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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 鄭原忠 | zh_TW |
| dc.contributor.advisor | Yuan-Chung Cheng | en |
| dc.contributor.author | 賴思帆 | zh_TW |
| dc.contributor.author | Szu-Fan Lai | en |
| dc.date.accessioned | 2024-07-29T16:10:51Z | - |
| dc.date.available | 2024-07-30 | - |
| dc.date.copyright | 2024-07-29 | - |
| dc.date.issued | 2024 | - |
| dc.date.submitted | 2024-07-16 | - |
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| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/93309 | - |
| dc.description.abstract | 我們從微觀角度推導了一個包含非馬可夫動力學 (non-Markovain dynamics) 的量子朗之萬方程式 (quantum Langevin equation)，並使用譜密度 (spectral density) 來描述環境影響。我們將此量子朗之萬方程式加入含時薛丁格方程式，成為薛丁格——朗之萬方程式以模擬波函數的動力學。在此之上我們探究了此波函數動力學能夠具有馬可夫性質的參數範圍。為此，我們定義了馬可夫係數 (Markovian coefficient) 並用於薛丁格—朗之萬方程式的馬可夫近似。我們的結果顯示在德魯德—勞侖茲譜密度環境下，當系統頻率低且耦合 (coupling) 強度低的情況馬可夫近似是合適的。但以超歐姆 (super-Ohmic) 譜密度環境下馬可夫近似在低頻表現不佳，但在中等頻率下表現較好。而耦合強度幾乎不影響此近似。 | zh_TW |
| dc.description.abstract | We present a derivation of a quantum Langevin equation (QLE) from a microscopic perspective. This approach includes non-Markovian dynamics, and describes the environmental effects using the spectral density based on the microscopic model. We further simulate the wavefunction dynamics based on the QLE, leading to a Schrödinger-Langevin equation (SLE). Furthermore, we investigate the regime where the dissipative dynamics can be considered Markovian. To this end, we define a Markovian coefficient and utilize it in the Markovian approximation of the Schrödinger-Langevin equation. Our results demonstrate that for the Drude-Lorentz bath, the Markovian approximation is accurate in the regime characterized by low system frequency and weak system-bath coupling; however, for the super-Ohmic bath, the Markovian approximation fails at low and high system frequency, but is reliable in the intermediate system frequency regime. The damping coefficient does not affect the approximation at intermediate system frequency apparently. | en |
| dc.description.provenance | Submitted by admin ntu (admin@lib.ntu.edu.tw) on 2024-07-29T16:10:51Z No. of bitstreams: 0 | en |
| dc.description.provenance | Made available in DSpace on 2024-07-29T16:10:51Z (GMT). No. of bitstreams: 0 | en |
| dc.description.tableofcontents | Acknowledgements i
摘要 iii Abstract v Contents vii List of Figures xi List of Tables xiii Denotation xv Chapter 1 Introduction 1 1.1 Open-system quantum dynamics . . . . . . . . . . . . . . . . . . . . 1 1.2 The quantum Langevin equation . . . . . . . . . . . . . . . . . . . . 2 1.3 The non-Markovian Schrödinger-Langevin equation . . . . . . . . . 3 Chapter 2 Methodology 5 2.1 Quantum Langevin equation . . . . . . . . . . . . . . . . . . . . . . 5 2.2 Schrödinger-Langevin equation . . . . . . . . . . . . . . . . . . . . 11 2.3 Explicit numerical simulation of the QLE . . . . . . . . . . . . . . . 13 2.3.1 Bath discretization . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.3.2 Sampling initial positions and momenta of bath oscillators from a Wigner quasi-distribution . . . . . . . . . . . . . . . . . . . . . . . 15 Chapter 3 QSLE dynamics of an oscillator coupled to a Drude-Lorentz bath 17 3.1 Model systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3.2 Validity of the QSLE . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3.3 The effect of random force . . . . . . . . . . . . . . . . . . . . . . . 20 Chapter 4 Markovian regime in a Drude-Lorentz bath 23 4.1 Markovian approximation . . . . . . . . . . . . . . . . . . . . . . . 23 4.1.1 The Mathematical condition for the Markovian dynamics . . . . . . 23 4.1.2 The Markovian coefficient . . . . . . . . . . . . . . . . . . . . . . 27 4.2 Markovian QSLE dynamics . . . . . . . . . . . . . . . . . . . . . . 29 4.3 Quantification of the Markovianity . . . . . . . . . . . . . . . . . . 32 Chapter 5 QSLE dynamics of an oscillator coupled to a super-Ohmic bath 35 5.1 Wavefunction dynamics with super-Ohmic spectral density . . . . . . 35 5.2 Influence of bath spectral density on dissipative dynamics . . . . . . 36 5.2.1 Normalization of spectral densities . . . . . . . . . . . . . . . . . . 38 5.2.2 Difference of spectral densities . . . . . . . . . . . . . . . . . . . . 40 5.2.3 Wavefunction dynamics comparison with different spectral densities 41 Chapter 6 Markovian regime for super-Ohmic bath 43 6.1 Markovian approximation for the super-Ohmic spectral density . . . 43 6.1.1 The derivation of the Markovian coefficient of the super-Ohmic spectral density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 6.2 Derivation of Markovian coefficient from potential renormalization . 45 6.3 Markovian dynamics with the proposed Markovian coefficient for the super-Ohmic spectral density . . . . . . . . . . . . . . . . . . . . . . 48 6.4 Quantification of the Markovianity . . . . . . . . . . . . . . . . . . 50 Chapter 7 Conclusions 53 References 57 Appendix A — Derivation of the friction operator 61 Appendix B — The computational details and the numerical convergence of the results 65 | - |
| dc.language.iso | en | - |
| dc.subject | 非馬可夫動力學 | zh_TW |
| dc.subject | 薛丁格—朗之萬方程式 | zh_TW |
| dc.subject | 量子朗之萬方程式 | zh_TW |
| dc.subject | 馬可夫近似 | zh_TW |
| dc.subject | Markovian approximation | en |
| dc.subject | quantum Langevin equation | en |
| dc.subject | non-Markovian dynamics | en |
| dc.subject | Schrödinger-Langevin Equation | en |
| dc.title | 從微觀角度出發的非馬可夫薛丁格—朗之萬方程式 | zh_TW |
| dc.title | A Non-Markovian Schrödinger-Langevin Equation from A Microscopic Perspective | en |
| dc.type | Thesis | - |
| dc.date.schoolyear | 112-2 | - |
| dc.description.degree | 碩士 | - |
| dc.contributor.oralexamcommittee | 郭哲來;許良彥 | zh_TW |
| dc.contributor.oralexamcommittee | Jer-Lai Kuo;Liang-Yan Hsu | en |
| dc.subject.keyword | 薛丁格—朗之萬方程式,非馬可夫動力學,馬可夫近似,量子朗之萬方程式, | zh_TW |
| dc.subject.keyword | Schrödinger-Langevin Equation,non-Markovian dynamics,Markovian approximation,quantum Langevin equation, | en |
| dc.relation.page | 67 | - |
| dc.identifier.doi | 10.6342/NTU202401786 | - |
| dc.rights.note | 同意授權(全球公開) | - |
| dc.date.accepted | 2024-07-17 | - |
| dc.contributor.author-college | 理學院 | - |
| dc.contributor.author-dept | 化學系 | - |
| 顯示於系所單位： | 化學系 | |
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