/0305-4470/26/14/004
  11. R. Koekoek and R. F. Swarttouw, Delft University Technology, Report No. 94-05, 1994 (unpublished).
  12. Jaynes E.T., Cummings F.W., Comparison of quantum and semiclassical radiation theories with application to the beam maser, 10.1109/proc.1963.1664
  13. Meystre P., Wright E. M., Measurements-induced dynamics of a micromaser, 10.1103/physreva.37.2524
  14. Hussin V., Nieto L. M., Ladder operators and coherent states for the Jaynes-Cummings model in the rotating-wave approximation, 10.1063/1.2137718
  15. Bérubé-Lauzière Y., Hussin V., Nieto L. M., Annihilation operators and coherent states for the Jaynes-Cummings model, 10.1103/physreva.50.1725
  16. Daoud M, Hussin V, General sets of coherent states and the Jaynes$ndash$Cummings model, 10.1088/0305-4470/35/34/310
  17. DAOUD M., DOUARI J., A GENERALIZED JAYNES–CUMMINGS MODEL: NONLINEAR DYNAMICAL SUPERALGEBRA u(1/1) AND SUPERCOHERENT STATES, 10.1142/s0217979203018302
  18. Balantekin A. B. (2003)
  19. Balantekin A B, Dereli T, Pehlivan Y, An exactly solvable model of interacting bosons, 10.1088/0954-3899/30/9/020
  20. Buck B., Sukumar C.V., Exactly soluble model of atom-phonon coupling showing periodic decay and revival, 10.1016/0375-9601(81)90042-6
  21. Chaichian M., Ellinas D., Kulish P., Quantum algebra as the dynamical symmetry of the deformed Jaynes-Cummings model, 10.1103/physrevlett.65.980
  22. Chang Zhe, Generalized Jaynes-Cummings model with an intensity-dependent coupling interacting with a quantum group-theoretic coherent state, 10.1103/physreva.47.5017
  23. H. Naderi M., Soltanolkotabi M., Roknizadeh R., Dynamical Properties of a Two-Level Atom in Three Variants of the Two-Photonq-Deformed Jaynes–Cummings Model, 10.1143/jpsj.73.2413
  24. Marchiolli Marcelo A, Missori Ricardo J, Roversi José A, Qualitative aspects of entanglement in the Jaynes–Cummings model with an external quantum field, 10.1088/0305-4470/36/49/010
  25. Chakrabarti R, Jagannathan R, A two-parameter deformation of the Jaynes-Cummings model: path integral representation, 10.1088/0305-4470/25/23/033
  26. Dresselhaus G., Spin-Orbit Coupling Effects in Zinc Blende Structures, 10.1103/physrev.100.580
  27. SCHLIEMANN JOHN, SPIN HALL EFFECT, 10.1142/s021797920603370x
  28. Shen Shun-Qing, Bao Yun-Juan, Ma Michael, Xie X. C., Zhang Fu Chun, Resonant spin Hall conductance in quantum Hall systems lacking bulk and structural inversion symmetry, 10.1103/physrevb.71.155316
  29. Shen Shun-Qing, Ma Michael, Xie X. C, Zhang Fu Chun, Resonant Spin Hall Conductance in Two-Dimensional Electron Systems with a Rashba Interaction in a Perpendicular Magnetic Field, 10.1103/physrevlett.92.256603
  30. Ali S. Twareque, Bagarello F., Some physical appearances of vector coherent states and coherent states related to degenerate Hamiltonians, 10.1063/1.1901343
  31. Gazeau Jean Pierre, Klauder John R, Coherent states for systems with discrete and continuous spectrum, 10.1088/0305-4470/32/1/013
  32. Antoine J.-P., Gazeau J.-P., Monceau P., Klauder J. R., Penson K. A., Temporally stable coherent states for infinite well and Pöschl–Teller potentials, 10.1063/1.1367328
  33. Ali Syed Twareque, Antoine Jean-Pierre, Gazeau Jean-Pierre, Coherent States, Wavelets and Their Generalizations, ISBN:9781461270652, 10.1007/978-1-4612-1258-4
  34. Scholtz Frederik G, Chakraborty Biswajit, Gangopadhyay Sunandan, Govaerts Jan, Interactions and non-commutativity in quantum Hall systems, 10.1088/0305-4470/38/45/008
  35. Scholtz Frederik G., Chakraborty Biswajit, Gangopadhyay Sunandan, Hazra Arindam Ghosh, Dual families of noncommutative quantum systems, 10.1103/physrevd.71.085005
  36. Hounkonnou M N, Sodoga K, Generalized coherent states for associated hypergeometric-type functions, 10.1088/0305-4470/38/36/004
  37. Simon Barry, The Classical Moment Problem as a Self-Adjoint Finite Difference Operator, 10.1006/aima.1998.1728
  38. Klauder J. R. (2001)
  39. Hinrichsen Haye, Kempf Achim, Maximal localization in the presence of minimal uncertainties in positions and in momenta, 10.1063/1.531501
  40. Quesne C., Penson K.A., Tkachuk V.M., Maths-type q-deformed coherent states for q>1, 10.1016/s0375-9601(03)00732-1
  41. Quesne C, Newq-deformed coherent states with an explicitly known resolution of unity, 10.1088/0305-4470/35/43/316
  42. Penson K. A., Solomon A. I., New generalized coherent states, 10.1063/1.532869
  43. Aragone C, Zypman F, Supercoherent states, 10.1088/0305-4470/19/12/014
  44. Orszag M, Salamo S, Squeezing and minimum uncertainty states in the supersymmetric harmonic oscillator, 10.1088/0305-4470/21/22/004
  45. F. Cooper, A. Khare, and U. Sukhatme, Supersymmetry in Quantum Mechanics, 2nd ed. (World Scientific, Singapore, 2004).
  46. Burban Ivan M., Klimyk Anatoli U., P,Q-differentiation, P,Q-integration, and P,Q-hypergeometric functions related to quantum groups, 10.1080/10652469408819035
  47. Gasper G., Basic Hypergeometric Series (1990)