Stress relaxation above and below the jamming transition

TL;DR

This study numerically examines stress relaxation in soft athermal disks near the jamming transition, revealing different critical slowing down behaviors from jammed and unjammed phases linked to vibrational density of states.

Contribution

It uncovers the asymmetric divergence of relaxation times from both sides of the jamming transition and connects this to the vibrational density of states, challenging conventional critical scaling.

Findings

Divergence of relaxation time differs dramatically from both sides of jamming.

An extra slow mode in vibrational density of states appears below jamming.

The relaxation behavior deviates from conventional dynamic critical scaling.

Abstract

We numerically investigate stress relaxation in soft athermal disks to reveal critical slowing down when the system approaches the jamming point. The exponents describing the divergence of the relaxation time differ dramatically depending on whether the transition is approached from the jammed or unjammed phase. This contrasts sharply with conventional dynamic critical scaling scenarios, where a single exponent characterizes both sides. We explain this surprising difference in terms of the vibrational density of states (vDOS), which is a key ingredient of linear viscoelastic theory. The vDOS exhibits an extra slow mode that emerges below jamming, which we utilize to demonstrate the anomalous exponent below jamming.