在本論文中，我們利用嚴格主方程來研究線性光子開放系統的非馬可夫動力學。透過嚴格主方程與非平衡態格林函數之間的連結，我們推導出描述該類量子開放系統非馬可夫動力學的解析解。在進一步分析我們所得到的解析結果後，我們依其動力學演化的特性將我們所研究的量子開放系統所有可能的動力學演化過程分成四類，並給出了由環境造成的量子退相干所導致的量子─古典變遷的物理圖像。在完整的討論並分析非馬可夫動力學的定性行為後，我們應用這套理論方法來研究光子晶體中的空腔系統在任意有限溫度下的動力學演化，並進一步探討光子晶體中的光子能隙結構對空腔動力學的影響。

In this thesis, we present an analytic solution of non-Markovian dynamics for non-interacting photonic open quantum systems. We explore the non-Markovian dynamics of such open quantum systems through the solutions of the exact master equation, and carry out the detailed analysis of non-Markovian dynamics from these solutions. By further analyzing these analytic solutions, we capture the main features of the non-Markovian dynamics and categorize them into four different time evolution scenarios. This provides a general picture on the quantum-to-classical transition, which is caused by the environment-induced decoherence. After the comprehensive discussions about the qualitative behaviors of non-Markovian decoherence dynamics, we apply the theory to study the non-Markovian cavity dynamics in photonic crystals at finite temperature, and explicitly show the influence of the photonic band gap on the cavity photon field.

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