Dissipation and diffusion in one-dimensional solids

Abstract

Using a nonperturbative classical model for ionic motion through one-dimensional (1D) solids, we explore how thermal lattice vibrations affect ionic transport properties. Based on analytic and numerical calculations, we find that the mean dissipation experienced by the mobile ion is similar to that of the non-thermal case, with thermal motion only contributing stochastic noise. A nonmonotonic dependence of drag on speed, predicted in earlier work, persists in the presence of thermal motion. The inverse relation between drag and speed at high speeds results in non-Fickian diffusion dominated by L\'{e}vy flights. This suppression of drag at high speeds, combined with enhanced activation frequency, improves the particle mobility at high temperatures, where typical particles move faster.