The nonexistence of the linear diffusion equation beyond Fick's law

Abstract

The self-diffusion of a tagged particle in a 3-dimensional fluid of identical particles cannot be described by a linear diffusion equation which contains corrections to Fick's law proportional to 4n, 6n, … For long times a t divergence is found for the super-Burnett coefficient, the proportionality coefficient of the 4-term, both from the mode-mode coupling theory and the kinetic theory of hard spheres. Furthermore, higher asymptotic corrections of the form t-2+2-n (n = 2, 3, …) to the t--time tail of the velocity autocorrelation function are calculated from both theories and the results are compared.