Concentration dependence of the conductivity and diffusivity in one-dimensional anharmonic lattices

Low-temperature conductivity and diffusivity of the generalized Frenkel-Kontorova model, which takes into account realistic (anharmonic) interaction of particles subjected to a periodic substrate potential, are investigated analytically in the framework of a phenomenological approach which treats a system of strongly interacting atoms as a system of weakly interacting quasiparticles (kinks). Using phenomenology of the ideal kink gas, where the low-temperature ground state of the chain is described as that consisting of ``residual'' kinks supplemented by thermally excited kinks, we describe the ground state of the system as a hierarchy of consequently ``melted'' kink lattices. System dynamics is then described in terms of the kink dynamics. The motion equation for a single kink is reduced to a Langevin-type equation which is investigated with the help of the Kramers theory. In this way, we qualitatively analyze dependence of the susceptibility, conductivity, and chemical diffusivity of the chain on the concentration of atoms in the chain. The model leads to a series of effects which we expect are related to the experimentally observed phenomena in several quasi-one-dimensional systems, in particular, superionic conductors and anisotropic layers of atoms adsorbed on crystal surfaces.