Cycle By Quantum Chaos Hit The Gyro System

In this thesis, we construct a periodically kicked free top system as our research model. We have done following work in the paper:In classical dynamics, through the study of the space phase diagram of the system, we find that as the kicked strength increases the phase space is filled with ring first, then island chain appears in rule area and finally the phase space is full of chaos.In quantum dynamics, we study time evolution operator’s eigenvalue distribution and energy level accumulation density, and nearest energy level distribution. We also calculated the spectral rigidity, variance, skewness, excess and so on. The specific research is the energy level spacing distribution and the average spectral rigidity distribution when the kicked strength increases. Then we also study the fidelity [1,2], time evolution of quantum average energy and quantum dynamical tunneling [3]. The results show that the eigenvalue spectrum of one step time evolution operator distributes on unit circle of eigenvalue space. No matter how kicked strength changes, what’s j value, distribution of the eigenvalue don’t spread to the center of the circle. Energy spectra according to nearest neighbor distance distribution is Poisson distribution when kicked strength is small, with the increase of kicked strength, distribution deviates from the Poisson distribution to the Wigner distribution.Fidelity dependents on which classical phase space area the initial state belongs to. If the initial coherent state corresponds to fixed point in periodic orbits of phase space the fidelity changes periodically, if the initial coherent state corresponds to regular area of phase space the fidelity change irregularly, if the initial coherent state corresponds to the chaotic region fidelity is greatly reduced. Coherent states correspond to one center of the island and another in the phase space can tunnel to each other. As the time evolution operator eigenvalue discontinuities, we obtain the quantum average energy changes periodically. But coherent state selection in regular regional and in the chaotic region will lead to that period change show a regular fluctuation and unstable fluctuation two forms.