利用耗散子運動方程組研究有關在二能級系統中的熱傳輸

Abstract

在近幾十年的科學發展，高段的奈米技術已帶動了半導體製程，量子元件製程以及生物和醫學的發展。當元件逐漸縮到奈米的尺度下時，有許多物理量如電導率和熱導率都沒辦法在利用巨觀的物理來解釋，原因是在奈米的尺度下，量子的效應特別明顯。我們的研究主題是探討在一維二能級系統中的熱傳輸。在我們的研究中，熱能從溫度較高的熱庫通過二能級系統傳輸到溫度較低的熱庫，此模型可考慮成具有兩個不同溫度熱庫的spin-Boson 模型。目前在文獻中的計算引入一些近似方法來計算有關於熱傳輸和熱傳導率。在我們的研究中，我們利用耗散子運動方程組探討有關熱傳輸的問題。耗散子運動方程組除了可以計算有關系統算符的物理量演化，也可以計算同時含有系統算符和熱庫操作子組合的物理量以及其多時的關聯函數。除此之外，耗散子運動方程組可以運用在計算系統-熱庫耦合常數從強到弱，熱庫溫度從低到高的情況。在計算耗散子運動方程組時，微分方程的初始值可以假設系統與熱庫處於可分離的狀態或者是他們一起處於糾纏的狀態。在我們的研究中，我們利用耗散子運動方程組計算在不同熱庫的截斷頻率下，熱流傳輸以及在熱流雜訊頻譜中熱流的關聯函數的動態行為。

In recent decades, the advance of nanotechnology has led to a lot of developments such as semiconductor manufacturer, quantum device manufacturer or even in the biology and medical research at the nanoscales. Nanostructure devices also display interesting phenomena with physical quantities such as electric conductivity or thermal conductivity that cannot be well explained by macroscopic or classical models. Quantum effects are important in understanding these phenomena at nanoscales and low temperatures. My research topic focuses on a problem of one-dimensional heat transfer via a nanoscale quantum two-level system. Proposals that phonons carrying heat can be manipulated similarly to electrons and photons have been put forward, thus enabling controlled heat transport. Here we investigate the heat transfer properties of a local quantum two-level system driven by a temperature bias described by a spin-Boson model with attached two phononic reservoirs (baths) at two different temperatures. Several theoretical methods have been suggested to calculate the heat transfer, heat current and thermal conductivity of the quantum heat transport problems in the literature but they involve various and different degrees of approximations. We adopt here a so-called dissipaton equation of motion (DEOM) formalism to investigate the heat transport problems. The DEOM approach is not only suitable for solving the dynamics of the reduced system but also convenient to calculate physical quantities and multi-time correlation functions involving both system and bath operators. Furthermore, the DEOM formalism can deal with cases with system-bath coupling strength from weak to strong and bath temperature from low to high. It also can accommodate either a factorized (tensor product) or a correlated (entangled) initial system-bath state. Using the DEOM approach, we investigate the behaviors of the heat transport currents and current-current two-time correlation functions which lead to heat current noise spectrum for different bath cutoff frequencies.