臺灣博碩士論文加值系統

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.

口試委員會審定書i
Acknowledgements ii
Chinese Abstract iii
Abstract iv
1 Introduction 1
1.1 Comparison between hierarchical equation of motion(HEOM) formalism
and Dissipaton equation of motion(DEOM) . . . . . . . . . . . . 4
2 Theoretical Introduction 7
2.1 DEOM formalism with Bosonics Bath . . . . . . . . . . . . . . . . . . 9
2.1.1 Model description . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.1.2 Method for bath decomposition . . . . . . . . . . . . . . . . . 10
2.1.3 Many Dissipaton Density Operators(MDDOs) . . . . . . . . . 13
2.1.4 Wick''s-like Contractions . . . . . . . . . . . . . . . . . . . . . 15
2.1.5 Inference of the DEOM . . . . . . . . . . . . . . . . . . . . . . 16
2.1.6 Two Time Correlation Functions of hybridized system and bath
operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3 Numerical method for decomposition of bath correlation function 25
3.1 MDDOs for decomposition bath correlation function . . . . . . . . . . 26
4 The model for heat transport via two quantum two level system 32
4.1 Heat current dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . 32
4.2 Heat current noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
5 Numerical Result and Discussion 42
5.1 BCF and Heat current dynamics based on paper [1] . . . . . . . . . . 43
5.2 Numerical result of Left Heat current dynamics and Left Heat current
current CF dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
5.2.1 Numerical result of Left Heat current dynamics . . . . . . . . 49
5.2.2 Numerical result for Heat Current Noise . . . . . . . . . . . . 54
6 Conclusions 59
Appendix A Hierarchical equation of motion formalism 60
Appendix B System Hybrid Bath Two Time Correlation Function 68
Bibliography 69

[1] Haobing Wang Kirill A. Velizhanin and Michael Thoss. Chem. Phys. Lett.,
460:325, 2008.
[2] Keiji Saito and Takeo Kato. Phys. Rev. Lett., 111:214301, 2013.
[3] Jie Ren Chen Wang and Jianshu Cao. Scienti c Reports, 5:11787, 2015.
[4] Y. Nakamura A. O. Niskanen and J. P. Pekola. Phys. Rev. B., 76:174523, 2007.
[5] Lei Wang Gang Zhang Peter Hanggi Nianbei Li, Jie Ren and Baowen Li. Rev. Mod. Phys., 84:1045, 2012.
[6] Youn es Ezzahri Karl Joulain, J er emie Drevillon and Jose Ordonez-Miranda.
Phys. Rev. Lett., 116:200601, 2016.
[7] Lei Wang and Baowen Li. Phys. Rev. Lett., 99:177208, 2007.
[8] Dvira Segal. Phys. Rev. B., 87:195436, 2013.
[9] M. Thorwart S. Weiss, J. Eckel and R. Egger. Phys. Rev. B., 77:195316, 2008.
[10] Rui-Xue Xu and Yi Jing Yan. Phys. Rev. E., 75:031107, 2007.
[11] Xin-Qi Li Yan Mo Rui-Xue Xu, Ping Cui and Yi Jing Yan. J. Chem. Phys.,
122:041103, 2005.
[12] RuiXue Xu YiJing Yan, Jinshuang Jin and Xiao Zheng. Front. Phys.,
11(4):110306, 2016.
[13] JunYan Luo-Xin Qi Li Ping Cui Rui Xue Xu Jinshuang Jin, Sven Welack and Yi Jing Yan. J. Chem. Phys., 126:134113, 2007.
[14] William H. Miller Michael Thoss, HaobinWang. J. Chem. Phys., 115:2991, 2001.
[15] Ulrich Weiss. Quantum Dissipative Systems, Second Edition.
[16] Christoph Meier and David J. Tannor. J. Chem. Phys., 111:3365, 1999.
[17] Yi Jing Yan. J. Chem. Phys, 140:054105, 2014.
[18] Nazim Boudjada and Dvira Segal. J. Phys. Chem. A, 118:11323, 2014.
[19] Feng Jiang Rui Xue Xu Jie Hu, Meng Luo and Yi Jing Yan. J. Chem. Phys.,
134:224106, 2011.
[20] Rui-Xue Xu Jie Hu and YiJing Yan. J. Chem. Phys., 133:101106, 2010.
[21] Kerson Huang. Quantum Field Theory; From Operators to Path Integrals.
[22] H. J. Carmichael. Statistical Methods in Quantum Optics 1: Master Equations and Fokker - Planck Equations.
[23] Dmitrii E. Makarov and Nancy Makri. Phys. Rev. E., 52:5863, 1995.
[24] Lena Nicolin and Dvira Segal. J. Chem. Phys.,135:164106, 2011.
[25] Michael Thoss Kirill A. Velizhanin and Haobin Wang. J. Chem. Phys.,133:084503, 2010.
[26] J. L. Garc a-Palacios Juzar Thingna and Jian-Sheng Wang. Phys. Rev. B.,85:195452, 2012.
[27] Liao-Ao Wu and Dvira Segal. J. Phys. A: Math. Theor., 42:025302, 2009.
[28] Xiao Zheng Jinshuang Jin, Shikuan Wang and YiJing Yan. J. Chem. Phys.,142:234108, 2015.
[29] J. M. Berroir D. C. Glattli B. Pla cais G. F eve M. Albert C. Flindt F. D. Parmentier,E. Bocquillon and M. Buttiker. Phys. Rev. B., 85:165438, 2012.