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

Abstract

A time-convolutionless master equation is established for describing the transportproperties of amide-I vibrons coupled with acoustic phonons in a lattice of H-bondedpeptide units. Within the non-adiabatic weak coupling limit, it is shown that the vibrondynamics strongly depends on the nature of the phonons and two distinct mechanisms havebeen identified. Harmonic phonons, which support spatial correlations over aninfinite length scale, induce a fast dephasing–rephasing mechanism in the shorttime limit. Consequently, the vibron keeps its wavelike nature and a coherentvibrational energy flow takes place whatever the temperature. By contrast, anharmonicphonons carry spatial correlations over a finite length scale, only. As a result,the rephasing process no longer compensates the dephasing mechanism so thatdephasing-limited band motion occurs. It gives rise to the incoherent diffusion of the vibroncharacterized by a diffusion coefficient whose temperature dependence scales as1/Tα. In the weak anharmonicity limit, the exponentα is about 2. It becomes smaller than unity in the strong anharmonicity limit, indicating thatthe diffusion coefficient behaves as a slowly decaying function of the temperature.