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

TL;DR

This study investigates how shear-induced diffusion in soft athermal particles near jamming is governed by relaxation dynamics and long-time tails, revealing critical scaling and divergence phenomena.

Contribution

It introduces a detailed analysis of shear-induced diffusion near jamming, highlighting the role of relaxation dynamics and long-time tails in two-dimensional systems.

Findings

Auto-correlation functions are stretched exponential below jamming or at high shear rates.

Long-time tails cause divergence of the diffusion coefficient at low shear rates above jamming.

Critical scaling relations describe the behavior of relaxation times and diffusion near jamming.

Abstract

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 auto-correlation 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 auto-correlation 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.