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Correlating exciton coherence length, localization, and its optical lineshape. I. a finite temperature solution of the Davydov soliton model

The lineshape of spectroscopic transitions offer windows into the local environment of a system. Here, we present a novel approach for connecting the lineshape of a molecular exciton to finite-temperature lattice vibrations within the context of the Davydov soliton model (A. S. Davydov and N. I. Kislukha, Phys. Stat. Sol. {\bf 59},465(1973)). Our results are based upon a numerically exact, self-consistent treatment of the model in which thermal effects are introduced as fluctuations about the zero-temperature localized soliton state. We find that both the energy fluctuations and the localization can be described in terms of a parameter-free, reduced description by introducing a critical temperature below which exciton self-trapping is expected to be stable. Above this temperature, the self-consistent ansatz relating the lattice distortion to the exciton wavefunction breaks down. Our theoretical model coorelates well with both experimental observations on molecular J-aggregate and resolves one of the critical issues concerning the finite temperture stability of soliton states in alpha-helices and protein peptide chains.