Diffusion and velocity autocorrelation at the jamming transition.

We perform numerical simulations to examine particle diffusion at steady shear in a soft-disk model in two dimensions and zero temperature around the jamming density. We find that the diffusion constant depends on shear rate as D approximately gamma below jamming and as D approximately gammaqD with qD<1 at the transition and set out to relate this to properties of the velocity autocorrelation function. It is found that this correlation function is governed by two processes with different time scales. The first time scale, the inverse of the externally applied shear rate, controls an exponential decay of the correlations whereas the second time scale, equal to the inverse shear stress, governs an algebraic decay with time. The obtained value of qD is related to these properties of the correlation function.