臺灣博碩士論文加值系統

為超越傳統微擾論於描述光合作用系統中的激發態能量傳遞之困境，我們發展一小極化子座標下的量子主方程方法。本文將探討該主方程的適用範圍、小極化子理論在不同激發態耦合與激發態─環境耦合結構下所預測激發態能量傳輸速率的特殊性質、 以及小極子理論下吸收與放射光譜的計算方法。本研究中我們確認小極子主方程可準確的描述光合作用系統中的激發態能量傳遞並提出一簡單的判別式來檢測該主方程的適用性，在小極化子能量傳輸速率常數中分離出離域激發態與激發態躍遷貢獻的速率分量，並提出小極化子架構下吸收與放射光譜的計算方法，以利小極化子理論日後應用於描述真實系統中的激發態能量傳遞。

Excitation energy transfer is crucial to the efficiency of solar energy harvesting. The small polaron quantum master equation (SPQME) is a promising approach to describe coherent excitation energy transfer dynamics in complex molecular systems and exceeds the limits of conventional F"orster and Redfield theories. Here we first demonstrate that the polaronic Markovian energy transfer rate presents a unified framework to elucidate the behaviour and mechanisms of exciton transfer. From the polaron rate expression we elicit two major factors affecting the exciton transfer rate: the multitude of energy-dissipation pathways that facilitates exciton transfer and the fluctuation-induced localization that causes exciton self-trapping. Second, we conduct a comprehensive benchmark of the small polaron population dynamics comparing with numerically-exact quasi-adiabatic path integral calculations, where we discover that the small polaron theory is applicable in a wide parameter range. Moreover, we show that the performance of SPQME depends strongly upon the extent of exciton delocalization and polaron formation rate. Therein we propose a criterion to assess the regime of applicability for SPQME. Finally, we present our newly developed methods for computation of absorption and emission spectra within the polaron framework so as to facilitate practical modeling of light-harvesting systems using the small polaron theory.

口試委員審定書 i
致謝iii
中文摘要 v
Abstract vii
Contents ix
Nomenclature xiii
List of Figures xv
1 Introduction 1
2 The Small Polaron Theory 5
2.1 The Frenkel Exciton Model . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 The Polaron Transformation . . . . . . . . . . . . . . . . . . . . . . . . 6
2.3 Small Polaron Master Equation . . . . . . . . . . . . . . . . . . . . . . . 8
2.4 Dimer Model System . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.5 Dynamical Localization . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.6 Small Polaron Dynamics: A Preview . . . . . . . . . . . . . . . . . . . . 12
3 Polaron Transfer Rate 15
3.1 Markovian Energy Transfer Rate . . . . . . . . . . . . . . . . . . . . . . 16
3.2 Delocalization and Hopping on EET Rate . . . . . . . . . . . . . . . . . 20
3.3 Energy Matching Condition . . . . . . . . . . . . . . . . . . . . . . . . 21
3.4 Effect of Correlated Bath Modes . . . . . . . . . . . . . . . . . . . . . . 23
3.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4 Regimes of Applicability 29
4.1 The Magnitude of Perturbation . . . . . . . . . . . . . . . . . . . . . . . 29
4.2 Variational Polaron Studies: A Brief Review . . . . . . . . . . . . . . . . 31
4.3 Coherent Dynamics versus Polaron Formation . . . . . . . . . . . . . . . 32
4.4 Coherent versus Incoherent Dynamics . . . . . . . . . . . . . . . . . . . 36
4.5 Temperature Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.6 Criterion for the Regime of Applicability . . . . . . . . . . . . . . . . . 41
4.7 Non-Equilibrium Bath Dynamics . . . . . . . . . . . . . . . . . . . . . . 43
4.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
5 Lineshape Simulation 49
5.1 Absorption Lineshape: A Review . . . . . . . . . . . . . . . . . . . . . 50
5.1.1 Direct Second-Order Expansion . . . . . . . . . . . . . . . . . . 51
5.1.2 Equilibrium-Bath Approximation . . . . . . . . . . . . . . . . . 54
5.2 Cumulant Expansion Method . . . . . . . . . . . . . . . . . . . . . . . . 57
5.3 Emission Lineshape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
5.3.1 Time-Local and Time-Nonlocal Expressions . . . . . . . . . . . 63
5.3.2 Emission Lineshape with a Dimer Model . . . . . . . . . . . . . 65
6 Conclusion 75
A Derivation of Master Equations 79
A.1 Derivation of SPQME . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
A.2 Master Equation for Emission . . . . . . . . . . . . . . . . . . . . . . . 82
A.3 Derivation of Redfield Equation . . . . . . . . . . . . . . . . . . . . . . 82
A.4 Derivation of F&;#246;rster-Type Theories . . . . . . . . . . . . . . . . . . . . 83
B Bath Correlation Functions 87
B.1 Bath Correlation Functions of Displacement Operators . . . . . . . . . . 87
B.2 Bath Correlation Functions of Mixed Operators . . . . . . . . . . . . . . 88
C Delocalization Length 89
D Dipolar Time-Correlation Functions 91
D.1 Long-Time Behaviour of Zeroth-Order Dipolar Time-Correlation Functions 91
D.1.1 Correlation Funtion with Superohmic Spectral Density . . . . . . 92
D.2 Convergence of Direct Expansion . . . . . . . . . . . . . . . . . . . . . 93
D.3 Second Cumulant in Absorption Lineshape . . . . . . . . . . . . . . . . 95
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