Bio-energy Transport as a Dressed Vibrational Exciton in Protein Molecules*

Following the ideas of Davydov's soliton theory, we study the bio-energy transport in protein molecules. By using a quantum Brownian motion model for a phonon dressed vibrational exciton, we calculate the time-dependence on the mean square distance, diffusion coefficient, and energy of the vibrational exciton. We find the time-dependence by solving the quantum Langevin equation and find oscillatory behaviors due to the super-diffusive non-ohmic dissipation. We find that the vibrational exciton gains an overall energy due to the coupling to the phonon bath, it also dissipates its energy to the environment as it propagates. The amount of energy gain and the oscillatory features depend on both temperature and the phonon-vibron coupling.