On the Dynamics of a Phonon-Damped Proton Coupled System

Abstract

The dynamics of a coupled system between phonons and proton tunneling mode are investimated. Concerning proton dynamics, the energy decay processes to the heat bath, as well as the coupling mechanism to a particular phonon mode, are taken into account in the generalized-Langevin equation describing the coupled system. An explicit expression of phonon spectral density distribution in the energy-momentum space is derived within RPA approximation. This expression seems to give an unified form which includes the various treatments hitherto discussed as its extreme cases. Particularly a continuous cross-over behavior from underdamped regime to the overdamped regime associated with proton tunneling mode is discussed using the obtained unified expression.