We derive the stochastic Schrodinger equation for the system wave vector and use it to describe the excitation energy transfer dynamics in molecular aggregates. We suggest a quantum-measurement based method of estimating the excitation transfer time. Adequacy of the proposed approach is demonstrated by performing calculations on a model system. The theory is then applied to study the excitation transfer dynamics in a photosynthetic pigment-protein Fenna-Matthews-Olson (FMO) aggregate using both the Debye spectral density and the spectral density obtained from earlier molecular dynamics simulations containing strong vibrational high-frequency modes. The obtained results show that the excitation transfer times in the FMO system are affected by the presence of the vibrational modes, however the transfer pathways remain the same.
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