近年來，有關在量子混沌分析和控制上的研究日趨重要，但缺乏像古典混沌中軌跡發散的概念來分析量子混沌。本論文提出以複數軌跡方法，連結牛頓力學和量子力學之間的橋梁，來進行量子混沌控制。本文針對二維帶電非等向簡諧振子的物理系統，將狀態變數複數化後，從複數空間的軌跡建立量子混沌行為。藉由量子動態方程式的建立，吾人證實古典的控制理論也能應用至量子系統。本論文使用滑動模式控制(Sliding mode control)，讓系統對量子初值擾動具有強健功能，以達到混沌同步化(chaos synchronization)的目的。本論文藉由數值模擬的結果，證實所設計的控制器在初始條件的擾動下，可達到混沌行為的強健控制目的。吾人同時利用傳統混沌分析方法，在滑動模式控制的作用下，觀察從混沌到週期性之間的變化。

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.

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