UBC Theses and Dissertations
Excitonic modes and phonons in biological molecules Zhu, Zhen
There are two kinds of environmental modes in open quantum systems: the delocalized modes which can typically be modeled by "oscillator bath" models and the localized modes which can be mapped to "spin bath" modes. To understand the quantum phenomena in photosynthetic energy transfer, we at first conduct thorough studies of the proper modeling of light harvesting molecules as well as their interactions with the central system. These modes can couple to the system by either modulating the on-site energy (Holstein coupling) or modulating the hopping amplitude (Peierls coupling). Only the Holstein couplings of delocalized modes have been extensively studied. The importance of other types of couplings is rarely discussed in the literature. For the spin bath, we study a particle hopping around a general lattice, coupled to a spin bath. Analytical results are found for the dynamics of the influence functional and for the reduced density matrix of the particle in various parameter regimes. Spin baths behave qualitatively differently from oscillator baths and dissipation and decoherence happen independently in different parameter regimes. For the Peierls couplings, we start with a dimer model for light harvesting molecules, which contains a reaction center and both types of phonon couplings. We find that the effect of Peierls type coupling on the transfer rate can be significant even when it is not noticeable in the spectrum. Our study suggests that Peierls couplings cannot be easily neglected in light harvesting molecules in which the energy difference between the sites is usually much larger than the hopping amplitude. We apply our method to a real light harvesting model. Although we do not have much detailed information of the Peierls couplings in vivo, we find that vibrational phonons can affect the path-selecting of the central particles as well as increasing the transfer rate.
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