Low-temperature diffusion and transport properties of the generalized Frenkel–Kontorova model are investigated analytically in the framework of a phenomenological approach which treats a system of strongly interacting atoms as a system of weaklyinteracting quasiparticles (kinks). The model takes into account realistic (anharmonic) interaction of particles subjected into a periodic substrate potential, and such a generalization leads to a series of novel effects which we expect are related to the experimentally-observed phenomena in several quasi-one-dimensional systems. Analysing the concentration dependences in the framework of the kink phenomenology, we use the renormalization procedure when the atomic structure with a complex unit cell is treated as (more simple) periodic structure of kinks. Using phenomenology of the ideal kink gas, the low-temperature states of the chain are described as those consisting of "residual" kinks supplemented by thermally-excited kinks. This approach allows us to describe the ground states of the chain as a hierarchy of "melted" kink lattices. Dynamical and diffusion properties of the system are then described in terms of the kink dynamics and kink diffusion. The motion equation for a single kink is reduced to a Langevin-type equation which is investigated with the help of the Kramers theory. Susceptibility, conductivity, self-diffusion and chemical diffusion coefficients of the chain are calculated as functions of the kink diffusion coefficient. In this way, we qualitatively analyze, for the first time to our knowledge, dependence of the different diffusion coefficients on the concentration of atoms in the chain. The results are applied to describe peculiarities in conductivity and diffusion coefficients of quasi-one-dimensional systems, in particular, superionic conductors and anisotropic layers of atoms adsorbed on crystal surfaces which were earlier investigated experimentally.
