Finite-temperature large acoustic polaron dynamics in quasi-one-dimensional molecular crystals

We report the results of theoretical examinations of large polaron motion in one-dimensional (1D) molecular crystals under the influence of thermal fluctuations of the host lattice and constant electric field. Such a situation may arise in biological macromolecules such as an alpha helix where charge (electron) transfer may be achieved by a polaron (soliton) mechanism. In that case, the electric field represents the effective endogenous electric field which is always present in realistic conditions. We derive and solve the Fokker-Planck equation for the distribution function of the soliton's center-of-mass position. It is shown that the soliton effectively exhibits a random walk. Moreover, in order to examine statistical properties of the soliton wave function, we calculate the mean value of the soliton probability density: and we find that, for sufficiently large times, thermal fluctuations destruct the soliton, which transforms into the Gaussian packet. These results were used in order to estimate the relevance of the soliton model of charge transfer in polypeptide chains.