Non-Markovian Second-Order Quantum Master Equation and Its Markovian Limit: Electronic Energy Transfer in Model Photosynthetic Systems
Non-Markovian Second-Order Quantum Master Equation and Its Markovian Limit: Electronic Energy Transfer in Model Photosynthetic Systems
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发表时间：
2011-06
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通讯作者：
Navinder Singh;P. Brumer
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作者：
Navinder Singh;P. Brumer
一个直接的数值算法求解的时间非本地非马尔可夫主方程在第二玻恩近似的介绍和实用的范围内，这种近似，和马尔可夫近似，分析了传统的二聚体系统，模型激发能量转移在光合作用。具体地说，耦合的积分微分方程的约化密度矩阵求解的一个有效的辅助函数方法在能量和网站表示。除了给出精确的结果，这种方法使我们能够计算评估的范围内的重组能量和声子自相关函数的衰减率的马尔可夫Redfield理论和二阶近似是有效的。例如，在Fenna-Mathews-Olson（FMO）型系统中使用$\lambda> 10 \textrm{cm}^{-1}$的Redfield理论是错误的。此外，解析不等式的马尔可夫近似的有效性的情况下，弱和强共振耦合的制度，允许快速确定的马尔可夫动力学的效用在参数区域。最后，在一个二聚体系统中的状态的演变，有和没有初始的相干性，结果进行了比较，以评估初始相干性的作用。
A direct numerical algorithm for solving the time-nonlocal non-Markovian master equation in the second Born approximation is introduced and the range of utility of this approximation, and of the Markov approximation, is analyzed for the traditional dimer system that models excitation energy transfer in photosynthesis. Specifically, the coupled integro-differential equations for the reduced density matrix are solved by an efficient auxiliary function method in both the energy and site representations. In addition to giving exact results to this order, the approach allows us to computationally assess the range of the reorganization energy and decay rates of the phonon auto-correlation function for which the Markovian Redfield theory and the second order approximation is valid. For example, the use of Redfield theory for $\lambda> 10 \textrm{cm}^{-1}$ in systems like Fenna-Mathews-Olson (FMO) type systems is shown to be in error. In addition, analytic inequalities are obtained for the regime of validity of the Markov approximation in cases of weak and strong resonance coupling, allowing for a quick determination of the utility of the Markovian dynamics in parameter regions. Finally, results for the evolution of states in a dimer system, with and without initial coherence, are compared in order to assess the role of initial coherences.