Relaxation dynamics and long-time tails explain shear-induced diffusion of soft athermal particles near jamming

We numerically study shear-induced diffusion of soft athermal particles in two dimensions. The Green-Kubo (GK) formula is applicable to the shear-induced diffusion coefficient, where both mean-squared transverse velocity and relaxation time included in the GK formula are well described by critical scaling near jamming. We show that the autocorrelation function of transverse velocities is stretched exponential if the system is below jamming or shear rate is large enough. However, if the system is above jamming and the shear rate is sufficiently small, the autocorrelation function exhibits a long-time tail such that time integral in the GK formula diverges in two dimensions. We propose an empirical scaling relation for the critical exponents and show that the long-time tail is consistent with the divergence of the shear-induced diffusion coefficient.