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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 | 劉凱丞 | zh_TW |
| dc.contributor.author | Kai-Cheng Liu | en |
| dc.date.accessioned | 2025-07-11T16:19:12Z | - |
| dc.date.available | 2025-07-12 | - |
| dc.date.copyright | 2025-07-11 | - |
| dc.date.issued | 2025 | - |
| dc.date.submitted | 2025-07-03 | - |
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| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/97716 | - |
| dc.description.abstract | 層次運動方程式（Hierarchical Equations of Motion, HEOM）方法可在諧振環境下對開放量子系統動力學進行數值精確模擬，然而在強系統-環境耦合或極低溫條件下，HEOM 方法的計算成本將變得難以負擔。此外，HEOM 模擬中所採用的環境頻譜密度（spectral density）常受限於 Debye–Lorentz 形式，以利時間相關函數（Time Correlation Function, TCF）的指數展開。為克服這些限制，我們提出一種有效熱振盪模型（Effective Thermal Oscillator Model, ETOM），此方法可直接將 TCF 解釋為一系列振盪性的指數衰退項，避免了低溫修正的繁瑣處理，並顯著減少在模擬任意頻譜密度時所需的輔助密度算符（Auxiliary Density Operators, ADO）數量。此外，我們亦結合 GPU 加速以提升計算效率，使 HEOM 方法能更快速地模擬開放量子系統的動力學。針對一系列模型系統，我們應用 ETOM-HEOM 方法進行族群動力學與二維電子光譜（2D electronic spectra）模擬並分析光譜峰值訊號變化帶來的非馬可夫性質。最後，我們將 ETOM-HEOM 與標準 HEOM 及其他數值精確方法進行比較，驗證新方法之正確性與可靠性。我們期望 ETOM-HEOM 能成為一套功能強大且開放原始碼的模擬工具，為化學與物理領域中重要的量子動力學現象提供高效且精確的模擬工具。 | zh_TW |
| dc.description.abstract | Hierarchical equations of motion (HEOM) approach offers exact numerical simulations of open quantum system dynamics under harmonic baths, but it becomes computationally intractable for strong system-bath coupling or low temperature regime. Furthermore, the bath spectral density used in HEOM simulations is often constrained to the Debye–Lorentz form for time correlation function (TCF) exponential expansion. To overcome these limitations, we propose an effective thermal oscillator model (ETOM), which directly interprets TCF to a series of oscillatory exponential terms and avoids both cumbersome low-temperature corrections and large number of auxiliary density operators needed to simulate arbitrary spectral densities. Moreover, we also incorporate GPU acceleration to enhance computational efficiency, enabling faster simulations of open quantum system dynamics using the HEOM approach. Applications of the ETOM-HEOM method for calculations of population dynamics as well as 2D electronic spectra for a series of model systems across a wide parameter regime were carried out to analyze the variance in 2D peaks signal and explore the non-Markovian property of the system. Finally, we compared ETOM-HEOM with standard HEOM and other numerically exact method to confirm the validity of the new approach. We expect ETOM-HEOM to become a powerful and open source tools for efficient and accurate simulations of quantum dynamical phenomena important in chemistry and physics. | en |
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| dc.description.provenance | Made available in DSpace on 2025-07-11T16:19:12Z (GMT). No. of bitstreams: 0 | en |
| dc.description.tableofcontents | Verification Letter from the Oral Examination Committee i
Acknowledgements iii 摘要 v Abstract vii Contents ix List of Figures xiii List of Tables xix Denotation xxi Chapter 1 Introduction 1 1.1 Open Quantum System . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Hierarchical Equation of Motion (HEOM) . . . . . . . . . . . . . . . 2 1.2.1 Comparison with Förster Theory and Redfield Theory . . . . . . . . 3 1.3 Limitations of HEOM Approach . . . . . . . . . . . . . . . . . . . . 7 1.3.1 Debye-Lorentz Spectral Density Constraints: Parametrization Strat-egy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.3.2 Low-Temperature Challenges in HEOM: Review of Numerical Ap-proaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.3.3 Pseudomode-Based Methods: A Survey of Recent Advances . . . . 11 1.4 Scope and Organization of This Work . . . . . . . . . . . . . . . . . 12 Chapter 2 Methodology 13 2.1 Open Quantum System Model . . . . . . . . . . . . . . . . . . . . . 13 2.1.1 Exciton–Bath Composite Hamiltonian . . . . . . . . . . . . . . . . 13 2.1.2 Spectral Density and Bath Correlation Function . . . . . . . . . . . 14 2.2 Hierarchical Equations of Motion (HEOM) for Open System Dynamics 16 2.2.1 Matsubara Expansion for Debye–Lorentz Spectral Densities . . . . 16 2.2.2 Reduced System Density Operator Evolution . . . . . . . . . . . . 18 2.2.3 General HEOM Structure and Truncation Rule . . . . . . . . . . . . 20 2.2.4 Computational Bottlenecks in HEOM . . . . . . . . . . . . . . . . 