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

Abstract: We numerically study shear-induced diffusion of soft athermal particles in two dimensions. The Green-Kubo (GK) relation is applicable to diffusion coefficient of the particles near jamming, where both mean squared particle velocities and relaxation time included in the GK formula are well explained by critical scaling. We show that auto-correlation functions of the transverse velocities are 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 auto-correlations exhibit long-time tails such that time integral in the GK formula diverges in two dimensions. We propose empirical scaling relations for the critical exponents and demonstrate that the long-time tails cause finite size effects on the shear-induced diffusion coefficient.