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We address the effects of quantum coherences on the optical line shape of anexciton in the presence of dynamic disorder. We consider a one-dimensionalexcitonic system that consists of two levels placed at regular intervals.Detailed analytical calculations of line shape have been carried out by usingKubo's stochastic Liouville equation (K-QSLE). We make use of the observationthat in the site representation, the Hamiltonian of our system with constantoff-diagonal coupling J is a tridiagonal Toeplitz matrix (TDTM) whoseeigenvalues and eigen functions are known analytically. This identification isparticularly useful for long chains where the eigen values of TDTM help tounderstand crossover between static and fast modulation limits. We summarizethe new results as follows. (i) In the slow modulation limit when the bathcorrelation time is large, the effects of spatial correlation are notnegligible. Here the line shape is broadened and the number of peak increasesbeyond the ones obtained from TDTM (constant off-diagonal coupling element Jand no fluctuation). (ii) However, in the fast modulation limit when the bathcorrelation time is small, the spatial correlation is less important (iii)Importantly, we find that the line shape can capture that quantum coherenceaffects in the two limits differently.

Signatures of quantum coherence in the optical line shape of an exciton in the presence of dynamic disorder