动力学对称性破坏研究的拓扑途径——互作用玻色子模型中应用示例

TOPOLOGICAL APPROACH TO THE STUDY OF DYNAMICAL SYMMETRY BREAKING IN IBM SYSTEM

运用拓扑观点对原子核相互作用玻色子模型系统的动力学对称性破坏的过程进行研究,着重揭示了与能级免交叉现象联系的奇异行为及其根源。它实际上是动力学映射的不稳定不动点所导致的结果,越过该不稳定不动点后,为了给出连续映射,必须涉及能级的置换操作,因而呈现出能级免交叉,并使得映射不再能表示为动力学群生成元的函数,于是动力学对称性局域地实质性地受到了破坏。

The process of the dynamical symmetry breaking in nuclearIBM (Interacting Boson Model) system is studied by using the topological approach and Laying stress on the singular behavior and origin of the energy levels avoided crossing. It is shown that avoided erossing 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 essentially destroyed.