22 2.3 Effective Thermal Oscillator Model (ETOM) . . . . . . . . . . . . . 23 2.3.1 Representation via Underdamped Mode Decomposition . . . . . . . 24 2.3.2 Flexibility and Temperature Dependence . . . . . . . . . . . . . . . 25 Chapter 3 ETOM Expanded Time Correlation Functions 27 3.1 Mode Expansion of Bath Correlations via ETOM . . . . . . . . . . 27 3.1.1 Debye–Lorentz TCF Approximation . . . . . . . . . . . . . . . . . 28 3.1.2 Super-Ohmic TCF Approximation . . . . . . . . . . . . . . . . . . 28 3.2 Scaling Behavior of System-Bath Coupling Strengths . . . . . . . . . 30 Chapter 4 ETOM-HEOM Population Dynamics Simulations 31 4.1 Debye–Lorentz Bath: Population Dynamics . . . . . . . . . . . . . 31 4.1.1 Benchmarking with Traditional HEOM . . . . . . . . . . . . . . . 32 4.1.2 ETOM-HEOM vs. QuTiP-BoFiN Under Cryogenic Limits . . . . . 34 4.2 Super-Ohmic Bath: Population Dynamics . . . . . . . . . . . . . . 37 4.2.1 Coupling Effects on Decoherence and Damping . . . . . . . . . . . 38 4.2.2 Energy Gap and Coupling Effects on Population Localization and Oscillation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 4.2.3 Cryogenic Effect on Preservation of Quantum Coherence . . . . . . 42 Chapter 5 2DES Simulations from ETOM-HEOM 45 5.1 Dynamics Simulation of 2DES Spectrum . . . . . . . . . . . . . . . 45 5.1.1 Overview of 2DES and Its Relevance to Excitonic Dynamics . . . . 45 5.1.2 Laser–Matter Interaction and Exciton Manifold Construction . . . . 46 5.1.3 Finite-Pulse 2DES Signal within the HEOM Framework . . . . . . 48 5.1.4 2D Fourier Analysis and Spectrum Construction . . . . . . . . . . . 49 5.2 Population-Time Evolution of 2D Spectral Peaks in an Ohmic Dimer 50 5.2.1 Population–dynamics signatures in 2DES . . . . . . . . . . . . . . 50 5.2.2 ETOM–HEOM simulation of an Ohmic dimer . . . . . . . . . . . . 51 5.3 Spectral Diffusion Analysis via Central Line Slope . . . . . . . . . . 53 5.3.1 Time-Resolved CLS and its Connection to Environmental Memory . 54 5.3.2 Spectral-Diffusion Kinetics Revealed by CLS . . . . . . . . . . . . 54 5.4 Quantum Beating Signatures in Non-Rephasing Spectra . . . . . . . 56 5.4.1 Physical Origin of Quantum Beating in 2DES . . . . . . . . . . . . 56 5.4.2 Double-Sided Feynman Diagram Analysis of Coherence Pathways . 57 5.4.3 Impact of System–Bath Coupling Strength on Beating Frequency . . 58 Chapter 6 GPU Implementation 63 6.1 GPU Program Workflow . . . . . . . . . . . . . . . . . . . . . . . . 64 6.2 Parallel Performance of ETOM–HEOM . . . . . . . . . . . . . . . . 66 6.2.1 Nominal scaling and dominant bottlenecks . . . . . . . . . . . . . . 66 6.2.2 Runtime crossover as a function of system size . . . . . . . . . . . 67 6.3 Memory Bottlenecks and Further Optimization Strategies . . . . . . 69 6.3.1 Matrix–Product Compression of the HEOM . . . . . . . . . . . . . 69 6.3.2 MPS Decoposition with ETOM . . . . . . . . . . . . . . . . . . . . 71 6.3.3 GPU Acceleration with cuTensor and cuTensorNet . . . . . . . . . 72 Chapter 7 Conclusion 73 References 75 Appendix A — Limitations of the Cos–Sin TCF Decomposition 85 Appendix B — Parameter Correspondence between Thesis Notation and Source Code 89 | - |
| dc.language.iso | en | - |
| dc.subject | 圖形處理器 | zh_TW |
| dc.subject | 任意譜密度 | zh_TW |
| dc.subject | 非馬可夫動力學 | zh_TW |
| dc.subject | 層次運動方程 | zh_TW |
| dc.subject | GPU | en |
| dc.subject | Hierarchical Equations of Motion | en |
| dc.subject | Non-Markovian-Dynamics | en |
| dc.subject | Arbitrary Spectral Density | en |
| dc.title | 具有有效熱振子模型框架的層次運動方程 | zh_TW |
| dc.title | Effective Thermal Oscillator Model Framework for HEOM | en |
| dc.type | Thesis | - |
| dc.date.schoolyear | 113-2 | - |
| dc.description.degree | 碩士 | - |
| dc.contributor.oralexamcommittee | 金必耀;許良彥;林倫年 | zh_TW |
| dc.contributor.oralexamcommittee | BIH-YAW JIN;Liang-Yan Hsu;Michitoshi Hayashi | en |
| dc.subject.keyword | 層次運動方程,非馬可夫動力學,任意譜密度,圖形處理器, | zh_TW |
| dc.subject.keyword | Hierarchical Equations of Motion,Non-Markovian-Dynamics,Arbitrary Spectral Density,GPU, | en |
| dc.relation.page | 90 | - |
| dc.identifier.doi | 10.6342/NTU202501504 | - |
| dc.rights.note | 同意授權(全球公開) | - |
| dc.date.accepted | 2025-07-04 | - |
| dc.contributor.author-college | 理學院 | - |
| dc.contributor.author-dept | 化學系 | - |
| dc.date.embargo-lift | 2025-07-12 | - |
| 顯示於系所單位： | 化學系 | |
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