Drift-diffusion of a localized quantum state along a thermal gradient in a model α-helix

We consider here a model for the transport of a self-trapped exciton on a lattice under thermal bias in order to develop a quantum mechanical theory for vibrational energy transport along a molecular wire that is in contact with thermal reservoirs at either end of the molecule. For the specific case of the migration of a C=O vibrational excitation along a poly-amide α-helix, we find that within our model a C=O vibrational exciton can become self-trapped due to strong hydrogen bonding interactions with amide groups even at physiologically relevant temperatures. Furthermore, we find that under the non-equilibrium condition in which the temperature of the two baths are different, the self-trapped state will diffuse towards the cooler end with a diffusion constant proportional to the average temperature of the lattice D∝(Thot+Tcold)/2 and a drift proportional to the temperature gradient (Thot-Tcold)/N.