Quantum motion of particles along one-dimensional pathways with static and dynamic energy disorder

We have theoretically studied the competitive effects of static and dynamic energy disorder on the quantum-mechanical propagation of charge carriers and excitations along one-dimensional pathways consisting of coupled classical oscillators. Both the probability to survive in the initially occupied state and the propagation along the chain were investigated. By using the simple tight-binding band approximation, we have demonstrated that the propagation proceeds in two stages. At short times the particles move ballistically, while at larger times their propagation becomes close to diffusive with increasing dispersion for a higher degree of static disorder. The existence of two stages is due to distinct effects of static and dynamic disorder on the particle motion. While the static disorder always creates a 'friction' for the particle propagation, the dynamic disorder can either facilitate or suppress the inter-site transfer depending on the degree of static disorder. It has been shown that the competition of these effects gives rise to a behaviour of the particle diffusivity typical for the metal-insulator transition.