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

作　　者：杨双波[1] 刘达克[1] 

机构地区：[1]“大规模复杂系统数值模拟”江苏省重点实验室,南京师范大学物理科学与技术学院,江苏南京210023

出　　处：《南京师大学报（自然科学版）》2013年第1期48-53,共6页Journal of Nanjing Normal University(Natural Science Edition)

摘　　要：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.

关 键 词：陀螺 准能谱统计 相空间 干草叉分岔 

分 类 号：O413.1[理学—理论物理]