周期受击简谐振子系统的经典动力学与准能谱统计

Classical Dynamics and Quasi-Energy Spectral Statistics of a Periodically Kicked Harmonic Oscillator

研究一个周期受击简谐振子系统在非谐振情况下的经典动力学与准能谱统计.研究发现,随着打击强度κ的增加,经典相空间结构从可积(环)到完全混沌时,准能谱按最近邻能级间距分布仍保持Poisson分布不变,这与周期受击转子系统的结果相同.谱刚度的计算表明,除了κ=30的情况外,κ=0.13、1.6、2.0、2.6等的谱刚度在L<0.1的范围内随L线性变化,呈束状;在L>0.1以后发散开来,呈非线性变化,且κ=0.13的谱刚度趋于饱和.数方差Σ2及高阶矩γ1,γ2随κ的变化不敏感.

This paper studies the classical dynamics and quasienergy spectral statistics for a periodically kicked Harmonic oscillator system, under the nonresonance condition. It is found that as we increase the kicking strength K, and the phase space structure starts from tori for integrable system to completely chaotic for nonintegrable system, the nearest neighbor spacing distribution for the quasienergy spectral keeps the Poissonian distribution, and this is similar to that of the periodically kicked free rotor. The result of spectral rigidities shows that except the case of K = 30, the rigidities for K = 0. 13,1. 6,2.0,2. 6, bunched, increase linearly with L for L 〈 0. 1, and spread, increase nonlinearly with L, and the rigidity for K = 0. 13 tends to saturation for L 〉 0. 1. The number variance ∑^Q , skewness Tl , excess T2 are not sensitive to the change of K.