Statistical Characteristics Of Split Energy Levels For Small Size Clusters

Clusters are the relatively stable microscopic or submicroscopic aggregates, consisting several to thousands of atoms, molecules or ions. Their physical and chemical properties are strongly depend on the size. Clusters are the new kind of matter forms with their sizes between atomic and macroscopic scales. The investigation on them is helpful to the understanding of the properties and the mechanism for how they are built. Base on previously structure models of Pb clusters, we calculate the corresponding energy eigenvalues of Pb clusters through Density Functional theory (DFT) and study their quantum chaos feature through Random matrix theory (RMT). We have found when the sizes of the clusters are fewer than 20, the higher relative stability a cluster has, the less significant quantum chaotic characteristics it shows. Oppositely, when the sizes of the clusters are more than 20, the higher relative stability a cluster has, the more significant quantum chaotic characteristics it shows. Furthermore, we study the influence of the number of electric charge, relative molecular mass, and the structure of clusters on quantum chaotic characteristics. The results shows that the feature of quantum chaos becomes more apparently when the size of a cluster increases, but it is less apparently when the molecular mass or the stability increases.The contents of this thesis are as follows:In Sec. I, an overview is made to describe the development of chaos, quantum chaos and cluster science. In Sec. â…¡, we introduce the basics theory and methods required for the current work. In Sec. â…¢, we focus on the research status of clusters. In Sec. IV, we discuss and analyze the results of calculation in detail. The conclusion and prospective are given in Sec. V.