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 V4n, V6n .... For long times a t 1/2 divergence is found for the super-Burnett coefficient, the proportionality coefficient of the V4-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-3/2-time tail of the velocity autocorrelation function are calculated from both theories and the results are compared.