- 學位論文
使用Keldysh方法計算量子淬火動力學：Kondo-Luttinger模型
Quench Dynamics of the Kondo-Luttinger Model: The Keldysh Green's Function Approach
摘要
本文探索了在量子淬火之後，於量子臨界點附近的Kondo-Luttinger 模型中可測量的時間動態演化。我們證明了相同的方法也可以適用於研究耗散量子點和弱連接模型。利用Keldysh 非平格林函數，我們通過在t = 0 時突然打開電位差來改變系統。我們推導了這些模型中的電流和電導，並得到電流及電導在淬火後隨時間之演化關係，我們的結果可以恢復在淬火前分析中發現的長時間穩態行為。我們還發現，在量子臨界點上，Kondo-Luttinger 模型可以簡化為簡單的弱鏈接模型，我們更進一步的將在 Kondo-Luttinger 模型中得到的結果嚴格地映射到耗散量子點的模型中。我們也討論此研究結果與實驗之關聯。
關鍵字
量子淬火並列摘要
In this thesis we explore the time dynamical evolution of measurable quantities in the Kondo-Luttinger model near a quantum critical point following a quantum quench. We show that the same process allow an analogous study of a dissipative quantum dot model and a coupled noninteracting lead model as well. Utilizing Keldysh non-equilibrium Green's function techniques, we quench this system by suddenly initiating a potential bias at time $t_0=0$. We derive the current and conductance in this models, and obtain the time evolution of current and conductance after quench. We show that we recover long time steady state behavior found in a non-quench analysis after relaxing through a previously unexplored intermediate relaxation state. We also find that at the quantum critical point, the Kondo-Luttinger model reduces to the simplistic coupled noninteracting lead model assuming definite spin orientation. Our results for the Kondo-Luttinger model can be directly generalized to the dissipative quantum dot system via a rigorous mapping. The relevance of our results for experiments is discussed.