经典混沌系统在相应于初始相干态的量子子空间中的随机性

STOCHASTICITY OF THE EFFECTIVE SUBSPACE TAKEN UP BY A COHERENT STATE IN QUANTUM SYSTEM CORRESPONDING TO CLASSICAL CHAOTIC ONE

Ｐｏｉｎｃａｒｅ截面是反映经典系统是否达到混沌的有力手段，无规矩阵理论被看成是显示量子系统规则运动与不规则运动特征的有效方法．那么，当一个经典相点在混沌体系的某一能量面Ｅ０上的不变环面被全部破坏后，与这一相点所对应的中心能量Ｅ０等于Ｅ０的相干态波包在它所占据的量子系统的子空间中有何表现呢？以原子核Ｌｉｐｋｉｎ模型为例，用重整化约化方法，对ＳＵ（３）群的广义相干态所占据的量子子空间进行了约化后对其中有关量的随机性作了考察，结果表明，在这样的等效子空间内能级间距的涨落，等效哈密顿量的矩阵元以及从可积体系的子空间到这一等效子空间的一一映射的矩阵元的分布均与无规矩阵理论的预言相符合。

Abstract It is well known that all torus are destroyed in the Poincare′ section with a certain energy E 0 when a classical system is in completely chaotic state.But in its quantum counterpart,the features of the subspace taken up by a coherent state with central energy 0=E 0 is not yet clear.In the present paper,taking nuclear Lipkin model as an example,we study the properties of such a subspace taken up by the coherent state of SU(3) group.An effective subspace is obtained by using a new renormalization approach.Our results show that in such an effective subspace the distribution of the nearest level spacings,the elements of effective Hamiltonian matrix,and the one to one correspondent map from the subspace of an integrable system to that of nonintegrable one are all consistent with predictions of random matrix theory.