具有经典混沌转变系统的能谱性质 耦合自旋模型的数值计算

SPECTRAL PROPERTIES OF A SYSTEM IN TRANSITION TOCLASSICAL CHAOS NUMERICAL RESULTS ON COUPLED SPIN MODEL

用数值方法研究了一耦合自旋模型的最近邻能级间距涨落和能级随参数变化曲线的免交叉行为。计算结果表明,当变化参数,系统的经典运动出现从规则→混沌→规则的转变时,间距涨落分布P(s)的Brody参数很好地反映了混沌区域在相空间中占据的比例。在有大量混沌运动的参数范围里,计算观察到了大量的免交叉及它们的重叠,并且能级曲线图呈现相对无规的形貌。这些结果被看作经典混沌在量子能谱中的表现或痕迹。

This article presents numerical results on the distribution ol nearest-neighbor level spac-ings Shd the avoided crossing behavior of quanitum energy curves for a cpupled spin model coming from nuclear many body theory. When the system undergoes a transition from classical regular to chaos and then to regular as varying a model parameter,the Brody parameter of the level spacing distribution p(s) could be fairly associated to the fraction of classical chaotic tra-jectories in phase space.;ln the regime of parameters with large chaotic regions, a number of overlapping avoided crossings were discovered from the results of computations, Which lead the energy curves looked irregular These results are considered as quantum manifestation or 'scars' pf classidal chaos in spectrum.