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  • Letter
  • Open Access

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

Kuniyasu Saitoh1 and Takeshi Kawasaki2,3

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Phys. Rev. Research 8, L012069 – Published 24 March, 2026

DOI: https://doi.org/10.1103/bf83-xrjp

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 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.

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Phys. Rev. Research 8, L012069– Published 24 March, 2026
  • Received 21 April 2022
  • Accepted 17 December 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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