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Exciton transfer dynamics and quantum diffusion in a lattice of two level systems: Interplay between transport and coherent population transfer dynamics

We study excitation transfer dynamics in a lattice of two level systems characterized by dynamic disorder. The diagonal and off-diagonal energy disorders arise from the coupling of system and bath. We consider both the same and the independent bath limits. In case of independent bath all diagonal and off-diagonal bath coupling elements fluctuate independently of each other and the dynamics is complicated. We obtain the time dependent population distribution by solving quantum stochastic Liouville equation (QSLE) derived by Kubo. The main result of our study is both the population transfer dynamics and the mean square displacement of the exciton behave the similar way in the same and independent bath cases in the Markovian limit. However, these two baths can give rise to markedly different behavior in the non-Markovian limit where coherent transport becomes important. There are also several additional new results as follows. (i) Exciton migration remains coherent all the time for an average, non-zero off-diagonal coupling value J for the same bath case while it becomes incoherent for independent bath case in the Markovian limit. (ii) An oscillatory behavior of the population transfer dynamics supports the coherent mode of transfer of exciton. (iii) Agreement with available analytical expression of mean squared displacement is good in the Markovian limit for independent bath case with off-diagonal fluctuation but only qualitative in the non-Markovian limit for which no complete analytical solution is available. (iv) Transition from coherent to incoherent transport is observed in the independent bath case with diagonal fluctuation when the bath is made progressively more Markovian. (v) The correlation time of the bath plays a unique role in dictating the diffusive spread that is not anticipated in a Markovian treatment.