Xin Chen, Jianshu Cao, Robert Silbey
The recent experimental discoveries about excitation energy transfer (EET) in light harvesting antenna (LHA) attract a lot of interest. In order to study the associated questions, we need a more rigorous theoretical framework to understand the system-environement interaction and therein the evolution of the reduced quantum system. A phonon is often used to model the fluctuating environment and convolutes the reduced quantum system temporarily. In this paper, we propose a novel way to construct complex-valued Gaussian processes to describe thermal quantum phonon bath exactly by converting the convolution of influence functional into the time correlation of a complex Gaussian random field. Based on the construction, we propose a rigorous and efficient computational method, the covariance decomposition (CD) and conditional propagation scheme, to simulate the temporarily entangled reduced system. The new method allows us to study the non-Markovian effect without perturbation under the influence of different spectral densities of the linear system-phonon coupling coefficients. Its application in the study of EET in the Fenna-Matthews-Olson (FMO) model Hamiltonian under four different spectral densities is discussed. Since the scaling of our method is linear due to its Monte Carlo nature, the future application of the method for large LHA systems is attractive. In addition, this method can be used to study the effect of correlated initial condition on the reduced dynamics in the future.
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http://arxiv.org/abs/1304.3143
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