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Prog. Theor. Phys. Vol. 103 No. 4 (2000) pp. 733-745

[ Full Text PDF : FREE ACCESS (137K) ]

The Lipkin Model in a New Boson Realization

— Basic Idea —

Atsushi Kuriyama, Constança Providência,*) João da Providência*) and Masatoshi Yamamura

Faculty of Engineering, Kansai University, Suita 564-8680, Japan
*)Departamento de Fisica, Universidade de Coimbra, P3000 Coimbra, Portugal

(Received December 10, 1999)

Abstract:

With the use of the basic idea of the boson mapping method, a new boson realization, which is suitable for the Lipkin model, is proposed. This realization is different from the forms which are obtained with the Holstein-Primakoff and the Schwinger boson representations for the su(2) spin system. Further, with the aid of the basic idea of the TDHF method in canonical form, a method analysing the Lipkin model in the framework of classical mechanics is developed. The condition for the solution of the Hamilton equation of motion is discussed.


URL : http://ptp.ipap.jp/link?PTP/103/733/
DOI : 10.1143/PTP.103.733

[ Full Text PDF : FREE ACCESS (137K) ] Citation:

References:

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  2. T. Marumori, M. Yamamura and A. Tokunaga, Prog. Theor. Phys. 31 (1964), 1009[PTP].
  3. A. Klein and E. R. Marshalek, Rev. Mod. Phys. 63 (1991), 375[APS].
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  5. M. Yamamura and A. Kuriyama, Prog. Theor. Phys. Suppl. No. 93 (1987), 1[PTP].
  6. T. Holstein and H. Primakoff, Phys. Rev. 58 (1940), 1098[APS].
  7. J. Schwinger, in Quantum Theory of Angular Momentum, ed. L. Biedenharn and H. Van Dam (Academic Press, New York, 1955), p. 229.

Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 104 No. 1 (2000) pp. 143-153 :
    On the Coupling of Two su(1,1) Spins in the Holstein-Primakoff Type Boson Representation
    Atsushi Kuriyama, Constança Providência, João da Providência and Masatoshi Yamamura
  2. Progress of Theoretical Physics Vol. 104 No. 1 (2000) pp. 155-172 :
    A Note on a Boson Realization in Many-Boson System
    Atsushi Kuriyama, Constança Providência, João da Providência and Masatoshi Yamamura
  3. Progress of Theoretical Physics Vol. 107 No. 6 (2002) pp. 1273-1278 :
    On the Multiboson Coherent State in Deformed Boson Scheme
    Atsushi Kuriyama, Constança Providência, João da Providência, Yasuhiko Tsue and Masatoshi Yamamura
  4. Progress of Theoretical Physics Vol. 107 No. 6 (2002) pp. 1279-1284 :
    Two Contrastive Boson-Pair Coherent States in Deformed Boson Scheme
    Atsushi Kuriyama, Constança Providência, João da Providência, Yasuhiko Tsue and Masatoshi Yamamura
  5. Progress of Theoretical Physics Vol. 116 No. 1 (2006) pp. 87-105 :
    The Lipkin Model in Many-Fermion System as an Example of the su(1,1) ⊗ su(1,1)-Algebraic Model
    Constança Providência, João da Providência, Yasuhiko Tsue and Masatoshi Yamamura
  6. 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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