Elastic strings in solids: Discrete kink diffusion

The diffusive dynamics of a single discrete phi (4) soliton coupled to an overdamped heat bath is analyzed in detail. The Langevin equation for the soliton center of mass is derived in general form and compared with the outcome of extensive numerical simulation. The effective mass of the moving soliton must he renormalized dynamically for lattice constants of the order of its size or smaller. The corresponding mobility curve and diffusion coefficient are determined numerically: At variance with the earlier literature, discreteness effects persist even at high temperature and in the presence of strong drives.