Self-diffusion beyond Fick's law

Abstract

The Van Hove self-correlation function, the intermediate incoherent scattering function and its Laplace transform are determined asymptotically for a one component fluid in equilibrium, using the mode coupling theory. The results reproduce in the hydrodynamic limit the predictions from Fick's law. The corrections to Fick's law are consistent with a long time tail in the velocity correlation function and with a diverging super Burnett coefficient in the linear diffusion equation.