Narrow band exciton coupled with acoustical anharmonic phonons: application to the vibrational energy flow in a lattice of H-bonded peptide units

A time-convolutionless master equation is established for describing the transport properties of amide-I vibrons coupled with acoustic phonons in a lattice of H-bonded peptide units. Within the non-adiabatic weak coupling limit, it is shown that the vibron dynamics strongly depends on the nature of the phonons and two distinct mechanisms have been identified. Harmonic phonons, which support spatial correlations over an infinite length scale, induce a fast dephasing-rephasing mechanism in the short time limit. Consequently, the vibron keeps its wavelike nature and a coherent vibrational energy flow takes place whatever the temperature. By contrast, anharmonic phonons carry spatial correlations over a finite length scale, only. As a result, the rephasing process no longer compensates the dephasing mechanism so that dephasing-limited band motion occurs. It gives rise to the incoherent diffusion of the vibron characterized by a diffusion coefficient whose temperature dependence scales as 1/Tα. In the weak anharmonicity limit, the exponent α is about 2. It becomes smaller than unity in the strong anharmonicity limit, indicating that the diffusion coefficient behaves as a slowly decaying function of the temperature.