周期受击陀螺的经典动力学及准能谱统计

Classical Dynamics and Quasienergy Spectral Statistics for a Periodically Kicked Free Top

研究一个周期受击陀螺系统的经典动力学与准能谱统计.发现在打击强度较弱(λ≤2.0)时,经典相空间的运动是规则的,最近邻能级间距分布呈泊松型;当打击强度λ≥2.5时,经典相空间的结构随着固定点(π/2,0)和(π/2,π)的干草叉(pitchfork)分岔变得越来越复杂直至λ≥6时的完全混沌.这时最近邻能级间距分布也由近泊松型朝着维格那型转化.文章中也计算了谱刚度、数方差、偏斜度、过度、数平均等统计量.

This paper studies the classical dynamics and quasienergy spectral statistics for a periodically kicked free top. It is found that at weak kicking strength（λ≤2.0） , the motion in classical phase space is regular, the nearest neighbor spacing distribution for the quasienergy levels is approximately Poisson type;and at λ≥2.5, with the pitchfork bifurcation of the fixed points（π/2,0）and（π/2,π）,the structure of the phase space becomes more and more complicate until becomes completely chaotic at λ≥6, and then the nearest neighbor spacing distribution for the energy levels changes from Poissonian to Wiguer type gradually. We also calculated spectral rigidity, number variance, skewness, excess, and number average.