在本論文中，我們研究了奈米電子元件的瞬時輸運電流和瞬時電流關聯函數。輸運電流和電流關聯函數是研究奈米結構的電子量子輸運裡最主要的兩個物理量，他們刻劃了電子的量子輸運行為並且是直接的實驗可觀測量。我們利用量子郎之萬方程(quantum Langevin equation)研究並計算了瞬時電流關聯函數及其對應的瞬時噪聲譜，給出了它們的具體解析形式。在沒有取寬帶極限(wide band limit)的條件下，我們針對單能階量子點奈米結構進行系統性的分析，得到了在不同的溫度和偏壓下的瞬時電流關聯函數和瞬時噪聲譜。從中我們探討了在不同時刻電子輸運與奈米系統的能量結構之間的關係以及電子不同輸運方向到達穩態的時間尺度。另外，我們利用量子郎之萬方程導出了嚴格的含初始關聯的量子主方程，並由此建立了一個含初始關聯的量子輸運理論。藉由量子主方程，我們得到了含初始關聯的瞬時輸運電流。我們證明了，當系統存在局域態(localized state)時，不管是在系統中電子輸運到達穩態前還是到達穩態後，初始關聯都會對量子輸運造成各種不同程度的影響，充分顯示出量子輸運過程中的非馬可爾夫記憶(non-Markovian memory)效應。

Transport current and current-current correlations are major quantities for the study of quantum transport through nanostructures. They characterize the transport properties, and can be examined through experimental measurements. In this thesis, we investigate quantum transport current and current-current correlations in the transient regime. In particular, utilizing the quantum Langevin equation, we obtain a general formalism for transient current-current correlations and transient noise spectra for noninteracting nanostructures. The exact solution of transient current correlations in both the time and the frequency domains are explicitly carried out for a single-level quantum dot system. We investigate transient current-current correlations with different bias voltages at different temperatures, without taking the wideband limit. Transient noise spectra over the whole frequency range are found. Various time scales associated with the energy structures of nanostructures are extracted through the transient current-current correlations and transient noise spectra. We also derived the exact master equation incorporating initial
system-lead correlations through the quantum Langevin equation. The transient electron transport current incorporating initial correlations is obtained by solving the master equation. We show that the initial correlations can affect quantum transport not only in the transient regime, but also in the steady-state limit when system-lead couplings are strong enough such that electron localized states occur in the device system, which sufficiently manifests non-Markovian memory effects.

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