Quantum Chaos Control by Complex Trajectories

• Main Authors: Yen-JiunChen, 陳彥均
• Other Authors: Ciann-Dong Yong
• Format: Others
• Language: zh-TW
• Published: 2010
• Online Access: http://ndltd.ncl.edu.tw/handle/23849657514169077641

碩士 === 國立成功大學 === 航空太空工程學系碩博士班 === 98 === In recent years, analysis and control of quantum chaos is increasingly important, but the lack of the concept of trajectory makes it impossible to analyze quantum chaos by the methods used in classical chaos. The aim of this thesis is to connect the Newton’s world to the quantum world by the complex mechanics so that quantum chaos can be analyzed and controlled by the complex-extended Newtonian mechanics. Through the bridge of complex mechanics, in this thesis we model quantum motions for 2D charged anisotropic harmonic oscillator by complex-valued dynamic equations based on which quantum chaos can be analyzed by using well-known methods used in classical chaos. With the established quantum dynamic model, we then apply the sliding-mode control method to control the chaotic quantum behavior of the considered quantum system. The simulation results show that chaotic motions can be changed into periodic motions by the proposed chaos control and meanwhile, chaos synchronization can be achieved in the presence of variations of initial conditions. Several signatures of chaos are introduced here to justify the chaos to periodicity process under the sliding-mode control law.