We study excitation transfer and migration in a one-dimensional lattice characterized by dynamic disorder. The diagonal and off-diagonal energy disorders arise from the coupling of system and bath. We consider both same bath (when baths are spatially correlated) and independent bath (when baths are completely uncorrelated) limits. In the latter case, all diagonal and off-diagonal bath coupling elements fluctuate independently of each other and the dynamics is complicated. We obtain time dependent population distribution by solving Kubo’s quantum stochastic Liouville equation. In the Markovian limit, both energy transfer dynamics and mean square displacement of the exciton behave the similar way in same and independent bath cases. However, these two baths can give rise to a markedly different behavior in the non-Markovian limit. We note that previously only the same bath case has been studied in the non-Markovian limit. The other main results of our study include the following. (i) For an average, non-zero off-diagonal coupling value J, exciton migration remains coherent in same bath case even at long times while it becomes incoherent in independent bath case in the Markovian limit. (ii) Coherent transfer is manifested in an oscillatory behavior of the energy transfer dynamics accompanied by faster-than diffusive spread of the exciton from the original position. (iii) Agreement with available analytical expression of mean squared displacement is good in Markovian limit for independent bath (off-diagonal fluctuation) case but only qualitative in non-Markovian limit for which no complete analytical solution is available. (iv) We observe transition from coherent to incoherent transport in independent bath (diagonal fluctuation) case when the bath is made progressively more Markovian. We present an analytical study that shows coherence to propagate through excited bath states. (v) The correlation time of the bath plays a unique role in dictating the diffusive spread that is not anticipated in a Markovian treatment.

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