量子混沌在谱涨落统计特征上的表象

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

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。揭示出经典耗散系与经典保守系的量子对应体系之本征值谱可遵从不同的涨落统计规律。

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.