简并谱的涨落统计特征分析

Analyses Statistics Character of Fluctuations in Degenerated Spectra

通过引入权重的方式，使简并谱的积累函数形式上连续递增，并用带权重的多元线性拟 合提取涨落谱，由此建立一套适用于分析简并谱的ＮＮＳ分布、谱刚度、能谱分维函数等涨落统计特 征的方法，并具体分析了 Ｈ_２Ｏ、 ＮＨ_３及 ＣＨ_４分子的振动能谱进行涨落统计特征分析：发现它们的规 则谱和约化非简并谱的涨落统计特征均已非Ｐｏｉｓｓｏｎ化；而且约化非简并谱的非Ｐｏｉｓｓｏｎ化程度较 规则谱明显，即前者的能级斥力较后者大；此外，随着简并度的增加，Ｈ_２Ｏ、ＮＨ_３、ＣＨ_４的涨落统计特 征由非 Ｐｏｉｓｓｏｎ型向近 Ｐｏｉｓｓｏｎ型过渡．

The degeneracy appears generally in the energy level spedra. It is related closely to the symmetrical character of the corresponding Hamiltonian random matrix. According to the fact that the state space of Hamiltonian matrix for degenerated spectra can be expanded into a series of sub-space corresponding to different eigenvalues, the degenerated spectra is dealed with by a special way, By introducing weights of the levels, the accumulative function curve of the degeneratal spectra is smoothed. Therefore the fluctuation spectra can be unfolded by means of polynomial expansion fitting with weights. Then a set of methods that are used to analyses statistical character of fluctuation such as the NNS distribution, the spectra rigidity and the fractal dimension function for energy levels are suggested. Further more, the degenerated spectra such as the vibrational energy spectra of the molecules of H_2O、 NH_3、 CH_4 are analyzed with this method. It's turns out that both their regular spectra and reduced non-degenerated spectra are nonpoissonized, further more, the former is obviously further nonpoissonized compared with the latter, i.e., the level repulsion of the reduced non-degenerated spectra is greater than the corresponding regular one. However, the statistic character of fluctuations in energy spectra of the H_2O, NH_3, CH_4 are different because of their degeneracies: they transform from the obviously nonpoissonized type to the closely poisson type.