Topological Approach to the Study of Dynamical Symmetry Breaking in IBM System

FU Deji; YANG Yatian; WANG Wenge; XU Gongou

Chinese Physics C> 1993, Vol. 17> Issue(11) : 1032-1039

Topological Approach to the Study of Dynamical Symmetry Breaking in IBM System

Institute of Nuclear Research,Shanghai,Academy Sinica,Shanghai 2018002 Fujian Normal University,Fuzhou 3500073 Nanjing University,Nanjing 2100084 Lanzhou University,Lanzhou 7300005 Institute of Modern Physics,Academia Sinica,Lanzhou 730000

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The process of the dynamical symmetry breaking in nuclear IBM system is studied by using the topological approach and laying stress on the singular behavior and origin of the energy levels of avoided crossing.It is shown that avoided crossing is really due to unstable fixed point of the dynamical mapping.Beyond such point,to perform the continuous mapping requires a localized permutation of the two levels concerned,and the mapping can no longer be expressible by the generators of the dynamical group.Thus,dynamical symmetry is localized and essentially destroyed.

References

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Y. Nambu, Proceedings of the Yoshio Nishina CentennialSymposium, Tokyo, Japan, Dec. 5-7,1990 Springer-Verlag, p.51.[2]Dieperink, A. E. L.，Progress in Particle and Nuclear Physics, Vol. 9, D. Wilkinson(Ed),NY:Pergamon, p 121.[3]Ginocchio,J. N.，Kirson, M. W.，Phys. Rev. Lett. , 44 (1980 ) ,1744 ; Feng , D. H.，Gilmore , R.，Deans , S. R.Phys. Rev. , C23 (1981) ,1254;梁世东，傅德基，徐躬藕，高能物理与核物理，16(1992),573.[4]Ha Yiming, Fu Deji, Chinese Journal of Nuclear Physics, 12(1990),151;Casten, A. S，Warner, D. D.，Rev.Mod. Phys. ,60(1988),389;傅德基，梁世东，狄尧民，哈益明，戴子高，兰州大学学报(自然科学版)27(1991),56.[5]Graffi, S.，Proceedings of a NATO Advanced Workshop on Quantum Chaos, Sep. 22-26, 1986, Como, I-taly. NATO Series B. V. 161 ,p. 163.[6]Xu Gongou, Wang Wenge, Yang Yatian, Phys. Rev. A45(1992),5401.[7]Xu Gongou, Wang Wenge, Yang Yatian, Fu Deji, Topological Approach to the Study of Quantum Nonintegra-bility, (to be published in Journal of Physics A.)，傅德基，量子系统映射的若干问题.第三届全国动力系统及其应用学术讨论会(广州，1992年1月)邀请报告. 傅德基，免交叉与原子核动力学对称性.第四届全国核结构讨论会(大庸市，1992)邀请报告文集.[8]Ziman, J. M.，Element of Quatum Theory (Cambridge University Press ,1969).[9]Hose, G.，Taylor, H. S.，Phy.Rev.Lett. ,51(1983),947.[10]Armstrong, M. A. ,Basis Topology (Mc. Graw-Hill, Berkshire, England,1979).

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FU Deji, YANG Yatian, WANG Wenge and XU Gongou. Topological Approach to the Study of Dynamical Symmetry Breaking in IBM System[J]. Chinese Physics C, 1993, 17(11): 1032-1039.

FU Deji, YANG Yatian, WANG Wenge and XU Gongou. Topological Approach to the Study of Dynamical Symmetry Breaking in IBM System[J]. Chinese Physics C, 1993, 17(11): 1032-1039. shu

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Received: 1900-01-01
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沈阳化工大学材料科学与工程学院沈阳 110142

Topological Approach to the Study of Dynamical Symmetry Breaking in IBM System

Corresponding author: FU Deji,

Institute of Nuclear Research,Shanghai,Academy Sinica,Shanghai 2018002 Fujian Normal University,Fuzhou 3500073 Nanjing University,Nanjing 2100084 Lanzhou University,Lanzhou 7300005 Institute of Modern Physics,Academia Sinica,Lanzhou 730000

Received Date: 1900-01-01

Accepted Date: 1900-01-01

Available Online: 1993-11-05

Abstract: The process of the dynamical symmetry breaking in nuclear IBM system is studied by using the topological approach and laying stress on the singular behavior and origin of the energy levels of avoided crossing.It is shown that avoided crossing is really due to unstable fixed point of the dynamical mapping.Beyond such point,to perform the continuous mapping requires a localized permutation of the two levels concerned,and the mapping can no longer be expressible by the generators of the dynamical group.Thus,dynamical symmetry is localized and essentially destroyed.

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Topological Approach to the Study of Dynamical Symmetry Breaking in IBM System

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