[1]杨双波,刘达克.周期受击陀螺的经典动力学及准能谱统计[J].南京师大学报(自然科学版),2013,36(01):48-53.
　Yang Shuangbo,Liu Dake.Classical Dynamics and Quasienergy Spectral Statistics for a Periodically Kicked Free Top[J].Journal of Nanjing Normal University(Natural Science Edition),2013,36(01):48-53.
点击复制

周期受击陀螺的经典动力学及准能谱统计()
分享到：

《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

卷:
第36卷
期数:
2013年01期
页码:
48-53
栏目:
物理学
出版日期:
2013-03-31

文章信息/Info

Title:
Classical Dynamics and Quasienergy Spectral Statistics for a Periodically Kicked Free Top
作者:
杨双波; 刘达克
“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
Author(s):
Yang Shuangbo; Liu Dake
Jiangsu Key Laboratory for NSLSCS,School of Physics and Technology,Nanjing Normal University,Nanjing 210023,China
关键词:
陀螺; 准能谱统计; 相空间; 干草叉分岔
Keywords:
free top; quasienergy spectral statistics; phase space; pitchfork bifurcation.
分类号:
O413.1
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.
Abstract:
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 Wigner type gradually.We also calculated spectral rigidity,number variance,skewness,excess,and number average.

参考文献/References:

[1] 杨双波,韦栋.周期受击简谐振子系统的经典与量子动力学[J].南京师大学报:自然科学版,2011,34(4):49-54.
[2]杨双波,韦栋.周期受击简谐振子系统的经典动力学与准能谱统计[J].南京师大学报:自然科学版,2012,35(3):37-42.
[3]Casati D,Chirikov BV,Izrailev FM,et al.Stochastic behavior of a quantum pendulum under a periodic perturbation[M]//Casati D,Ford J.Stochastic Behavior in Classical and Quantum Hamiltonian Systems,Leture Notes in Physics.Berlin:Springer-Verlag,1979,93:334-352.
[4]Nakamura K,Okazaki Y,Bishop A R.Periodically pulsed spin dynamics:scaling behavior of semiclassical wave functions[J].Physical Review Letters,1986,57(1):5-8.
[5]Haak F.Quantum Signatures of Chaos[M].Berlin,Heidelberg:Springer,1991:52,169.
[6]Mehta M L.Random Matrices and the Statistical Theory of Energy Levels[M].New York:Academic,1965.
[7]Dyson F J,Mehta M L.Statistical theory of the energy levels of complex systems[J]J Math Phys,1963,4(5):701-712.
[8]Huang Liang,Lai Yingcheng,Grebogi Celso.Characteristics of level-spacing statistics in chaotic graphene billiards[J].Chaos,2011,21,013102-1-013102-11.
[9]Honig A,Wintgen D.Spectral properties of strongly perturbed Coulomb systems:fluctuation properties[J].Physical Review A,1989,39(6):5 642-5 657.
[10]Mehta M L.Random Matrices[M].Second edition.San Diego:Academic Press,1991.
[11]Strzys M P,Graefe E M,Korsch H J.Kicked bose-hubbard system and kicked tops-destruction and stimulation of tunneling[J].New Journal of Physics,2008,10:013024-013038.
[12]Stejskal E O,Tanner J E.Spin diffusion measurements:spin echoes in the presence of a time-dependent field gradient[J].J Chem Phys,1965,42(1):288-293.

相似文献/References:

[1]刘达克,杨双波.周期受击陀螺的保真度隧道效应及能量量子期待值[J].南京师大学报(自然科学版),2014,37(02):60.
　Liu Dake,Yang Shuangbo.Fidelity,Tunneling,and Quantum Expectation Value of Energy for a Periodically Kicked Free Top[J].Journal of Nanjing Normal University(Natural Science Edition),2014,37(01):60.

备注/Memo

备注/Memo:
收稿日期:2012-09-17. 通
讯联系人:杨双波,博士,教授,研究方向:量子混沌.E-mail:yangshuangbo@njnu.edu.cn
更新日期/Last Update: 2013-03-31