Unification of polaron and soliton theories of exciton transport

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Abstract
We present a unified theory of polaron and soliton dynamics by combining time-dependent variational methods recently applied to the theory of Davydov solitons with partial-dressing methods well known from polaron theory. We focus on the simplest partial-dressing assumption, applying a common dressing fraction to all phonon modes. Our fundamental result is a system of nonlinear evolution equations in which the tendency of a system to form Davydov solitons is balanced against its tendency to form small polarons. We subsequently apply time-independent variational methods to determine the optimal dressing fraction in a mean-field manner. The characterization of the partially dressed soliton states that results is complete with respect to the system parameter space. Consistent with prior works from polaron theory, we find a self-trapping transition that is only weakly modified by our inclusion of nonlinearities, and we reinterpret this transition in terms of our newly obtained soliton states. Applying our results to a central problem in bioenergetics, we obtain results markedly different from well-known results of Davydov’s theory.

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