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We study excitation transfer dynamics in a lattice of two level systemscharacterized by dynamic disorder. The diagonal and off-diagonal energydisorders arise from the coupling of system and bath. We consider both the sameand the independent bath limits. In case of independent bath all diagonal andoff-diagonal bath coupling elements fluctuate independently of each other andthe dynamics is complicated. We obtain the time dependent populationdistribution by solving quantum stochastic Liouville equation (QSLE) derived byKubo. The main result of our study is both the population transfer dynamics andthe mean square displacement of the exciton behave the similar way in the sameand independent bath cases in the Markovian limit. However, these two baths cangive rise to markedly different behavior in the non-Markovian limit wherecoherent transport becomes important. There are also several additional newresults as follows. (i) Exciton migration remains coherent all the time for anaverage, non-zero off-diagonal coupling value J for the same bath case while itbecomes incoherent for independent bath case in the Markovian limit. (ii) Anoscillatory behavior of the population transfer dynamics supports the coherentmode of transfer of exciton. (iii) Agreement with available analyticalexpression of mean squared displacement is good in the Markovian limit forindependent bath case with off-diagonal fluctuation but only qualitative in thenon-Markovian limit for which no complete analytical solution is available.(iv) Transition from coherent to incoherent transport is observed in theindependent bath case with diagonal fluctuation when the bath is madeprogressively more Markovian. (v) The correlation time of the bath plays aunique role in dictating the diffusive spread that is not anticipated in aMarkovian treatment.

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