SU（2）线性非自治量子系统的互补混沌及其应用
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摘要
SU(2)线性非自治量子系统，就是指其哈密顿量为SU(2)生成子的线性泛函而其迭加系数与时间有关。它是具有重要实用价值的时间有关的量子系统。目前非线性科学最重要的成就之一就在于对混沌现象的认识。因此，讨论SU(2)线性非自治量子系统的混沌问题具有一定的理论意义和实用价值。
利用SU(2)代数动力学方程讨论了SU(2)线性非自治量子系统中的混沌问题，并且发现了一个非常重要而有趣的结果：SU(2)线性非自治量子系统中存在着互补混沌，同时计算了分形图形的记盒维数。
同时，在此基础上，利用SU(2)代数动力学方程研究了加速器中带自旋离子的极化对磁场的含时无规扰动的稳定性问题，发现：低度极化的系统对磁场无规扰动十分敏感，而高度极化的系统对磁场无规扰动十分稳定；自旋守恒导致自旋的纵向分量的无规涨落和横向分量的无规涨落存在着互补性。这一结果表明，在产生离子束极化的实验中，在离子束低度极化的前期阶段，磁场应具有较高的稳定性，而在离子束极化度较高的后期阶段，磁场的稳定性要求可以放松；自旋的纵向分量的无规涨落和横向分量的无规涨落的互补性有可能用来做成稳定离子极化的负反馈。
The linear SU(2) nonautonomous quantum system means its Hamiltonian is the linear function of SU(2) generators whose coefficients have relation with time. It is a time-dependent quantum system of important practical value. At present, one of the most important achievements of nonlinear sciences consists in the knowledge of chaos. Therefore, it is of certain theoretical significance and practical value to discuss the chaos problem of the linear SU(2) nonautonomous quantum system.
Based on the equation of SU(2)algebra dynamic, the chaos problem is discussed in the linear SU(2) nonautonomous quantum system. And a very important and interesting result is found that the complementary chaos phenomenon exists in the system. Besides, the box dimension of fractal graph is calculated.
At the same time, on the basis of above results, the stability problem of the polarization of particle self-spin is discussed in irregular magnetic field of accelerator. The discovery that the low degree polarization system is very sensitive to the irregular magnetic field while the high degree polarization system is very stable is found. The
irregular fluctuation of the vertical ponderance is complementary to that of the horizontal ponderance due to the self-spin conservation. These results indicate that the magnetic field should have upper stability when the particle beam is low polarized while the requirement of the stability of the magnetic field can be lowered when the particle beam is high polarized in the experiment of producing the polarization of the particle beam. And the complementariness can be used as a negative feedback to stabilize the polarization of particle.
利用SU(2)代数动力学方程讨论了SU(2)线性非自治量子系统中的混沌问题，并且发现了一个非常重要而有趣的结果：SU(2)线性非自治量子系统中存在着互补混沌，同时计算了分形图形的记盒维数。
同时，在此基础上，利用SU(2)代数动力学方程研究了加速器中带自旋离子的极化对磁场的含时无规扰动的稳定性问题，发现：低度极化的系统对磁场无规扰动十分敏感，而高度极化的系统对磁场无规扰动十分稳定；自旋守恒导致自旋的纵向分量的无规涨落和横向分量的无规涨落存在着互补性。这一结果表明，在产生离子束极化的实验中，在离子束低度极化的前期阶段，磁场应具有较高的稳定性，而在离子束极化度较高的后期阶段，磁场的稳定性要求可以放松；自旋的纵向分量的无规涨落和横向分量的无规涨落的互补性有可能用来做成稳定离子极化的负反馈。
The linear SU(2) nonautonomous quantum system means its Hamiltonian is the linear function of SU(2) generators whose coefficients have relation with time. It is a time-dependent quantum system of important practical value. At present, one of the most important achievements of nonlinear sciences consists in the knowledge of chaos. Therefore, it is of certain theoretical significance and practical value to discuss the chaos problem of the linear SU(2) nonautonomous quantum system.
Based on the equation of SU(2)algebra dynamic, the chaos problem is discussed in the linear SU(2) nonautonomous quantum system. And a very important and interesting result is found that the complementary chaos phenomenon exists in the system. Besides, the box dimension of fractal graph is calculated.
At the same time, on the basis of above results, the stability problem of the polarization of particle self-spin is discussed in irregular magnetic field of accelerator. The discovery that the low degree polarization system is very sensitive to the irregular magnetic field while the high degree polarization system is very stable is found. The
irregular fluctuation of the vertical ponderance is complementary to that of the horizontal ponderance due to the self-spin conservation. These results indicate that the magnetic field should have upper stability when the particle beam is low polarized while the requirement of the stability of the magnetic field can be lowered when the particle beam is high polarized in the experiment of producing the polarization of the particle beam. And the complementariness can be used as a negative feedback to stabilize the polarization of particle.
引文
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