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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/10129
標題: | 非馬可夫系統的雙時關聯函數: 精確解與微擾近似的研究 Non-Markovain Two-Time correlation functions: Exact Result v.s Perturbation Approach |
作者: | Yu-An Tsai 蔡宇安 |
指導教授: | 管希聖(Hsi-Sheng Goan) |
關鍵字: | 開放量子系統,非馬可夫過程,雙時關聯函數,自發性幅射的光譜,精確解, open quantum system,non-Markovain,two-timecorrelation function,spontaneous emission spectrum,exact solution, |
出版年 : | 2011 |
學位: | 碩士 |
摘要: | 我們研究了一個二能級自發性幅射到真空場的模型,也就是透過 Jaynes-Cummings 模型在旋轉波近似下的研究。當我們考慮最多只有一個激發態時,這個模型能夠被精確的解出。這裡我們使用兩種方法得出非馬可夫開放系統的雙時關聯函數:第一個是直接精確的計算系統運算子隨時間的演化。另一種方法是透過微擾的非馬可夫主宰方程進行計算,我們將非馬可夫主宰方程寫成對時間是非卷積的形式。為了計算雙時關聯函數,我們將系統-環境之間的交互作用,用微擾的方式展開到第四階的近似。我們將以上兩種方法做了一些比較。在這邊,我們同時找到了一種使微擾近似更準確的方法,我們是把加速數列收斂的技術應用在微擾展開的主宰方程上。我們的結果發現,非馬可夫主宰方程比下面幾種方法都還要更接近精確解:馬可夫微擾、非馬可夫微擾與精確解並使用量子退化定理。這樣的結果表式,我們找到的非馬可夫主宰方程是相當有用同時正確的。另外,我們也研究了自發性幅射的光譜,我們發現它在強耦合與弱耦合下有非常不相同的行為。 A two-level system which decays spontaneously into field vacuum is studied through the Jaynes-Cummings model in the rotating wave approximation (RWA).When at most one excitation is considered, this model is exactly solvable. Here we evaluate the non-Markovian two-time correlation functions (CF's) of system operators for this model in two ways: one by directly solving the system-environment evolution,and the other by using the perturbative time-convolutionless non-Markovian master equation approach. We derive valid to fourth order in system-bath coupling strength a non-Markovain evolution equation for the two-time CF's of system operators. We use the derived evolution equation to calculate a two-time CF for the two-level model and compare it with the exact result obtained by direct evaluation. Another numerical series acceleration method is applied to the calculation of the perturbation decay, and this method is found to improve the accuracy of the evolution equation. The result obtained by the derived perturbative two-time evolution equation is much better than those by the perturbative Markovian Quantum regression theorem(QRT), the non-Markovian QRT and exact QRT as it agrees more closely with the exact result even when the model is in the regime where the bath correlation time is comparable to the system relaxation time.This demonstrates the validity and usefulness of our derived non-Markovain two-time evolution equation. The exact spontaneous emission spectrum is also calcukated, and it has very different behaviours in the strong coupling an the weak coupling regions. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/10129 |
全文授權: | 同意授權(全球公開) |
顯示於系所單位: | 物理學系 |
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