Transport in the Frenkel-Kontorova model. I. Diffusion and single-particle motion

Abstract

The author formulates the relations needed for calculating the diffusion coefficient D. The Kubo formula for D, or the closely related mobility, involves a time autocorrelation function and a static susceptibility chi . He discusses the interpretation of chi as a mean square fluctuation of interparticle distance, a thermodynamic derivative and a density of kink excitations. The single-particle motion is discussed in terms of the time-dependent mean square displacement Z(t). He shows how general arguments based only on the existence of D yield the Z approximately t1/2 behaviour at long time, going over ultimately to Z approximately t, as discussed by previous authors on the basis of kink phenomenology. The resulting formulae for the coefficients expressed as functions of D and chi are valid even when a description in terms of kink excitations is not justified.