量子混沌在谱涨落统计特征上的表象

通过对Ｈｅｎｏｎ－Ｈｅｉｌｅｓ模型、Ｂａｒｂａｎｉｓ模型和刚环转球模型这两类三种守恒体系之对应量子体系的研究，具体地剖析了本征值谱涨落统计特征与体系动力学行为的联系，说明了量子混沌现象的两种表现形式。同时，通过将本质上属于经典耗散系范畴的Ｌｏｔｋａ－Ｖｏｌｔｅｒｒａ模型之演化方程哈密顿化，发现其量子对应系本征值谱的涨落统计特征超出了Ｐｏｉｓｓｏｎ－ＧＯＥ（Ｗｉｇｎｅｒ）或ＧＵＥ框架。揭示出经典耗散

Expressions of Quantum Chaos in the Statistical Characteristics of Eigenvalue-Spectral Fluctuations

Through studying the quantum counterparts of two kinds of classical conservative systems, such as Henon-Heiles model, Barbains model and the model of the rotating-ball a-long a rigid ring, this title explains the connections of statistical characteristics of the fluctuations in energy spectra with the dynamic behavior of these models. Then, as a result, it reveals that there are two kinds of expressions of quantum chaos in the statistical characteristics of spectral fluctuations. Furthermore, by hamiltonizing the evolution equation of Lotka-Volterra model which belongs to classical dissipative systems in principle, we find that the statistical characteristics of the fluctuations in eigenvalue-spectra of its quantum counterpart go completely beyond the frame of Poisson-GOE(Winger) or GUE distribution. It shows that the fluctuations in eigenvalue-spectra of the quantum counterparts of the classical dissipative and the conservative systems follow different statistical regularities respectively.