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Prog. Theor. Phys. Vol. 91 No. 1 (1994) pp. 49-67

[ Full Text PDF : FREE ACCESS (1735K) ]

A Possible Classical Description for su(1, 1)-Spin Systems

Yasuhiko Tsue, Atsushi Kuriyama* and Masatoshi Yamamura*

Department of Physics, Kochi University, Kochi 780
*Faculty of Engineering, Kansai University, Suita 564

(Received July 28, 1993)

Abstract:

With the aim of investigating dynamics of systems governed by su(1, 1)-algebra, a possible state which can give us a classical counterpart for the su(1, 1)-spin system properly is examined and constructed explicitly. By the use of canonicity conditions developed in the time-dependent Hartree-Fock theory, the c-number analogue of the Holstein-Primakoff boson representation is obtained for the su(1, 1)-algebra. It is noted that it is important to introduce a character of two-mode coherent state in order to present a suitable classical counterpart for the su(1, 1)-spin. Furthermore, it is shown that the spreading of uncertainty relations appears inevitably, which suggests that a certain fluctuation can be introduced.


URL : http://ptp.ipap.jp/link?PTP/91/49/
DOI : 10.1143/PTP.91.49

[ Full Text PDF : FREE ACCESS (1735K) ] Citation:

References:

  1. M. Yamamura and A. Kuriyama, Prog. Theor. Phys. Suppl. No. 93 (1987) and references cited therein.
  2. M. Yamamura, A. Kuriyama and Y. Tsue, Prog. Theor. Phys. 88 (1992), 719[PTP].
  3. E. Celeghini, M. Rasetti, M. Tarlini and G. Vitiello, Mod. Phys. Lett. B3 (1989), 1213.
  4. E. Celeghini, M. Rasetti and G. Vitiello, Ann. of Phys. 215 (1992), 156[CrossRef].
  5. T. Marumori, T. Maskawa, F. Sakata and A. Kuriyama, Prog. Theor. Phys. 64 (1980), 1294[PTP].
  6. Y. Tsue, A. Kuriyama and M. Yamamura,“Thermal Effects and Dissipation in su(1, 1)-Algebraic Model by Means of Time-Dependent Variational Approach", Kochi University Preprint.

Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 91 No. 3 (1994) pp. 469-494 :
    Thermal Effects and Dissipation in su(1, 1)-Algebraic Model by Means of Time-Dependent Variational Approach
    Yasuhiko Tsue, Atsushi Kuriyama and Masatoshi Yamamura
  2. Progress of Theoretical Physics Vol. 93 No. 3 (1995) pp. 541-558 :
    On the Hamiltonians Expressed in Terms of su(1, 1)-Generators for Describing Thermal Effects in Nuclear su(2)-Models
    Yasuhiko Tsue, Atsushi Kuriyama and Masatoshi Yamamura
  3. Progress of Theoretical Physics Vol. 93 No. 6 (1995) pp. 1037-1057 :
    Description of Thermal Effects in su(1, 1)-Algebraic Model Derived from Nuclear su(2)-Model
    Yasuhiko Tsue, Atsushi Kuriyama and Masatoshi Yamamura
  4. Progress of Theoretical Physics Vol. 95 No. 1 (1996) pp. 79-96 :
    Note on Boson Expansion and Boson Coherent State for the su(2)-Spin System
    Atsushi Kuriyama, João da Providência, Yasuhiko Tsue and Masatoshi Yamamura
  5. Progress of Theoretical Physics Vol. 96 No. 1 (1996) pp. 125-144 :
    Thermal Effect in the Lipkin Model. III
    Atsushi Kuriyama, João da Providência, Yasuhiko Tsue and Masatoshi Yamamura
  6. Progress of Theoretical Physics Vol. 96 No. 2 (1996) pp. 387-406 :
    Three Forms of Boson Expansions for the su(2)-Spin System and Their c-Number Counterparts
    Atsushi Kuriyama, Jo&ão da Providência, Yasuhiko Tsue and Masatoshi Yamamura
  7. Progress of Theoretical Physics Vol. 98 No. 2 (1997) pp. 381-392 :
    Three Forms of Coherent States in the su(2)-Spin System and Related Classical Counterparts
    Atsushi Kuriyama, João da Providência, Yasuhiko Tsue and Masatoshi Yamamura
  8. Progress of Theoretical Physics Vol. 98 No. 4 (1997) pp. 893-915 :
    A Boson System Interacting with an External Harmonic Oscillator
    Atsushi Kuriyama, João da Providência,* Yasuhiko Tsue** and Masatoshi Yamamura
  9. Progress of Theoretical Physics Vol. 99 No. 5 (1998) pp. 819-829 :
    Modification of the Conventional Holstein-Primakoff Boson Representation for the su(1,1)-Algebra and Its Classical Counterpart
    Atsushi Kuriyama, João da Providência, Yasuhiko Tsue and Masatoshi Yamamura
  10. Progress of Theoretical Physics Vol. 100 No. 5 (1998) pp. 993-1011 :
    A Possible Description of Many-Body System Composed of Three Kinds of Boson Operators
    Atsushi Kuriyama, João da Providência, Yasuhiko Tsue and Masatoshi Yamamura
  11. Progress of Theoretical Physics Vol. 100 No. 6 (1998) pp. 1181-1202 :
    A Boson System Interacting with an External Harmonic Oscillator
    Atsushi Kuriyama, João da Providência, Yasuhiko Tsue and Masatoshi Yamamura
  12. Progress of Theoretical Physics Vol. 103 No. 2 (2000) pp. 285-303 :
    On the Schwinger Boson Representation of an Extended (M+1)(N+1)-Dimensional Algebra Containing the su(M+1)- and the su(N,1)-Algebra
    Atsushi Kuriyama, João da Providência and Masatoshi Yamamura
  13. Progress of Theoretical Physics Vol. 103 No. 2 (2000) pp. 305-319 :
    A Possible Description of Many-Body System Composed of Four Kinds of Boson Operators
    Atsushi Kuriyama, João da Providência and Masatoshi Yamamura
  14. Progress of Theoretical Physics Vol. 104 No. 2 (2000) pp. 401-419 :
    Schwinger-Type Boson Realization for the su(4) Algebra
    Masatoshi Yamamura, Atsushi Kuriyama and Teiji Kunihiro
  15. Progress of Theoretical Physics Vol. 105 No. 5 (2001) pp. 717-728 :
    Utility of su(1,1)-Algebra in a Schematic Nuclear su(2)-Model
    Hideaki Akaike, Yasuhiko Tsue, Constança Providência, João da Providência, Atsushi Kuriyama and Masatoshi Yamamura
  16. Progress of Theoretical Physics Vol. 106 No. 4 (2001) pp. 765-781 :
    Deformed Boson Scheme including Conventional q-Deformation in Time-Dependent Variational Method. II
    Atsushi Kuriyama, Constança Providência, João da Providência, Yasuhiko Tsue and Masatoshi Yamamura
  17. Progress of Theoretical Physics Vol. 107 No. 2 (2002) pp. 443-448 :
    Note on the Deformed Boson Scheme in Time-Dependent Variational Method
    Atsushi Kuriyama, Constança Providência, João da Providência, Yasuhiko Tsue and Masatoshi Yamamura
  18. Progress of Theoretical Physics Vol. 108 No. 2 (2002) pp. 323-346 :
    Deformed Boson Scheme including Conventional q-Deformation in Time-Dependent Variational Method. IV
    Atsushi Kuriyama, Constança Providência, João da Providência, Yasuhiko Tsue and Masatoshi Yamamura
  19. Progress of Theoretical Physics Vol. 109 No. 1 (2003) pp. 77-86 :
    The su(1,1)-Algebraic Boson Model in the Deformed Boson Scheme
    Atsushi Kuriyama, Constança Providência, João da Providência, Yasuhiko Tsue and Masatoshi Yamamura
  20. Progress of Theoretical Physics Vol. 113 No. 1 (2005) pp. 153-168 :
    On the Eigenvalue Problem of the su(1,1)-Algebra and the Coupling Scheme of Two su(1,1)-Spins
    Seiya Nishiyama, Constança Providência, João da Providência, Yasuhiko Tsue and Masatoshi Yamamura
  21. Progress of Theoretical Physics Vol. 121 No. 6 (2009) pp. 1237-1287 :
    Many-Quark Model with su(4) Algebraic Structure
    Yasuhiko Tsue, Constança Providência, João da Providência and Masatoshi Yamamura
  22. Progress of Theoretical Physics Supplement No.141 (2001) pp. 113-178 :
    Time-Evolution of the Coherent and the Squeezed States of Many-Body Systems Based on the Basic Idea of the Boson Mapping and the TDHF Method
    Atsushi Kuriyama, João da Providência, Yasuhiko Tsue and Masatoshi Yamamura

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