Abstract
An efficient numerical algorithm for solving the time-non-local non-Markovian master equation in the second Born approximation with exponentially decaying bath correlation function is introduced. 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. As an application we consider the traditional dimer system that is used to model excitation energy transfer in photosynthetic systems, examining exact second order results and using them to assess the range of validity of the traditional Markov approximation. The method is also used to examine the dependence of the dynamics on the initial coherences in the case of two coupled oscillators. The computational results are augmented by a set of analytic inequalities obtained for the regime of validity of the Markov approximation in the cases of weak and strong resonance coupling, allowing for a rapid determination of the utility of the Markovian dynamics in various parameter regions.
Published Version
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