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| ???org.dspace.app.webui.jsptag.ItemTag.dcfield??? | Value | Language |
|---|---|---|
| dc.contributor.advisor | 管希聖(Hsi-Sheng Goan) | |
| dc.contributor.author | Po-Wen Chen | en |
| dc.contributor.author | 陳柏文 | zh_TW |
| dc.date.accessioned | 2021-06-15T07:06:45Z | - |
| dc.date.available | 2011-12-10 | |
| dc.date.copyright | 2010-12-10 | |
| dc.date.issued | 2010 | |
| dc.date.submitted | 2010-11-18 | |
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| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/48654 | - |
| dc.description.abstract | 本論文致力於在幾個不同物理系統中的非馬可夫(non-Markovian)動力過程的研究。具體地介紹，我們研究兩個量子位元在熱壓縮態環境(thermal squeezed bath)下的非馬可夫糾纏動力行為，一個奈米諧振子在量子點接觸器(quantum point contact)測量下的非馬可夫動力行為，和一個量子位元系統在熱庫環境下的不同時間關聯函數的非馬可夫演化過程。首先、在兩個量子位元在熱壓縮態環境下的非馬可夫糾纏動力行為研究中，我們發現非馬可夫的糾纏動力行為明顯地不同於其對應的馬可夫動力行為。我們顯示一個在非馬可夫過程中的無退相干的量子態(decoherence-free state)也同時是馬可夫過程中的無退相干的量子態，但是一個在馬可夫過程中的無退相干的量子態就不一定為非馬可夫過程中的無退相干的量子態。我們延伸對零溫壓縮態環境的計算到有溫度的壓縮態環境，並探究壓縮態環境溫度對糾纏動力行為的影響。第二、我們研究一個奈米諧振子在量子點接觸器或穿隧接面(tunnel junction)測量下的非馬可夫動力行為。我們推導在二階近似下的非馬可夫過程中與電子數目有關的條件式和與其無關的非條件式主方程式。在我們推導過程中，我們沒有做在光學系統中常用的兩種近似:也就是旋轉波近似(rotating wave approximation)和馬可夫近似。我們發現非馬可夫的動力行為有相當大的差別相對於其對應的馬可夫動力行為。我們計算可提供被測奈米諧振子資訊的隨時間變化的量子點接觸器傳輸電流。我們發現一個在研究相同問題的文獻中被忽略的含時瞬變電流項。此額外的含時瞬變電流項跟奈米諧振子位置與動量對稱化算符的期望值有關，並且其係數來自於量子點接觸器關聯函數的虛部分的組合。我們發現到此額外的項對非馬可夫的總和含時瞬變電流有實質上的貢獻並與其對應的馬可夫的瞬變電流不論在定性與定量上都有明顯的不同。此項額外瞬變電流的存在與否，可用來見證是否有非馬可夫動力行為特徵存在於此奈米諧振子與量子點接觸器模系統中。第三、我們使用量子主方程式方法去推導在有限溫度環境中對任何可分離的初始系統和環境的狀態(純態或者混態)的情況下的不同時間系統算符的非馬可夫關聯函數的演化方程式。此演化方程式是有效到系統與環境的耦合常數為微擾的二階近似。此演化方程式可應用到一般的開放性量子系統耦合到有限溫度的環境的模型，不論其在系統與環境的交互作用中的系統算符是否為Hermitian。我們給出在弱交互作用下，此演化方程式變為量子回歸定理(quantum regression theorem)的條件，並應用此推導出來的演化分程式到一個二能級系統(原子) 耦合到玻色子環境中(電磁場)的模型，其中在系統與環境的交互作用中的系統算符為non-Hermitian。 | zh_TW |
| dc.description.abstract | The thesis is devoted to the study of the non-Markovian dynamical process in several different physical systems. Specifically, we investigate the non-Markovian entangle-
ment dynamics of two quantum bits (qubits) in a thermal squeezed bath, the non-Markovian dynamics of a nanomechanical resonator (NMR) measured by a quantum point contact (QPC) detector and, the non-Markovian evolution of two-time correlation functions (CF’s) of a two-level atom coupled to a thermal bosonic bath. First, in the investigation of the non-Markovian entanglement dynamics of two qubits in a common squeezed bath, we see a remarkable difference between the non-Markovian entanglement dynamics and its Markovian counterpart. We show that a non-Markovian decoherence-free state is also decoherence free in the Markovian regime, but all the Markovian decoherence-free states are not necessarily decoherence free in the non-Markovian domain. We extend our calculation from a squeezed vacuum bath to a squeezed thermal bath, where we see the effect of finite bath temperatures on the entanglement dynamics. Second, we also investigate the dynamics of a NMR subject to a measurement by a low-transparency QPC or tunnel junction in the non-Markovian domain. We derive the non-Markovian number-resolved (conditional) and unconditional master equations valid to second order in the tunneling Hamiltonian without making the rotating-wave approximation and the Markovian approximation, generally made for systems in quantum optics. We find considerable difference in dynamics between the non-Markovian cases and its Markovian counterparts. We also calculate the time-dependent transport current through the QPC which contains information about the measured NMR system. We find an extra transient current term proportional to the expectation value of the symmetrized product of the position andmomentum operators of the NMR. This extra term, with a coefficient coming from the combination of the imaginary parts of the QPC reservoir correlation functions, was generally ignored in the studies of the same problem in the literature. But we find that it has a substantial contribution to the total transient current in the Non- Markovian case and differs qualitatively and quantitatively from its Markovian counterpart. Thus it may serve as a witness or signature of non-Markovian features for the coupled NMR-QPC system. Finally, we use the quantum master equation approach to derive, valid to second order in the system-environment interaction Hamiltonian, non-Markovian evolution equations of two-time CF’s of system operators at finite environment temperatures with any initial separable system-environment states (pure or mixed). When applied to a general model of a system coupled to a finite-temperature bosonic environment with a system coupling operator L in the system-environment interaction Hamiltonian, the resultant evolution equations are valid for both Her- mitian and non-Hermitian system coupling operator cases. We then give conditions on which the derived evolution equations reduced to the case of quantum regression theorem (QRT)in the weak system-environment coupling case, and apply the derived evolution equations to a problem of a two-level system (atom) coupled to a bosonic environment (electromagnetic fields) with $L = L^(＋)$. