本論文中，我們研究多個量子點（quantum dot）連接到電極的量子傳輸特性，每個量子點可包含多個能階及庫侖相互作用（Coulomb interaction）。我們從Liouville-von Neumann equation出發，完整保留了庫侖相互作用的效應，並對電極的自由度求積，首先得到修飾後波恩近似（modified Born approximation）下的非局域主方程式（master equation），接著進一步作馬可夫近似（Markovian approximation），得到局域主方程式。並從此主方程求得時間域（time domain）的傳輸電流。我們將此主方程應用到單個雜質安德森模型（single impurity Anderson model），證明了此方法在近藤溫度（Kondo temerature）以上，任意偏壓下皆可適用。接著我們進一步應用到AB干涉儀（Aharonov-Bohm interferometer）上，討論庫侖相互作用對兩個態之間同調性（coherence）的影響。最後我們提出一個實驗上可實現的同調性控制最佳方法，不但可使之達到純態（pure state），並可藉由外加磁場控制兩個態之間的相位差。

In this thesis, we utilize master equation approach to study the quantum dynamics of the interacting quantum dots system, including the double quantum dots and the multilevel quantum dots coupled to the source and the drain. We derive master equation based on the Liouville-von Neumann equation under modified Born and Born-Markovian approximation, in which the Coulomb interactions are exactly solved. We also obtain the transport current in time domain. We show that the approach works well for arbitrary bias above the Kondo temperature. The transport property of the single impurity Anderson model, and the role of Coulomb interaction on coherence
between two charge states of the Aharonov-Bohm interferometer are explored. We also propose an optimal coherence control of an qubit for realizing the quantum computation.

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