The Complementary Chaos Of The Linear Nonautonomous System With The SU(2) Dynamical Group And Its Application

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. Theirregular 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.