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-15T07:06:45Z (GMT). No. of bitstreams: 1 ntu-99-D94222008-1.pdf: 2626740 bytes, checksum: 9ccfc724befe79956769029c56ee922f (MD5) Previous issue date: 2010 | en |
| dc.description.tableofcontents | 1 INRODUCTION
1 2 Background and Methods 7 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2 Microscopic Derivation of the Master Equations . . . . . . . . . . . . 8 2.2.1 Approximation1: Weak coupling . . . . . . . . . . . . . . . . . 9 2.2.2 Approximation2: Markovian approximation . . . . . . . . . . 10 2.3 Non-Markovian Master Equations . . . . . . . . . . . . . . . . . . . . 11 2.3.1 Time-Convolution Projection Operator Technique . . . . . . . 12 2.3.2 Time-Convolutionless Projection Operator Technique . . . . . 14 2.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3 Decoherence-free subspace and disentanglement dynamics for two qubits in a common non-Markovian squeezed reservoir 18 3.1 Two qubits in a common non-Markovian squeezed reservoir . . . . . . 21 3.2 Difference between Markovian and non-Markovian dynamics . . . . . 23 3.3 Numerical results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 4 Non-Markovian dynamics of a nanomechanical resonator measured by a quantum point contact 34 4.1 Hamiltonian of the NMR-QPC model . . . . . . . . . . . . . . . . . . 37 4.2 Number-resolved quantum master equation . . . . . . . . . . . . . . . 39 4.3 Unconditional master equation and Markovian limit . . . . . . . . . . 48 4.3.1 Unconditional master equation . . . . . . . . . . . . . . . . . 48 4.3.2 Markovian limit . . . . . . . . . . . . . . . . . . . . . . . . . . 49 4.4 Dynamics of the NMR . . . . . . . . . . . . . . . . . . . . . . . . . . 52 4.5 Transport current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 4.6 Numerical Results and Analysis . . . . . . . . . . . . . . . . . . . . . 57 4.6.1 Effect of only the QPC reservoirs . . . . . . . . . . . . . . . . 58 4.6.2 Inclusion of the effect of thermal bosonic environment . . . . . 73 4.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 5 Non-Markovian finite-temperature two-times correlation functions of system operators 79 5.1 DERIVATIONS OF EVOLUTION EQUATIONS . . . . . . . . . . . 82 5.2 EVOLUTION EQUATION FOR THERMAL BOSONIC MODELS . 88 5.2.1 Conditions for the QRT to hold . . . . . . . . . . . . . . . . . 91 5.3 Application to a thermal spin boson model with L 6= L＋ . . . . . . . . 92 5.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 6 Conclusion 101 7 Appendix A: Derivation of the QBM Master Equation 114 | |
| dc.language.iso | en | |
| dc.subject | 非馬可夫 | zh_TW |
| dc.subject | 糾纏 | zh_TW |
| dc.subject | 傳輸性質 | zh_TW |
| dc.subject | 關聯函數 | zh_TW |
| dc.subject | Correlation Functions | en |
| dc.subject | Non-Markovian Dynamical Processes | en |
| dc.subject | Entanglement | en |
| dc.subject | Transport Properties | en |
| dc.title | 非馬可夫開放性物理系統的動力行為: 糾纏,傳輸性質和關聯函數的研究 | zh_TW |
| dc.title | Non-Markovian Dynamical Processes Of Open Quantum Systems:
Studies On Entanglement, Transport Properties and Correlation Functions | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 99-1 | |
| dc.description.degree | 博士 | |
| dc.contributor.oralexamcommittee | 朱仲夏,蘇正耀(Zheng Yao Su),高英哲(Ying-Jer Kao),陳岳男(Yueh-Nan Chen),陳柏中(Po-Chung Chen) | |
| dc.subject.keyword | 非馬可夫,糾纏,傳輸性質,關聯函數, | zh_TW |
| dc.subject.keyword | Non-Markovian Dynamical Processes,Entanglement,Transport Properties,Correlation Functions, | en |
| dc.relation.page | 119 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2010-11-18 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 物理研究所 | zh_TW |
| Appears in Collections: | 物理學系 | |
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| File | Size | Format | |
|---|---|---|---|
| ntu-99-1.pdf Restricted Access | 2.57 MB | Adobe PDF |
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